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1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.*; import java.util.*; public class Main { public static void main(String[] args) throws Exception { BufferedReader in = new BufferedReader(new InputStreamReader(System.in)); PrintWriter out = new PrintWriter(System.out); int t = Integer.parseInt(in.readLine()); for (int te = 0; te < t; te++) { StringTokenizer st = new StringTokenizer(in.readLine()); long n = Long.parseLong(st.nextToken()); long l = Long.parseLong(st.nextToken()); long r = Long.parseLong(st.nextToken()); long start = 1; StringBuilder sb = new StringBuilder(); for (int i = 1; i <= n; i++) { //System.out.println("START BEFORE " + start); if (start > r) { break; } if (start + (n-i)*2 - 1 < l) { start += (n-i)*2; continue; } //System.out.println("START AFTER " + start); for (int k = i+1; k <= n; k++) { if (start >= l && start <= r) { sb.append(i); sb.append(' '); } start++; if (start >= l && start <= r) { sb.append(k); sb.append(' '); } start++; } } if (start == r) { sb.append('1'); sb.append(' '); } out.println(sb.toString()); } out.close(); } } /* 1 3 1 7 */
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
T = int(input()) for _ in range(T): n, left, right = map(int, input().split()) l = [0]*n l[1] = 2*n-2 for i in range(2, n): l[i] = l[i-1]-2 l[-1] += 1 left_n = -1 right_n = -1 acc = 0 for i in range(1, n): if acc+1<=left: left_n = i acc += l[i] if right<=acc: right_n = i break #print(l) #print(left_n) #print(right_n) ans = [] for i in range(left_n, right_n+1): now = [] for j in range(l[i]): if j%2==0: now.append(i) else: if j==1: now.append(i+1) else: now.append(now[-2]+1) if i==n-1: now[-1] = 1 ans += now sta = left-sum(l[:left_n])-1 print(*ans[sta:sta+right-left+1])
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.OutputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.StringTokenizer; import java.io.IOException; import java.io.BufferedReader; import java.io.InputStreamReader; import java.io.InputStream; /** * Built using CHelper plug-in * Actual solution is at the top * * @author bhavy seth */ public class Main { public static void main(String[] args) { InputStream inputStream = System.in; OutputStream outputStream = System.out; InputReader in = new InputReader(inputStream); PrintWriter out = new PrintWriter(outputStream); TaskD solver = new TaskD(); solver.solve(1, in, out); out.close(); } static class TaskD { public void solve(int testNumber, InputReader sc, PrintWriter out) { int t = sc.nextInt(); while (t-- > 0) { int n = sc.nextInt(); long l = sc.nextLong(); long r = sc.nextLong(); long count = 0; int start = 0; for (int i = 1; i <= n; i++) { long x = Math.max(1, (n - i) * 2); if (l <= count + x) { start = i; break; } else { count += x; } } /* if(l==count+1){ out.print(start+" "); count++; }*/ int curr = start; long incnt = 0; { for (int i = 0; i < Math.max(2 * (n - start), 1); i++) { count++; incnt++; if (incnt % 2 == 0) { curr++; } if (count == l) { break; } } if (incnt % 2 == 0) { for (int i = curr; i <= n; i++) { if (count <= r) { out.print(i + " "); count++; } if (i == n) break; if (count <= r) { out.print(start + " "); count++; } if (count > r) break; } } else { for (int i = curr + 1; i <= n; i++) { if (count <= r) { out.print(start + " "); count++; } if (count <= r) { out.print(i + " "); count++; } if (count > r) break; } } if (count < r) { for (int i = start + 1; i < n; i++) { for (int j = i + 1; j <= n; j++) { if (count <= r) { out.print(i + " "); count++; } if (count <= r) { out.print(j + " "); count++; } if (count > r) break; } if (count > r) break; } } if (count <= r) out.print(1); } out.println(); } } } static class InputReader { BufferedReader br; StringTokenizer st; public InputReader(InputStream inputStream) { br = new BufferedReader(new InputStreamReader(inputStream)); } public String next() { while (st == null || !st.hasMoreElements()) { try { st = new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } } return st.nextToken(); } public int nextInt() { return Integer.parseInt(next()); } public long nextLong() { return Long.parseLong(next()); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; #pragma GCC optimize("Ofast") #pragma GCC optimize("no-stack-protector") #pragma GCC optimize("unroll-loops") #pragma GCC target("sse,sse2,sse3,ssse3,popcnt,abm,mmx,tune=native") const long long MOD = 998244353; long long gcd(long long a, long long b) { if (a < b) { swap(a, b); } while (b != 0) { long long tmp = b; b = a % b; a = tmp; } return a; } signed main() { cin.tie(0); cout.tie(0); ios_base::sync_with_stdio(0); long long t = 1; cin >> t; while (t--) { long long n, l, r; cin >> n >> l >> r; l--; long long cur_plus = 0; long long org = (n - 1) * 2; long long prev_org = 0; while (org < l) { n--; prev_org = org; org += (n - 1) * 2; cur_plus++; } while (l < r) { if (l % 2 == 1) { cout << (l - prev_org) / 2 + 2 + cur_plus << ' '; l++; } for (l = l; l < r && l < org; l += 2) { cout << 1 + cur_plus << ' '; if (l + 1 < r) { cout << (l - prev_org) / 2 + 2 + cur_plus << ' '; } } n--; prev_org = org; org += (n - 1) * 2; if (n == 1 && l < r) { cout << 1 << ' '; break; } if (n == 1) { break; } cur_plus++; } cout << "\n" << endl; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; const long long mod = 1000000007; long long powmod(long long a, long long b) { long long res = 1; a %= mod; assert(b >= 0); for (; b; b >>= 1) { if (b & 1) res = res * a % mod; a = a * a % mod; } return res; } long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; } const int N = 1e5 + 10; int n; long long l, r; long long sum[N]; int cal(long long x) { if (x > sum[n - 1]) return 1; int idx = lower_bound(sum, sum + n, x) - sum; int num = x - sum[idx - 1]; if (num & 1) return idx; return idx + num / 2; } int main() { int t; scanf("%d", &t); while (t--) { scanf("%d%lld%lld", &n, &l, &r); for (int i = 1; i < n; i++) { sum[i] = sum[i - 1] + 2ll * (n - i); } for (long long i = l; i <= r; i++) { printf("%d ", cal(i)); } puts(""); } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; void upgrade() { ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL); } int main() { upgrade(); int tc; cin >> tc; while (tc--) { long long n, l, r; cin >> n >> l >> r; long long add = 2 * n - 2, cnt = 0, h = 1; while (add != 0 && cnt + add < l) { cnt += add; add -= 2; h++; } if (add == 0) { cout << 1 << '\n'; continue; } long long diff = l - cnt; bool f = (diff % 2) == 1; long long st = (diff - 1) / 2 + h + 1; for (int i = 0; i < r - l + 1; i++) { if (f) { cout << h << ' '; } else { cout << st << ' '; if (st == n) { h++; st = h + 1; if (h == n && i != r - l) { cout << 1; break; } } else st++; } f = !f; } cout << '\n'; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
import math # Ρ€Π΅ΡˆΠ΅Π½Π° def task_1343_c(): b = int(input()) array = [int(num) for num in input().split()] maxPositive = 0 minNegative = -10000000000 res = 0 for i in range(b): if array[i] < 0: if i != 0 and array[i - 1] >= 0: res += maxPositive maxPositive = 0 minNegative = max(minNegative, array[i]) else: if i != 0 and array[i - 1] < 0: res += minNegative minNegative = -10000000000 maxPositive = max(maxPositive, array[i]) if minNegative == -10000000000: res += maxPositive else: res += maxPositive + minNegative print(res) # Π½Π΅ Ρ€Π°Π±ΠΎΡ‚Π°Π΅Ρ‚ ΠΎΡ‚ слова совсСм def task_1341_b(): heightLen, doorSize = map(int, input().split()) heights = [int(num) for num in input().split()] perf = [0 for i in range(heightLen)] a = 0 for i in range(heightLen - 1): if i == 0: perf[i] = 0 else: if heights[i - 1] < heights[i] and heights[i] > heights[i + 1]: a += 1 perf[i] = a perf[heightLen - 1] = a max_global = 0 left_global = 0 for i in range(heightLen - doorSize): max_local = perf[i + doorSize - 1] - perf[i] if max_local > max_global: max_global = max_local left_global = i print(max_global + 1, left_global + 1) # Ρ€Π΅ΡˆΠΈΠ», Ρ‡Ρ‚ΠΎΠ± Π΅Ρ‘ def task_1340_a(): n = int(input()) array = [int(i) for i in input().split()] for i in range(n - 1): if array[i] < array[i + 1]: if array[i] + 1 != array[i + 1]: print("No") return print("Yes") #Ρ€Π΅ΡˆΠΈΠ» def task_1339_b(): n = int(input()) array = [int(num) for num in input().split()] array.sort() output = [0 for i in range(0, n)] i = 0 h = 0 j = n - 1 while i <= j: output[h] = array[i] h += 1 i += 1 if h < n: output[h] = array[j] h += 1 j -= 1 for val in reversed(output): print(val, end=' ') # Ρ€Π΅ΡˆΠ΅Π½Π° def task_1338_a(): n = int(input()) inputArr = [int(num) for num in input().split()] max_sec = 0 for i in range(1, n): local_sec = 0 a = inputArr[i - 1] - inputArr[i] if a <= 0: continue else: b = math.floor(math.log2(a)) local_sec = b + 1 for j in range(b, -1, -1): if a < pow(2, j): continue inputArr[i] += pow(2, j) a -= pow(2, j) if local_sec > max_sec: max_sec = local_sec print(max_sec) def task_1334_d(): n, l ,r = map(int, input().split()) res = [] count = 0 start_pos = l for i in range(1, n + 1): count += (n - i) * 2 if count >= l: for j in range(n - i): res.append(i) res.append(j + i + 1) else: start_pos -= (n - i) * 2 if count >= r: break res.append(1) for i in range(start_pos - 1, start_pos + (r - l)): print(res[i], end=" ") print() a = int(input()) for i in range(a): task_1334_d()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; const long long N = 3e5 + 5, K = 11, M = N * 4; const long long MOD = 998244353, oo = 1e9, OO = 1e18, mod = MOD; const double pi = acos(-1), eps = 1e-17; long long di[] = {0, 0, 1, -1}; long long dj[] = {1, -1, 0, 0}; int32_t main() { ios_base::sync_with_stdio(false); cin.tie(0); ; long long t; cin >> t; while (t--) { long long n, l, r; cin >> n >> l >> r; long long now = 0, st = 1; long long sum = l; for (long long i = n - 1; i > 0; i--) { now = i * 2; l -= now; r -= now; if (l <= 0) { l += now; r += now; sum = i; break; } st++; } long long ans = 0; long long p = 0; for (long long i = sum; "Hello"; i--) { long long tmp = i * 2; long long dor = st; if (st == n) dor = 1, tmp = 1; long long cnt = st + 1; while (tmp--) { ans++; if (ans >= l && ans <= r) { cout << dor << " "; } if (dor == st) dor = cnt++; else dor = st; if (ans > r) goto A; } st++; if (ans > r) goto A; } A: cout << endl; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; const int maxn = (int)1e6 + 100; const int mod = (int)1e9 + 7; void solve() { long long n, l, r; scanf("%lld%lld%lld", &n, &l, &r); long long pos = -1, pre = 0; for (auto i = (1); i <= (n); ++i) { long long now = (n - i) * 2; if (now == 0) now = 1; if (pre < l && pre + now >= l) { pos = i; break; } pre += now; } long long num = r - l + 1, st = l - pre, fr = pos == n ? 1 : pos, se = (st + 1) / 2 + pos; for (auto i = (1); i <= (num); ++i) { if (st % 2) printf("%lld ", fr > n ? 1 : fr); else printf("%lld ", se > n ? 1 : se), se++; st++; if (se > n) { pos++; st = 1; fr = pos; se = pos + 1; if (fr == n) fr = 1; if (se > n) se = 1; } } puts(""); } int main() { int T; cin >> T; while (T--) solve(); }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
from sys import stdin,stdout from math import gcd,sqrt,factorial,pi,inf from collections import deque,defaultdict from bisect import bisect,bisect_left from time import time from itertools import permutations as per input=stdin.readline R=lambda:map(int,input().split()) I=lambda:int(input()) S=lambda:input().rstrip('\r\n') L=lambda:list(R()) P=lambda x:stdout.write(str(x)+'\n') lcm=lambda x,y:(x*y)//gcd(x,y) nCr=lambda x,y:(f[x]*inv((f[y]*f[x-y])%N))%N inv=lambda x:pow(x,N-2,N) sm=lambda x:(x**2+x)//2 N=10**9+7 for _ in range(I()): n,l,r=R() if l==r==(n-1)*n+1:print(1);continue p=0 for i in range(n-1,0,-1): p+=i*2 if p>=l: k=n-i if l%2==0: x=(n-i)+(l-(p-i*2))//2 print(x,end=' ') l+=1 j=x+1 if x==n: k+=1 j=k+1 else: j=(n-i)+(l+1-(p-i*2))//2 for i in range(r-l+1): if i%2: print(j,end=' ') if j==n: j=k+1 k+=1 j+=1 else: if k!=n:print(k,end=' ') else:print(1,end=' ') break print()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.ArrayList; import java.util.Arrays; import java.util.HashMap; import java.util.InputMismatchException; import java.util.List; import java.util.Map; import java.util.Map.Entry; public class Main { private static final int MAXN = 5000; private static final String NO = "NO"; private static final String YES = "YES"; InputStream is; PrintWriter out; String INPUT = ""; private static final long MOD = 1000000007L; private static final int MAX = 200000; void solve() { int Q = ni(); while (Q-- > 0) { int N = ni(); long l = nl() - 1; long r = nl() - 1; long cur = 0; for (int i = 1; i <= N && cur <= r; i++) { if (cur + 2 * (N - i) < l) cur += 2 * (N - i); else { for (int j = i + 1; j <= N && cur <= r; j++) { if (cur >= l && cur <= r) out.print(i + " "); cur++; if (cur >= l && cur <= r) out.print(j + " "); cur++; } } } // tr(cur, r); if (cur <= r) out.print(1); out.println(); } } class segTree { int[] tree; int[] lazy; public segTree(int n) { tree = new int[4 * n + 2]; lazy = new int[4 * n + 2]; } public void build(int node, int l, int r, int[] ar) { if (l == r) { tree[node] = ar[l]; return; } int mid = (l + r) / 2; build(2 * node, l, mid, ar); build(2 * node + 1, mid + 1, r, ar); tree[node] = Math.min(tree[2 * node], tree[2 * node + 1]); } public void update(int node, int l, int r, int s, int e, int val) { if (lazy[node] != 0) { tree[node] += lazy[node]; if (l != r) { lazy[2 * node] += lazy[node]; lazy[2 * node + 1] += lazy[node]; } lazy[node] = 0; } if (l > e || r < s) return; if (l >= s && r <= e) { tree[node] += val; if (l != r) { lazy[2 * node] += val; lazy[2 * node + 1] += val; } return; } int mid = (l + r) / 2; update(2 * node, l, mid, s, e, val); update(2 * node + 1, mid + 1, r, s, e, val); tree[node] = Math.min(tree[2 * node], tree[2 * node + 1]); } } long power(long a, long b) { long x = 1, y = a; while (b > 0) { if (b % 2 != 0) { x = (x * y) % MOD; } y = (y * y) % MOD; b /= 2; } return x % MOD; } private long gcd(long a, long b) { while (a != 0) { long tmp = b % a; b = a; a = tmp; } return b; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms"); } public static void main(String[] args) throws Exception { new Main().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private boolean vis[]; private int readByte() { if (lenbuf == -1) throw new InputMismatchException(); if (ptrbuf >= lenbuf) { ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if (lenbuf <= 0) return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while ((b = readByte()) != -1 && isSpaceChar(b)) ; return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char) skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' // ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while (p < n) { if (!(isSpaceChar(b))) buf[p++] = (char) b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for (int i = 0; i < n; i++) map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for (int i = 0; i < n; i++) a[i] = ni(); return a; } private List<Integer> na2(int n) { List<Integer> a = new ArrayList<Integer>(); for (int i = 0; i < n; i++) a.add(ni()); return a; } private int[][] na(int n, int m) { int[][] a = new int[n][]; for (int i = 0; i < n; i++) a[i] = na(m); return a; } private int ni() { int num = 0, b; boolean minus = false; while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ; if (b == '-') { minus = true; b = readByte(); } while (true) { if (b >= '0' && b <= '9') { num = num * 10 + (b - '0'); } else { return minus ? -num : num; } b = readByte(); } } private long[] nl(int n) { long[] a = new long[n]; for (int i = 0; i < n; i++) a[i] = nl(); return a; } private long nl() { long num = 0; int b; boolean minus = false; while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ; if (b == '-') { minus = true; b = readByte(); } while (true) { if (b >= '0' && b <= '9') { num = num * 10 + (b - '0'); } else { return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
import sys import heapq def input(): return sys.stdin.readline().strip() def iinput(): return int(input()) def rinput(): return map(int, input().split()) def rlinput(): return list(map(int, input().split())) def YES(flag): if flag: return "YES" return "NO" def main(): def F(): return l <= w and w <= r #n = int(sys.stdin.readline().strip()) n, l, r = rinput() res = [] w = 1 if F(): res.append(1) for i in range(2, n): w += 1 if F(): res.append(i) w += 1 if F(): res.append(1) w += 1 if F(): res.append(n) for i in range(2, n): w += 1 if F(): res.append(i) for o in range(max(w + 1, l), min(w + (n - i - 1) * 2 + 1, r + 1)): if (o - w) % 2 == 0: res.append(i) else: res.append((o - w - 1) // 2 + i + 1) w += (n - i - 1) * 2 + 1 if F(): res.append(n) w += 1 if F(): res.append(1) print(*res) for i in range(iinput()): main()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; const int INF = 1e9; ifstream fin("input.txt"); ofstream fout("output.txt"); long long fast_exp(long long base, long long exp) { long long res = 1; while (exp > 0) { if (exp % 2 == 1) res = (res * base) % 1000000007; base = (base * base) % 1000000007; exp /= 2; } return res % 1000000007; } int palindromecheck(string s) { int n = s.size(); for (int i = 0; i < n / 2; ++i) { if (s[i] != s[n - i - 1]) { return 0; } } return 1; } int gcd(int a, int b) { while (a && b) a > b ? a %= b : b %= a; return a + b; } int val(char c) { if (c >= '0' && c <= '9') return (int)c - '0'; else return (int)c - 'A' + 10; } long long pows(int a, int b) { long long res = 1; for (int i = 0; i < b; ++i) { res *= a; } return res; } long long logx(long long base, long long num) { int cnt = 0; while (num != 1) { num /= base; ++cnt; } return cnt; } long long divisibles(long long a, long long b, long long m) { if (a % m == 0) return (b / m) - (a / m) + 1; else return (b / m) - (a / m); } string bitstring(int n, int size) { string s; while (n) { s += (n % 2) + '0'; n /= 2; } while (s.size() < size) { s += '0'; } reverse(s.begin(), s.end()); return s; } vector<int> root(200001, 0); vector<int> size(200001, 1); int find(int x) { while (x != root[x]) x = root[x]; return x; } bool same(int a, int b) { return find(a) == find(b); } void unite(int a, int b) { a = find(a); b = find(b); if (size[a] < size[b]) swap(a, b); size[a] += size[b]; root[b] = a; } vector<int> vis(200001, 0); vector<int> adj[200001]; int main() { std::ios::sync_with_stdio(false); int t; cin >> t; while (t--) { int n; long long l, r; cin >> n >> l >> r; vector<long long> vec(n + 1); long long sum = 0; int j = 1; for (int i = n; i >= 1; --i) { sum += (i - 1) * 2; vec[j] = sum; if (i == 1) ++vec[j]; ++j; } long long idxl = lower_bound(vec.begin(), vec.end(), l) - vec.begin(); long long idxr = lower_bound(vec.begin(), vec.end(), r) - vec.begin(); if (vec[idxl] > l && idxl > 1) { --idxl; } vector<pair<long long, long long>> ans; int temp = vec[idxl]; if (idxl == 1) temp = 1; long long start; if (idxl != 1) start = vec[idxl - 1] + 1; for (int i = idxl; i <= idxr; ++i) { for (int j = i + 1; j <= n; ++j) { ans.push_back(make_pair(i, start++)); ans.push_back(make_pair(j, start++)); } if (i + 1 > n) { ans.push_back(make_pair(1, start)); } } long long begin; if (idxl == 1) { begin = l - 1; } else { for (int i = 0; i < ans.size(); ++i) { if (ans[i].second == l) { begin = i; break; } } } for (int i = begin; i <= begin + (r - l); ++i) cout << ans[i].first << " "; cout << "\n"; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
import sys def minp(): return sys.stdin.readline().strip() def mint(): return int(minp()) def mints(): return map(int, minp().split()) def stupid(x, n): k = (n-1)*2 r = 0 while x >= k: x -= k r += 1 k -= 2 return r def findl(x, n): l, r = 0, n while r - l > 1: c = (l + r) // 2 if (2*n - 1 - c)*c <= x: l = c else: r = c #if l != stupid(x, n): # print(l, stupid(x, n), x, n); # raise 123 return l def solve(): n, l, r = mints() res = [] f = (r == n*(n-1) + 1) r -= l + f - 1 l -= 1 x = findl(l, n) l -= (2*n-1-x)*x k = (n-1-x)*2 x += 1 while False:#l >= k: print(l, k) l -= k x += 1 k -= 2 y = x + 1 + l // 2 if l % 2: while r >= 2: res.append(y) if y == n: x += 1 y = x + 1 else: y += 1 res.append(x) r -= 2 if r != 0: res.append(y) else: while r >= 2: res.append(x) res.append(y) if y == n: x += 1 y = x + 1 else: y += 1 r -= 2 if r != 0: res.append(x) if f: res.append(1) print(' '.join(map(str,res))) for i in range(mint()): solve()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; using ll = long long int; int main() { ios::sync_with_stdio(0); cin.tie(0); int t; cin >> t; while (t--) { int n; cin >> n; ll l, r; cin >> l >> r; ll idx = 1; bool done = false; for (int start = 1; start <= n; start++) { if (idx <= l && idx + (n - start) * 2ll > l) { int now = start; int nxt = start + 1; for (; idx < l; idx++) { int prev_now = now; now = nxt; nxt = (prev_now == start ? start : prev_now + 1); if (nxt == n + 1) { assert(now == start); now = ++start; nxt = start + 1; } } for (; idx <= r; idx++) { cout << now << " "; int prev_now = now; now = nxt; nxt = (prev_now == start ? start : prev_now + 1); if (nxt == n + 1) { assert(now == start); now = ++start; nxt = start + 1; if (now == n) { now = 1; } } } cout << endl; done = true; break; } else { idx += (n - start) * 2ll; } } if (!done) cout << 1 << '\n'; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; long long next() { long long x; cin >> x; return x; } const int maxn = 2e5 + 2, intf = 1e9; const long long inf = 2e18, mod = 1e9; const long double eps = 1e-6; long long n; void _print(long long bucket_id, long long l, long long r) { if (l > r) return; if (bucket_id == n) { cout << 1; return; } for (long long i = l; i <= r; i++) { if (i % 2 == 0) { cout << bucket_id << ' '; } else { cout << (i / 2) + 1 + bucket_id << ' '; } } } void solve() { long long l, r; cin >> n >> l >> r; l--, r--; long long sum = 0; for (long long bucket_id = 1; bucket_id <= n; bucket_id++) { long long cur_l = sum, cur_r = sum + 2 * (n - bucket_id) - 1; if (bucket_id == n) { if (r >= cur_l) { _print(bucket_id, 0, 1); } continue; } cur_l = max(cur_l, l) - sum; cur_r = min(cur_r, r) - sum; _print(bucket_id, cur_l, cur_r); sum += 2 * (n - bucket_id); } cout << '\n'; } signed main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cout.precision(20); for (int t = next(); t--;) { solve(); } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; long long t, n, i, j, k, x, y, z, l, r, mid, q, m, ans, s; vector<int> v[200005]; long long bs(long long l, long long r, long long z) { long long ans = -1; while (l <= r) { mid = (l + r) >> 1; if ((n - 1 + n - mid) * (mid) >= z) { ans = mid; r = mid - 1; } else l = mid + 1; } if (ans == -1) x = 1; else { x = ans; z -= (n - 1 + n - ans + 1) * (ans - 1); y = (z + 1) / 2 + x; } return ans; } int main() { ios::sync_with_stdio(NULL); cin.tie(0); cout.tie(0); cin >> t; while (t--) { cin >> n >> l >> r; ans = bs(1, n - 1, l); while (l <= r) { if (l % 2) cout << x << " "; else cout << y << " ", y++; l++; if (y > n) { x++; y = x + 1; if (x == n) x = 1; } } cout << "\n"; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.util.*; import java.io.*; public class d { static int n; static long l, r; public static void main(String[] args) { FS sc = new FS(); PrintWriter pw = new PrintWriter(System.out); int t = sc.nextInt(); for(int tt = 1; tt <= t; ++tt) { n = sc.nextInt(); l = sc.nextLong(); r = sc.nextLong(); // binary search for index i int lo = 1, hi = n; while(lo < hi) { int g = (lo + hi + 1) / 2; if(getNumBehind(g) < l) lo = g; else hi = g - 1; } // calculate start j? // System.out.println(lo); long idx = getNumBehind(lo) + 1; floop : for(int i = lo; ; ++i) { if(i == n) { pw.print("1 "); break; } for(int j = i + 1; j <= n; ++j) { if(idx++ >= l) pw.print(i + " "); if(idx > r) break floop; if(idx++ >= l) pw.print(j + " "); if(idx > r) break floop; } } pw.println(); } pw.flush(); } static long getNumBehind(int i) { long out = sum(n - 1); out -= sum(n - i); return out * 2; } static long sum(long in) { return in * (in + 1) / 2; } static class FS { BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); StringTokenizer st = new StringTokenizer(""); String next() { while(!st.hasMoreElements()) { try { st = new StringTokenizer(br.readLine()); } catch(Exception e) {} } return st.nextToken(); } int nextInt() { return Integer.parseInt(next()); } long nextLong() { return Long.parseLong(next()); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
#!/usr/bin/env python # coding: utf-8 # In[48]: #from __future__ import print_function #from sys import stdin # In[52]: cases = int( input() ) # In[53]: def ecycle(n,l,r): l-=1 cnt = r - l p = n-1 start = 1 while(l >= 2*p and p>0): l -= 2*p p -= 1 start += 1 if(start==n): start = 1 flag = (l+1)%2 nextn = start + 1 + l//2 while(cnt>0): cnt-=1 if(flag==1): print(start,end=" ") if(flag==0): print(nextn, end=" ") nextn += 1 if(nextn>n): start += 1 nextn = start + 1 flag = 0 if(start==n): start = 1 flag = 1-flag # In[54]: while(cases>0): n,l,r = map( int, input().split() ) ecycle(n,l,r) cases -= 1 # In[ ]:
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.FileInputStream; import java.io.FileNotFoundException; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.InputMismatchException; /** * @author Nikita Gorokhov <wackloner@yandex-team.ru> */ public class D { private void solve() { long n = nextInt(), l = nextLong() - 1, r = nextLong() - 1; long cnt = n; // out.println(n); // System.out.println(n); for (; cnt >= 0; ) { long cur = cnt - 1 + cnt - 1; // out.println("l=" + l + " cnt=" + cnt + " cur=" + cur); if (l >= cur) { l -= cur; r -= cur; cnt--; } else { break; } } int num = 0; // System.out.println("vars = " + l + " " + r + " " + cnt); for (long cur = n - cnt; cur < n - 1; cur++) { for (long next = cur + 1; next < n; next++) { if (l <= num && num <= r) { out.print(" " + (cur + 1)); } else if (r < num) { break; } num++; if (l <= num && num <= r) { out.print(" " + (next + 1)); } else if (r < num) { break; } num++; } } if (num <= r) { out.print(" 1"); } out.println(); } private final static String INPUT_FILENAME = "input.txt"; private final static boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null; private InputStream inputStream; private PrintWriter out; private void run() throws FileNotFoundException { inputStream = ONLINE_JUDGE ? System.in : new FileInputStream(INPUT_FILENAME); out = new PrintWriter(System.out); int t = nextInt(); for (int testNum = 0; testNum < t; testNum++) { solve(); } out.flush(); } public static void main(String[] args) throws Exception { new D().run(); } private byte[] buffer = new byte[1024]; private int bufferLen = 0, bufferPtr = 0; private int readByte() { if (bufferLen == -1) { throw new InputMismatchException(); } if (bufferPtr >= bufferLen) { bufferPtr = 0; try { bufferLen = inputStream.read(buffer); } catch (IOException e) { throw new InputMismatchException(); } if (bufferLen <= 0) { return -1; } } return buffer[bufferPtr++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while ((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nextDouble() { return Double.parseDouble(next()); } private char nextChar() { return (char) skip(); } private String next() { int b = skip(); StringBuilder sb = new StringBuilder(); while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private int nextInt() { int num = 0, b; boolean minus = false; while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) { ; } if (b == '-') { minus = true; b = readByte(); } while (true) { if (b >= '0' && b <= '9') { num = num * 10 + (b - '0'); } else { return minus ? -num : num; } b = readByte(); } } private long nextLong() { long num = 0; int b; boolean minus = false; while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) { ; } if (b == '-') { minus = true; b = readByte(); } while (true) { if (b >= '0' && b <= '9') { num = num * 10 + (b - '0'); } else { return minus ? -num : num; } b = readByte(); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.*; import java.util.ArrayList; import java.util.List; import java.util.PriorityQueue; import java.util.StringTokenizer; public class Main { public static void main(String[] args) { InputStream inputStream = System.in; OutputStream outputStream = System.out; InputReader in = new InputReader(inputStream); PrintWriter out = new PrintWriter(outputStream); solve(in, out); out.close(); } public static void solve(InputReader in, PrintWriter out) { int t = in.nextInt(); while (t-- > 0) { long n = in.nextLong(); long l = in.nextLong(); long r = in.nextLong(); long acc = 0; for (int i = 1; i <= n; ++i) { // System.out.println(acc); long currAcc = (n-i)*2; if (acc + currAcc < l) { acc += currAcc; continue; } else if (l > acc) { long start = l - acc; if (start % 2 == 0) { out.print(start / 2 + i); out.print(' '); start++; } long end = r - acc; while (start <= currAcc && start <= end) { out.print(i); out.print(' '); start++; if (start <= end) { out.print(start / 2 + i); out.print(' '); start++; } } acc += currAcc; continue; } else if (acc + currAcc < r) { long start = 1; while (start <= currAcc) { out.print(i); out.print(' '); start++; if (start <= currAcc) { out.print(start / 2 + i); out.print(' '); start++; } } acc += currAcc; continue; } else if (r >= acc) { long start = 1; long end = r - acc; while (start <= end) { out.print(i); out.print(' '); start++; if (start <= end) { out.print(start / 2 + i); out.print(' '); start++; } } acc += currAcc; break; } else break; } if (r == n*(n-1)+1) { out.print(1); } out.println(); } } // int[] a = new int[n]; // int[] p = new int[n]; // for (int i = 0; i < n; ++i) { // a[i] = in.nextInt(); // } // for (int i = 0; i < n; ++i) { // p[i] = in.nextInt(); // } // int m = in.nextInt(); // int[] b = new int[m]; // for (int i = 0; i < m; ++i) { // b[i] = in.nextInt(); // } // public static void solve(InputReader in, PrintWriter out) { // int t = in.nextInt(); // while(t-- > 0) { // int n = in.nextInt(); // long x = in.nextLong(); // List<Pair> p = new ArrayList<>(n); // Pair min = new Pair(Long.MAX_VALUE, Long.MAX_VALUE); // int index = -1; // for (int i = 0; i < n; ++i) { // Pair pair = new Pair(in.nextLong(), in.nextLong()); // p.add(pair); // if (pair.compareTo(min) < 0) { // min = pair; // index = i; // } // } // } // } static class Pair implements Comparable<Pair> { long a; long b; public Pair(long a, long b) { this.a = a; this.b = b; } @Override public int compareTo(Pair o) { int compare = Long.compare(this.a, o.a); if (compare == 0) { compare = Long.compare(this.b, o.b); } return compare; } } static class InputReader { public BufferedReader reader; public StringTokenizer tokenizer; public InputReader(InputStream stream) { reader = new BufferedReader(new InputStreamReader(stream), 32768); tokenizer = null; } public String next() { while (tokenizer == null || !tokenizer.hasMoreTokens()) { try { tokenizer = new StringTokenizer(reader.readLine()); } catch (IOException e) { throw new RuntimeException(e); } } return tokenizer.nextToken(); } public int nextInt() { return Integer.parseInt(next()); } public void skip() { tokenizer = null; } public long nextLong() { return Long.parseLong(next()); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(0); cin.tie(0); int t, i, j; long long n, l, r, pos; cin >> t; while (t--) { cin >> n >> l >> r; pos = 1; for (i = 1; i < n && pos < l; i++) { pos += 2 * (n - i); if (pos > l) { pos -= 2 * (n - i); break; } } for (; i < n; i++) { for (j = i + 1; j <= n; j++) { if (pos > r) break; if (pos < l) { if (pos == l - 1) cout << j << " "; pos += 2; } else { if (pos == r) { cout << i << " "; pos++; } else { cout << i << " " << j << " "; pos += 2; } } if (pos > r) break; } } if (r == pos) cout << "1"; cout << "\n"; } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
def check(x,n,l): val = 2*n*x-(x*x)-x if val < l: return True return False def solve(n,l,r,ans): low = 1 high = n-1 x = 0 while low <= high: mid = (low+high)//2 if check(mid,n,l): x = mid low = mid+1 else: high = mid-1 val = 2*n*x-(x*x)-x rem = l-val #print(x) temp = True prev = True for i in range(rem-1): if prev: if temp: x += 1 y = x else: y += 1 temp = False if y == n: temp = True prev = not prev #print(x,y) #print(temp,prev,y) arr = [] for i in range(r-l+1): if prev: if temp: x += 1 y = x if x == n: x = 1 arr.append(x) else: temp = False y += 1 arr.append(y) if y == n: temp = True prev = not prev ans.append(arr) def main(): t = int(input()) ans = [] for i in range(t): n,l,r = map(int,input().split()) solve(n,l,r,ans) for i in ans: for j in i: print(j,end = ' ') print() main()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; long long n, t, l, r, start, star, have; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> t; while (t--) { cin >> n >> l >> r; have = 0; star = start = n + 1; for (long long i = 1; i <= n; i++) if (2LL * n * i - i * (i + 1LL) >= l) { start = i; have = 2LL * n * (i - 1LL) - (i - 1LL) * i; break; } for (long long i = start + 1; i <= n; i++) if (have + 2 < l) have += 2LL; else { have += 2LL; if (have == l) { cout << i << " "; l++; star = i + 1; } else star = i; break; } for (long long i = start; i <= n; i++) for (long long j = (i == start) ? star : i + 1; j <= n; j++) { if (l == r) { cout << i << " "; i = n + 1; break; } if (l > r) { i = n + 1; break; } l += 2; cout << i << " " << j << " "; } if (r == n * (n - 1LL) + 1) cout << "1"; cout << "\n"; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
t = int(input()) for _ in range(t): n, l, r = map(int, input().split()) l -= 1 r -= 1 start_i = 1 pos = 0 while start_i < n: cur_i_len = 2 * (n-start_i) if pos + cur_i_len > l: break pos += cur_i_len start_i += 1 wanted_len = r-l+1 s = [] while len(s) < l-pos+wanted_len: if start_i < n: for i in range(start_i+1, n+1): s += [str(start_i), str(i)] else: s += ["1"] start_i += 1 print(*s[l-pos:l-pos+wanted_len])
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
R = lambda:map(int, input().split()) t = int(input()) def block(b, pos, n): if pos%2 == 0: return b return b + (pos+1)//2 def binary(k, n): left, right = 1, n+1 while left <= right: m = (left + right)//2 if m*(m+1) >= k > m*(m-1): return m if m*(m+1) < k: left = m + 1 if m*(m-1) >= k: right = m - 1 def whatis(k, n): k = n*(n-1) + 1 - k if k == 0: return 1 i = binary(k, n) return block(n - i, - k + i*(i+1), n) for _ in range(t): n, l, r = R() ans = [] for i in range(l, r+1): ans.append(whatis(i, n)) print(*ans)
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); long long int t; cin >> t; while (t--) { long long int n, l, r; cin >> n >> l >> r; long long int count = 0; long long int i = 1; while (i < n) { if (count + (2 * (n - i)) >= l) { long long int check = l - count; long long int start = i + ((check + 1) / 2); while (l <= r && i < n) { if (l % 2 == 0) { cout << start << " "; start++; } else { cout << i << " "; } if (start == n + 1) { i++; start = i + 1; } l++; } i = n; } count += 2 * (n - i); i++; } if (l <= r) { cout << 1; } cout << endl; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> const double PI = 3.141592653589793238462643383279502884197169399375105820974944; using namespace std; long long ModExp(long long x, long long y, long long m) { long long res = 1; x = x % m; while (y > 0) { if (y & 1) res = (res * x) % m; y = y >> 1; x = (x * x) % m; } return res; } void solve() { long long n, l, r; cin >> n >> l >> r; long long f = (n - 1) * 2; long long arr[((n - 1) * 2) + 1]; for (long long i = 1; i < f + 1; i++) { if (i % 2 == 1) { arr[i] = 1; } else { arr[i] = (i / 2) + 1; } } if (!(f < l || 1 > r)) { long long i1 = max(l - 1, 0LL); long long i2 = min(r - 1, f - 1); for (long long i = i1; i < i2 + 1; i++) { cout << arr[i + 1] << " "; } } long long ind = f + 1; for (long long i = 2; i < n + 1; i++) { long long sz = (n - i) * 2; long long st = ind; long long en = st + sz - 1; if (en < l) { } else if (st > r) { break; } else { long long i1 = max(l - st, 0LL); long long i2 = min(r - st, en - st); while (i1 <= i2) { if (i1 % 2 == 0) { cout << i << " "; } else { cout << ((i1 + 1) / 2) + i << " "; } i1++; } } ind = en + 1; } if (r == ((n * (n - 1)) + 1)) { cout << "1"; } cout << endl; } signed main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); ; long long t = 1; cin >> t; while (t--) { solve(); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.util.*; import java.io.*; public class MinimumEulerCycle { public static void main(String[] args) throws IOException { BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); int t = Integer.parseInt(br.readLine()); StringBuilder sb = new StringBuilder(); while (t-- > 0) { StringTokenizer st = new StringTokenizer(br.readLine()); int n = Integer.parseInt(st.nextToken()); long l = Long.parseLong(st.nextToken()); long r = Long.parseLong(st.nextToken()); int section = (n - 1) * 2; int base = 1; long shift = 0; while (section + shift < l && base < n) { shift += section; section -= 2; base++; } while (l <= r) { if ((l & 1) == 1) { sb.append(base < n ? base : 1); } else { sb.append(base + (l - shift) / 2); } sb.append(' '); if (++l > section + shift) { shift += section; base++; section -= 2; } } sb.setLength(sb.length()-1); sb.append('\n'); } br.close(); System.out.print(sb.toString()); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.OutputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.TreeMap; import java.util.InputMismatchException; import java.io.IOException; import java.util.ArrayList; import java.io.InputStream; /** * Built using CHelper plug-in * Actual solution is at the top * * @author Ribhav */ public class Main { public static void main(String[] args) { InputStream inputStream = System.in; OutputStream outputStream = System.out; FastReader in = new FastReader(inputStream); PrintWriter out = new PrintWriter(outputStream); DMinimumEulerCycle solver = new DMinimumEulerCycle(); solver.solve(1, in, out); out.close(); } static class DMinimumEulerCycle { public void solve(int testNumber, FastReader s, PrintWriter out) { int t = s.nextInt(); while (t-- > 0) { int n = s.nextInt(); long l = s.nextLong(); long r = s.nextLong(); TreeMap<Long, Long> oddMap = new TreeMap<>(); TreeMap<Long, Long> evenMap = new TreeMap<>(); long from = 0l; long curr = (long) (n - 1l); long to = 2l * (curr); long num = 1l; while (curr > 0) { oddMap.put(from + 1, num); from = to; curr--; to += 2 * (curr); num++; } oddMap.put(n * (n - 1l) + 1l, (long) 1); from = 2l; curr = (long) (n - 1l); num = 2l; while (curr > 0) { evenMap.put(from, num); from += 2 * (curr); curr--; num++; } // out.println(oddMap); // out.println(evenMap); ArrayList<Long> oddAns = new ArrayList<>(); ArrayList<Long> evenAns = new ArrayList<>(); for (long i = l; i <= r; i++) { if (i % 2l != 0l) { oddAns.add(oddMap.get(oddMap.floorKey(i))); } else { if (evenMap.containsKey(i)) { evenAns.add(evenMap.get(i)); } else { evenAns.add((i - evenMap.lowerKey(i)) / 2 + evenMap.get(evenMap.lowerKey(i))); } } } int currO = 0; int currE = 0; for (long i = l; i <= r; i++) { if (i % 2l == 0l) { out.println(evenAns.get(currE++)); } else { out.println(oddAns.get(currO++)); } } } } } static class FastReader { private InputStream stream; private byte[] buf = new byte[1024]; private int curChar; private int numChars; private FastReader.SpaceCharFilter filter; public FastReader(InputStream stream) { this.stream = stream; } public int read() { if (numChars == -1) { throw new InputMismatchException(); } if (curChar >= numChars) { curChar = 0; try { numChars = stream.read(buf); } catch (IOException e) { throw new InputMismatchException(); } if (numChars <= 0) { return -1; } } return buf[curChar++]; } public int nextInt() { int c = read(); while (isSpaceChar(c)) { c = read(); } int sgn = 1; if (c == '-') { sgn = -1; c = read(); } int res = 0; do { if (c < '0' || c > '9') { throw new InputMismatchException(); } res *= 10; res += c - '0'; c = read(); } while (!isSpaceChar(c)); return res * sgn; } public long nextLong() { int c = read(); while (isSpaceChar(c)) { c = read(); } int sgn = 1; if (c == '-') { sgn = -1; c = read(); } long res = 0; do { if (c < '0' || c > '9') { throw new InputMismatchException(); } res *= 10; res += c - '0'; c = read(); } while (!isSpaceChar(c)); return res * sgn; } public boolean isSpaceChar(int c) { if (filter != null) { return filter.isSpaceChar(c); } return isWhitespace(c); } public static boolean isWhitespace(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } public interface SpaceCharFilter { public boolean isSpaceChar(int ch); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; const long long INF = 1e17 + 9; long long n, l, r; void calc(long long ly, long long faltl, long long faltr) { if (ly == n) { r = 1; } else if (faltl >= 2 * n - ly * 2) { calc(ly + 1, faltl - 2 * n + ly * 2, faltr); } else { long long ind = ly + 1; long long guard = 0; for (long long i = 0; i < 2 * n - ly * 2 && faltl > 0; i++) { if (i % 2) ind++; faltl--; guard = i + 1; } for (long long i = guard; i < 2 * n - ly * 2 && faltr > 0; i++) { if (i % 2) cout << ind++ << " "; else cout << ly << " "; faltr--; } if (faltr > 0 && ly < n - 1) { calc(ly + 1, faltl, faltr); } else { r = faltr; } } } int main() { ios::sync_with_stdio(false); cin.tie(0); long long t; cin >> t; while (t--) { cin >> n >> l >> r; calc(1, l - 1, r - l + 1); if (r == 1) cout << 1 << '\n'; else cout << '\n'; } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; long long int power_mod(long long int a, long long int x) { if (x == 0) return 1; long long int y = power_mod(a, x / 2); long long int ans = (y * y) % 1000000007; if (x % 2) ans = (ans * a) % 1000000007; return ans; } long long int inv(long long int a) { return power_mod(a, 1000000007 - 2); } long long int power(long long int a, long long int x) { if (x == 0) return 1; long long int y = power(a, x / 2); long long int ans = (y * y); if (x % 2) ans *= a; return ans; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); int t; cin >> t; while (t--) { long long int n, l, r; cin >> n >> l >> r; long long int curr = 1; vector<long long int> v(n + 1); long long int sum = 0; long long int index = 1; vector<long long int> ans; for (long long int i = 1; i <= n - 1; i++) { if (sum + 2 * (n - i) >= l) { long long int curr = i; long long int curr_next = i + 1; long long int count = 2 * (n - i); for (long long int j = sum + 1; j <= min(n * (n - 1), r); j++) { if (j >= l) { ans.push_back(curr); } count--; if (count == 0) { i++; curr = i; curr_next = i + 1; count = 2 * (n - i); continue; } j++; if (j > r) break; if (j >= l) { ans.push_back(curr_next); } curr_next++; count--; if (count == 0) { i++; curr = i; curr_next = i + 1; count = 2 * (n - i); continue; } } break; } else { sum = sum + (2 * (n - i)); } } if (r == (n * (n - 1)) + 1) ans.push_back(1); for (auto i : ans) cout << i << " "; cout << endl; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; inline long long read() { register char c = ' '; register long long v = 0, x = 1; while ((c < '0') || (c > '9')) { if (c == '-') x = -1; c = getchar(); } while ((c >= '0') && (c <= '9')) { v = (v << 1) + (v << 3) + (c ^ 48); c = getchar(); } return v * x; } inline void write(register long long x) { if (x < 0) x = -x, putchar('-'); if (x > 9) write(x / 10); putchar(x % 10 ^ 48); } long long t, n, l, r, x, y; inline void calc(register long long m) { if (m > n * (n - 1) / 2) return (void)(x = y = 1ll); register long long a = 0, b = 0; while (a < m) a += n - 1 - b, b++; a -= n - b, x = b, y = m - a + b; } inline void nxt() { (y != n) ? (y++) : (x++, y = x + 1); if (x == n) x = 1; } int main() { t = read(); while (t--) { n = read(), l = read(), r = read(), calc((l + 1) >> 1); for (register long long i = l; i <= r; i++, putchar(' ')) (i & 1) ? write(x) : (write(y), nxt()); putchar('\n'); } return ~~(0 - 0); }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.BufferedReader; import java.io.IOException; import java.io.InputStreamReader; import java.io.PrintWriter; import java.util.StringTokenizer; public class ProblemD { public static void main(String[] args) { // TODO Auto-generated method stub FastReader s = new FastReader(); PrintWriter out = new PrintWriter(System.out); int t = s.nextInt(); for(int a=0;a<t;a++) { int n = s.nextInt(); long l = s.nextLong(); long r = s.nextLong(); long[] arr = new long[n]; long sum = 0; long val = 2*(n-1); for(int i=0;i<n-1;i++) { sum += val; val -= 2; arr[i] = sum; } arr[n-1] = arr[n-2] + 1; // for(int i=0;i<n;i++) // System.out.println(arr[i]); int index = upperBound(arr, l); //System.out.println(index); print(arr, l, r, index, out); out.println(); } out.flush(); } public static void print(long[] arr, long l, long r, int index, PrintWriter out) { int n = arr.length; if(index == n-1) { out.print(1+" "); return; } long val1 = index + 1, val2 = 0; long end = arr[index]; if(l%2 == 0) { val2 = n - (end-l)/2; } else { val2 = n - (end-l-1)/2; } for(long i=l;l <= Math.min(end, r);l++) { if(l%2 == 1) out.print(val1+" "); else { out.print(val2+" "); val2++; } } if(end < r) print(arr, end + 1, r, index + 1, out); } public static int upperBound(long[] arr, long v) { if(v > arr[arr.length-1]) return -1; if(arr[0] > v) return 0; int low = 0, high = arr.length - 1; while(low < high) { if(low == high - 1) { if(arr[low] >= v) high = low; else low = high; break; } int mid = (low + high)/2; if(arr[mid] >= v) high = mid; else low = mid + 1; } return low; } static class FastReader { BufferedReader br; StringTokenizer st; public FastReader() { br = new BufferedReader(new InputStreamReader(System.in)); } String next() { while (st == null || !st.hasMoreElements()) { try { st = new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } } return st.nextToken(); } int nextInt() { return Integer.parseInt(next()); } long nextLong() { return Long.parseLong(next()); } double nextDouble() { return Double.parseDouble(next()); } String nextLine() { String str = ""; try { str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } return str; } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.util.*; import java.io.*; public class MinimumEulerCycle { // https://codeforces.com/contest/1334/problem/D // WRONg public static void main(String[] args) throws IOException, FileNotFoundException { BufferedReader in = new BufferedReader(new InputStreamReader(System.in)); //BufferedReader in = new BufferedReader(new FileReader("MinimumEulerCycle")); int t = Integer.parseInt(in.readLine()); while (t --> 0) { StringTokenizer st = new StringTokenizer(in.readLine()); long n = Integer.parseInt(st.nextToken()); long l = Long.parseLong(st.nextToken()); long r = Long.parseLong(st.nextToken()); long curnum = 1; long cursum=1; while (cursum + (n-curnum)*2 < l) { cursum += (n-curnum)*2; curnum++; } StringBuilder sb = new StringBuilder(); while (cursum <= r) { if (cursum == n*(n-1)+1) break; for (long i=curnum+1; i<=n; i++) { if (cursum >= l && cursum <= r) { sb.append(curnum + " "); } cursum++; if (cursum >= l && cursum <= r) { sb.append(i + " "); } cursum++; } curnum++; } if (cursum <= r) sb.append("1 "); System.out.println(sb); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.ArrayList; import java.util.InputMismatchException; public class D { public static void main(String[] args) throws Exception { // TODO Auto-generated method stub InputReader s = new InputReader(System.in); PrintWriter p = new PrintWriter(System.out); int t = s.nextInt(); while (t-- > 0) { long n = s.nextLong(); long l = s.nextLong(); long r = s.nextLong(); long sum = 0; long a = 1; while (sum < l) { if (a == n + 1) { break; } sum += 2 * (n - a); a++; } a--; long rem = l - (sum - 2 * (n - a)); long element = (long) Math.ceil((double) rem / 2); long flag = rem % 2; long b = a + element; for (int i = 0; i < r - l + 1; i++) { if (b == n + 1 && flag == 1) { p.print(1 + " "); break; } if (flag == 0) { p.print(b + " "); b++; flag = 1; if (b == n + 1) { a++; b = a + 1; } } else { p.print(a + " "); flag = 0; } } p.println(); } p.flush(); p.close(); } static class pair implements Comparable<pair> { Long x, y; pair(long x, long y) { this.x = x; this.y = y; } public int compareTo(pair o) { int result = x.compareTo(o.x); if (result == 0) result = y.compareTo(o.y); return result; } public String toString() { return x + " " + y; } public boolean equals(Object o) { if (o instanceof pair) { pair p = (pair) o; return p.x - x == 0 && p.y - y == 0; } return false; } public int hashCode() { return new Long(x).hashCode() * 31 + new Long(y).hashCode(); } } static long gcd(long a, long b) { if (b == 0) return a; return gcd(b, a % b); } public static ArrayList<Long> Divisors(long n) { ArrayList<Long> div = new ArrayList<>(); for (long i = 1; i <= Math.sqrt(n); i++) { if (n % i == 0) { div.add(i); if (n / i != i) div.add(n / i); } } return div; } public static int BinarySearch(long[] a, long k) { int n = a.length; int i = 0, j = n - 1; int mid = 0; if (k < a[0]) return 0; else if (k >= a[n - 1]) return n; else { while (j - i > 1) { mid = (i + j) / 2; if (k >= a[mid]) i = mid; else j = mid; } } return i + 1; } public static long GCD(long a, long b) { if (b == 0) return a; else return GCD(b, a % b); } public static long LCM(long a, long b) { return (a * b) / GCD(a, b); } // static class pair implements Comparable<pair> { // Integer x, y; // // pair(int x, int y) { // this.x = x; // this.y = y; // } // // public int compareTo(pair o) { // int result = x.compareTo(o.x); // if (result == 0) // result = y.compareTo(o.y); // // return result; // } // // public String toString() { // return x + " " + y; // } // // public boolean equals(Object o) { // if (o instanceof pair) { // pair p = (pair) o; // return p.x - x == 0 && p.y - y == 0; // } // return false; // } // // public int hashCode() { // return new Long(x).hashCode() * 31 + new Long(y).hashCode(); // } // } static class InputReader { private final InputStream stream; private final byte[] buf = new byte[8192]; private int curChar, snumChars; private SpaceCharFilter filter; public InputReader(InputStream stream) { this.stream = stream; } public int snext() { if (snumChars == -1) throw new InputMismatchException(); if (curChar >= snumChars) { curChar = 0; try { snumChars = stream.read(buf); } catch (IOException e) { throw new InputMismatchException(); } if (snumChars <= 0) return -1; } return buf[curChar++]; } public int nextInt() { int c = snext(); while (isSpaceChar(c)) { c = snext(); } int sgn = 1; if (c == '-') { sgn = -1; c = snext(); } int res = 0; do { if (c < '0' || c > '9') throw new InputMismatchException(); res *= 10; res += c - '0'; c = snext(); } while (!isSpaceChar(c)); return res * sgn; } public long nextLong() { int c = snext(); while (isSpaceChar(c)) { c = snext(); } int sgn = 1; if (c == '-') { sgn = -1; c = snext(); } long res = 0; do { if (c < '0' || c > '9') throw new InputMismatchException(); res *= 10; res += c - '0'; c = snext(); } while (!isSpaceChar(c)); return res * sgn; } public int[] nextIntArray(int n) { int a[] = new int[n]; for (int i = 0; i < n; i++) { a[i] = nextInt(); } return a; } public String readString() { int c = snext(); while (isSpaceChar(c)) { c = snext(); } StringBuilder res = new StringBuilder(); do { res.appendCodePoint(c); c = snext(); } while (!isSpaceChar(c)); return res.toString(); } public String nextLine() { int c = snext(); while (isSpaceChar(c)) c = snext(); StringBuilder res = new StringBuilder(); do { res.appendCodePoint(c); c = snext(); } while (!isEndOfLine(c)); return res.toString(); } public boolean isSpaceChar(int c) { if (filter != null) return filter.isSpaceChar(c); return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } private boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } public interface SpaceCharFilter { public boolean isSpaceChar(int ch); } } static class CodeX { public static void sort(long arr[]) { merge_sort(arr, 0, arr.length - 1); } private static void merge_sort(long A[], long start, long end) { if (start < end) { long mid = (start + end) / 2; merge_sort(A, start, mid); merge_sort(A, mid + 1, end); merge(A, start, mid, end); } } private static void merge(long A[], long start, long mid, long end) { long p = start, q = mid + 1; long Arr[] = new long[(int) (end - start + 1)]; long k = 0; for (int i = (int) start; i <= end; i++) { if (p > mid) Arr[(int) k++] = A[(int) q++]; else if (q > end) Arr[(int) k++] = A[(int) p++]; else if (A[(int) p] < A[(int) q]) Arr[(int) k++] = A[(int) p++]; else Arr[(int) k++] = A[(int) q++]; } for (int i = 0; i < k; i++) { A[(int) start++] = Arr[i]; } } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python2
def getK(index, N): k = 0 tot = 0 while True: k = k + 1 alt = tot + 2 * (N -k) #print(alt, index) if alt < index: tot = alt else: return k, tot def getLoop(k, indexInLoop): if indexInLoop % 2 == 0: return k return indexInLoop//2 + k + 1 T = int(raw_input()) for t in range(T): N, L, R = [int(v) for v in raw_input().split()] if L == N * (N-1) +1: print('1') else: k, tot = getK(L, N) indexInLoop = L - tot- 1 i = 0 out = [] R2 = R if R == N * (N-1) + 1: R2 = R -1 while i < R2 - L + 1: res = getLoop(k, indexInLoop) indexInLoop += 1 if indexInLoop >= 2 * (N -k): k += 1 indexInLoop = 0 out.append(str(res)) i += 1 if R == N * (N-1) + 1: out.append('1') print(' '.join(out))
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
for _ in range(int(input())): n, left, right = tuple(map(int, input().split())) maximal = n * (n - 1) + 1 if left == maximal: print('1') continue if right == maximal: end_1 = True else: end_1 = False a = [] summa = 0 i = (n - 1) * 2 cnt = 0 while summa + i < left: summa += i i -= 2 cnt += 1 left -= summa right -= summa summa = 0 # if cnt == 0: while left <= right: while left <= summa + i and left <= right: if left % 2 == 1: print(cnt + 1, end=' ') else: print(cnt + left // 2 + 1, end=' ') left += 1 left -= i right -= i summa = 0 i -= 2 cnt += 1 # print('!', i, sep='', end=' ') if i == 0 and end_1: print(1, end=' ') break print() # else: if left > right: continue # while left <= right: # start =
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
def main(): for j in range(int(input())): n,l,r=map(int,input().split()) b=1 for i in range(1,n): a=b b+=2*(n-i) if l < b: break x,y=i,(l-a)//2+i+1 b=(l-a)%2 for _ in range(r-l):# Imprimo solo la cantidad necesaria segun la entrada que me pasen if b: print(y,end=" ") y +=1 if y==n+1: x+=1 y=x+1 else: print(x,end=" ") b^=1 if r==n*(n-1)+1: print(1) else: print(y if b else x) if __name__=="__main__": main()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; int gcdExtended(int a, int b, int *x, int *y) { if (a == 0) { *x = 0, *y = 1; return b; } int x1, y1; int gcd = gcdExtended(b % a, a, &x1, &y1); *x = y1 - (b / a) * x1; *y = x1; return gcd; } long long int modInverse(int a, int m) { int x, y; int g = gcdExtended(a, m, &x, &y); long long int res = ((long long int)x % m + (long long int)m) % m; return res; } long long int poww(long long int x, long long int n) { if (n == 0) return 1; else if (n == 1) return x; else if (n % 2 == 0) return poww(x * x, n / 2); else return x * poww(x * x, (n - 1) / 2); } long long int modularExponentiation(long long int x, long long int n, long long int M) { long long int result = 1; while (n > 0) { if (n % 2 == 1) result = (result * x) % M; x = (x * x) % M; n = n / 2; } return result; } template <typename T> T maxx(T a, T b) { if (a < b) return b; return b; } template <typename T, typename... Args> T maxx(T a, T b, Args... args) { return (maxx(maxx(a, b), args...)); } template <typename T> T minn(T a, T b) { if (a < b) return a; return b; } template <typename T, typename... Args> T minn(T a, T b, Args... args) { return (minn(minn(a, b), args...)); } int gcd(int a, int b) { if (a == 0) return b; if (b == 0) return a; if (a == b) return a; if (a > b) return gcd(a - b, b); else return gcd(a, b - a); } long long int ncr(int n, int r) { long long int ans = 1; r = min(r, n - r); for (int i = 0; i < r; i++) { ans = (ans * (n - i) / (i + 1)) % 1000000007; } return ans; } int main() { ios::sync_with_stdio(false); cin.tie(NULL); int t = 1; cin >> t; while (t--) { long long int n, m, k, l, r; cin >> n >> l >> r; l--; m = 0; k = 1; while (m + (n - k) * 2 <= l && k < n) { m += (n - k) * 2; k++; } long long int temp = m; vector<long long int> v; while (m <= r) { long long int z = k; if (k != n) { for (int i = 0; i < (n - k); i++) { m += 2; v.push_back(k); v.push_back(++z); } k++; } else { v.push_back(1); break; } } for (int i = 0; i < r - l; i++) { cout << v[l - temp + i] << " "; } cout << '\n'; } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
#!/usr/bin/env python from __future__ import division, print_function import os import sys from io import BytesIO, IOBase if sys.version_info[0] < 3: from __builtin__ import xrange as range from future_builtins import ascii, filter, hex, map, oct, zip def solve(): n, l, r = [int(s) for s in input().strip().split()] if l == n * (n - 1) + 1: print(1) return i = 1 cnt = 0 while l > cnt + (n - i) * 2: cnt += (n - i) * 2 i += 1 A = [] while r > cnt + len(A): if i == n: A.append(1) else: A.extend([x for j in range(i + 1, n + 1) for x in [i, j]]) i += 1 result = A[l - cnt - 1:r - cnt] print(" ".join(str(x) for x in result)) def main(): for _ in range(int(input().strip())): solve() # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") def print(*args, **kwargs): """Prints the values to a stream, or to sys.stdout by default.""" sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout) at_start = True for x in args: if not at_start: file.write(sep) file.write(str(x)) at_start = False file.write(kwargs.pop("end", "\n")) if kwargs.pop("flush", False): file.flush() if sys.version_info[0] < 3: sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout) else: sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # endregion if __name__ == "__main__": main()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
// Don't place your source in a package import javax.swing.*; import java.lang.reflect.Array; import java.text.DecimalFormat; import java.util.*; import java.lang.*; import java.io.*; import java.math.*; import java.util.stream.Stream; // Please name your class Main public class Main { static FastScanner fs=new FastScanner(); static class FastScanner { BufferedReader br=new BufferedReader(new InputStreamReader(System.in)); StringTokenizer st=new StringTokenizer(""); public String next() { while (!st.hasMoreElements()) try { st=new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } return st.nextToken(); } int Int() { return Integer.parseInt(next()); } long Long() { return Long.parseLong(next()); } String Str(){ return next(); } } public static void main (String[] args) throws java.lang.Exception { PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out))); int T=Int(); for(int t=0;t<T;t++){ int n=Int(); long l=Long(); long r=Long(); Solution sol=new Solution(out); sol.solution(n,l,r); } out.close(); } public static int Int(){ return fs.Int(); } public static long Long(){ return fs.Long(); } public static String Str(){ return fs.Str(); } } class Solution{ PrintWriter out; public Solution(PrintWriter out){ this.out=out; } public void solution(int n,long l,long r){ long cur=2*(n-1); long sum=(2+cur)*(n-1)/2; if(l>sum){ out.println(1); return; } //20 18 16 14 12 10 8 ... sum=0; int first=1; while(sum+cur<l){ sum+=cur; cur-=2; first++; } for(long i=l;i<=r;i++){ if(i%2==1){ out.print(first+" "); } else{ long dis=i-sum; out.print((first+dis/2)+" "); } if(i==sum+cur){ sum+=cur; cur-=2; first++; if(first==n)first=1; } } out.println(); } //1 2 1 3 1 4 2 3 2 4 3 4 1 //1 2 1 3 1 4 1 5 2 3 2 4 2 5 3 4 3 5 4 5 1 //1 2 1 3 1 4 1 5 1 6 2 3 2 4 2 5 2 6 3 4 3 5 3 6 4 5 4 6 5 6 1 // 1 2 1 3 2 3 1 } /* ;\ |' \ _ ; : ; / `-. /: : | | ,-.`-. ,': : | \ : `. `. ,'-. : | \ ; ; `-.__,' `-.| \ ; ; ::: ,::'`:. `. \ `-. : ` :. `. \ \ \ , ; ,: (\ \ :., :. ,'o)): ` `-. ,/,' ;' ,::"'`.`---' `. `-._ ,/ : ; '" `;' ,--`. ;/ :; ; ,:' ( ,:) ,.,:. ; ,:., ,-._ `. \""'/ '::' `:'` ,'( \`._____.-'"' ;, ; `. `. `._`-. \\ ;:. ;: `-._`-.\ \`. '`:. : |' `. `\ ) \ -hrr- ` ;: | `--\__,' '` ,' ,-' free bug dog */
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; const int SIZE = 1e5 + 9; long long arr[SIZE]; int main() { int t; cin >> t; while (t--) { long long n, l, r; cin >> n >> l >> r; long long x = 2 * (n - 1); arr[1] = x; for (int i = 2; i < n; i++) { x -= 2; arr[i] = arr[i - 1] + x; } arr[n] = arr[n - 1] + 1; for (int i = 1; i <= n; i++) { if (l <= arr[i]) { long long d = arr[i] - l + 1; long long st = n - d / 2; if (d % 2 == 0) { cout << i << " "; st++; l++; } while (l <= r) { if (l % 2 != 0) { if (i == n) i = 1; cout << i << " "; st++; } else { cout << st << " "; if (st == n) { i = (i + 1 == n ? 1 : i + 1); st = i; } } l++; } break; } } cout << endl; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
import sys # 2 -> 1 2 1 # 3 -> 1 2 1 3 2 3 1 # 4 -> 1 2 1 3 1 4 2 3 2 4 3 4 1 # 5 -> 1 2 1 3 1 4 1 5 2 3 2 4 2 5 3 4 3 5 4 5 1 # for X(k, 1): first 2(k-1) are 1, i; then (k-1)(k-2) are X(k-1, 2) ; then 1 # 2(k-1), 2(k-2), 2(k-3) ... def binsearch(i, n): last = n*(n-1) ip = n*(n-1) - i #print(f"binsearch({i},{n}) last={last} ip={ip}") jprev = 0 j = n-1 while True: #print(f"j={j}, jprev={jprev}") #print(f"{j} {last-j*(j-1)} {last-(j-2)*(j-1)} ") step = max(1, abs(jprev-j)//2) jprev = j if j*(j-1) < ip: j += step elif j > 1 and (j-1)*(j-2) >= ip: j -= step else: break k = i - (last - j*(j-1)) return j, k def segment(n, l, r): res = [] j1, k1 = binsearch(l-1, n) j2, k2 = binsearch(r-1, n) # print(f"from {j1, k1} to {j2, k2}") for j in range(j1, j2-1, -1): for k in range(2*(j-1)): if not (j==j1 and k<k1) and not (j==j2 and k>k2): if k % 2 == 0: res.append(n-j+1) else: res.append(k // 2 + n-j + 2) if j2 == 1 and k2 == 0: res.append(1) return res t = int(input().strip()) for _ in range(t): n, l, r = list(map(int, input().strip().split())) print(' '.join(map(str, segment(n, l, r))))
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
#!/usr/bin/env python3 import sys input = sys.stdin.readline t = int(input()) for _ in range(t): n, l, r = map(int, input().split()) num = r - l + 1 init_num = 1 index = 0 for i in range(1, n): init_num = i if l <= (n - i) * 2: index = l l = 0 break else: l -= (n - i) * 2 # Last block if l > 0: print(1) continue ans = [] for i in range(1, n): if i < init_num: continue for j in range((n - i) * 2): if i == init_num and j < index - 1: continue elif j % 2 == 0: ans.append(i) num -= 1 else: ans.append((j+1) // 2 + i) num -= 1 if num == 0: break if num == 0: break if num > 0: ans.append(1) print(*ans)
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.BufferedReader; import java.io.InputStreamReader; import java.io.PrintWriter; import java.util.StringTokenizer; import java.util.*; public class D { void solve() throws Exception { long n = nl(); long l = nl(); long r = nl(); long h = 0L; long b = 1L; for (long i = n - 1; h + 2 * i < l && i > 0; i--) { h += 2*i; b++; } long c = b; if (b == n) { out.println(1); return; } while (h < l) { h++; if ((h & 1) == 1) { c++; } } while (h <= r) { if ((h & 1) == 1) { out.print(b + " "); } else { out.print(c + " "); c++; if (c > n) { b++; c = b + 1; if (b == n) { b = 1; } } } h++; } out.println(); } void run() throws Exception { initIO(); int t = ni(); while (t-- > 0) { solve(); out.flush(); } } public static void main(String[] args) throws Exception { new D().run(); } /** * IO. */ PrintWriter out; BufferedReader br; StringTokenizer tokenizer; void initIO() { out = new PrintWriter(System.out); br = new BufferedReader(new InputStreamReader(System.in)); tokenizer = null; } int ni() throws Exception { return Integer.parseInt(ns()); } long nl() throws Exception { return Long.parseLong(ns()); } double nd() throws Exception { return Double.parseDouble(ns()); } int[] nia(int n) throws Exception { int[] x = new int[n]; for (int i = 0; i < x.length; i++) { x[i] = ni(); } return x; } long[] nla(int n) throws Exception { long[] x = new long[n]; for (int i = 0; i < x.length; i++) { x[i] = nl(); } return x; } double[] nda(int n) throws Exception { double[] x = new double[n]; for (int i = 0; i < x.length; i++) { x[i] = nd(); } return x; } String ns() throws Exception { while (tokenizer == null || !tokenizer.hasMoreTokens()) tokenizer = new StringTokenizer(br.readLine()); return tokenizer.nextToken(); } String nline() throws Exception { tokenizer = null; return br.readLine(); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.BufferedReader; import java.io.IOException; import java.io.InputStreamReader; import java.io.PrintWriter; import java.util.ArrayList; import java.util.StringTokenizer; public class D { public static void main(String[] args) { FastScanner fs=new FastScanner(); int T=fs.nextInt(); PrintWriter out=new PrintWriter(System.out); for (int tt=0; tt<T; tt++) { int n=fs.nextInt(); long l=fs.nextLong()-1, r=fs.nextLong()-1; for (int start=1; start<=n; start++) { if (start!=n) { int left=n-start; int curSize=left*2; if (l>=curSize || r<0) { l-=curSize; r-=curSize; continue; } ArrayList<Integer> gen=new ArrayList<>(); for (int o=start+1; o<=n; o++) { gen.add(start); gen.add(o); } for (int i:gen) { if (l<=0&&r>=0) { out.print(i+" "); } l--; r--; } } else { //TODO: this ArrayList<Integer> gen=new ArrayList<>(); gen.add(1); for (int i:gen) { if (l<=0&&r>=0) { out.print(i+" "); } l--; r--; } } } out.println(); } out.close(); } static class FastScanner { BufferedReader br=new BufferedReader(new InputStreamReader(System.in)); StringTokenizer st=new StringTokenizer(""); public String next() { while (!st.hasMoreElements()) try { st=new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } return st.nextToken(); } public int nextInt() { return Integer.parseInt(next()); } public long nextLong() { return Long.parseLong(next()); } public int[] readArray(int n) { int[] a=new int[n]; for (int i=0; i<n; i++) { a[i]=nextInt(); } return a; } public double nextDouble() { return Double.parseDouble(next()); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
# Legends Always Come Up with Solution # Author: Manvir Singh import os import sys from io import BytesIO, IOBase from math import floor,sqrt def main(): for _ in range(int(input())): n,l,r=map(int,input().split()) if l== n*(n-1)+1: print(1) continue i=1 cnt=0 while l > cnt + (n - i) * 2: cnt += (n - i) * 2 i += 1 A = [] while r > cnt + len(A): if i == n: A.append(1) else: A.extend([x for j in range(i + 1, n + 1) for x in [i, j]]) i += 1 result = A[l - cnt - 1:r - cnt] print(" ".join(str(x) for x in result)) # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") if __name__ == "__main__": main()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.OutputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.math.BigInteger; import java.util.StringTokenizer; import java.io.*; import java.io.BufferedReader; import java.io.InputStreamReader; import java.io.InputStream; import java.util.*; public class Main { public static void main(String[] args) { InputStream inputStream = System.in; OutputStream outputStream = System.out; InputReader in = new InputReader(inputStream); PrintWriter out = new PrintWriter(outputStream); solve(in, out); out.close(); } static String reverse(String s) { return (new StringBuilder(s)).reverse().toString(); } static void sort(int ar[]) { int n = ar.length; ArrayList<Integer> a = new ArrayList<>(); for (int i = 0; i < n; i++) a.add(ar[i]); Collections.sort(a); for (int i = 0; i < n; i++) ar[i] = a.get(i); } static long ncr(long n, long r, long mod) { if (r == 0) return 1; long val = ncr(n - 1, r - 1, mod); val = (n * val) % mod; val = (val * modInverse(r, mod)) % mod; return val; } public static void solve(InputReader sc, PrintWriter pw) { int i, j = 0; // int t = 1; int t=sc.nextInt(); u: while (t-- > 0) { int n=sc.nextInt(); long l=sc.nextLong(); long r=sc.nextLong(); long d=r-l+1; long a[]=new long[n+1]; a[1]=(n-1)*2; // pw.println(1+" "+a[1]); for(i=2;i<=n;i++){ a[i]=(n-i)*2+a[i-1]; // if(i<5) // pw.println(i+" "+a[i]); } int y=n; int low=1,high=n; while(low<=high){ int mid=(low+high)/2; if(l<=a[mid]){ y=Math.min(y,mid); // low=mid+1; high=mid-1; } else{ // high=mid-1; low=mid+1; } } // y=1; // pw.println(y); l=l-a[y-1]; // long d=r-l+1; if(l%2==0){ pw.print((y+(l/2))+" "); d--; } for(long g=l/2+1;y+g<=n&&d>0;g++){ pw.print((y)+" "); d--; if(d==0) break; pw.print((y+g)+" "); d--; } for(i=y+1;i<=n&&d>0;i++){ for(long g=i+1;g<=n&&d>0;g++){ pw.print(i+" "); d--; if(d==0) break; pw.print(g+" "); d--; } } if(d>0) pw.print(1); pw.println(); } } static class Pair implements Comparable<Pair> { int a; int b; // int i; Pair(int a, int b) { this.a = a; this.b = b; // this.i=i; } public int compareTo(Pair p) { if (a != p.a) return (a - p.a); return (b - p.b); } } static boolean isPrime(int n) { if (n <= 1) return false; if (n <= 3) return true; if (n % 2 == 0 || n % 3 == 0) return false; for (int i = 5; i * i <= n; i = i + 6) if (n % i == 0 || n % (i + 2) == 0) return false; return true; } static int gcd(int a, int b) { if (b == 0) return a; return gcd(b, a % b); } static long fast_pow(long base, long n, long M) { if (n == 0) return 1; if (n == 1) return base % M; long halfn = fast_pow(base, n / 2, M); if (n % 2 == 0) return (halfn * halfn) % M; else return (((halfn * halfn) % M) * base) % M; } static long modInverse(long n, long M) { return fast_pow(n, M - 2, M); } static class InputReader { public BufferedReader reader; public StringTokenizer tokenizer; public InputReader(InputStream stream) { reader = new BufferedReader(new InputStreamReader(stream), 32768); tokenizer = null; } public String next() { while (tokenizer == null || !tokenizer.hasMoreTokens()) { try { tokenizer = new StringTokenizer(reader.readLine()); } catch (IOException e) { throw new RuntimeException(e); } } return tokenizer.nextToken(); } public int nextInt() { return Integer.parseInt(next()); } public long nextLong() { return Long.parseLong(next()); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
t = int(input()) for i in range(t): n, l, r = map(int, input().split()) if l == n * (n - 1) + 1: print(1) else: x = 1 summa = x * 2 * n rasn = x * (x + 1) while summa - rasn < l: summa += 2 * n rasn = (rasn // x) * (x + 2) x += 1 x -= 1 summa -= 2 * n rasn = (rasn // (x + 2)) * x first = x + 1 second = (l - summa + rasn + 1) // 2 + first if (l - summa + rasn) % 2 == 0: print(second, end=" ") if second == n: first += 1 second = first + 1 else: second += 1 ind = l + 1 else: ind = l while ind + 1 <= r: print(first, second, end=" ") if second == n: first += 1 second = first + 1 else: second += 1 ind += 2 if ind == r: if r == n * (n - 1) + 1: print(1) elif second == n: print(first) else: print(first) else: print()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
from sys import stdin, gettrace from math import sqrt if not gettrace(): def input(): return next(stdin)[:-1] # def input(): # return stdin.buffer.readline() def main(): def solve(): n,l,r = map(int, input().split()) lv = int((2*n+1 - sqrt((2*n-1)**2 -4*(l-1)))/2) lvs = -2*n+2*n*lv-lv*lv+lv lrd = l - lvs - 1 res = [] i = lv j = lv+lrd//2 + 1 if l%2 == 0: res = [j] if j < n: j+=1 else: i+=1 j = i+1 for _ in range(l-1, r, 2): res += [i,j] if j < n: j += 1 else: i +=1 j = i+1 if r == n*(n-1)+1: res[r-l] = 1 print(' '.join(map(str, res[:r-l+1]))) q = int(input()) for _ in range(q): solve() if __name__ == "__main__": main()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; int T; long long N; long long L, R; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> T; for (long long t = 0; t < T; t++) { cin >> N >> L >> R; if (L == N * (N - 1) + 1 && L == R) { cout << "1\n"; continue; } long long ini = 0; long long s = 1; long long len = N - 1; while (ini + 2 * len < L) { ini += 2 * len; len--; s++; } ini++; long long first = s; long long second = s + 1; while (ini < L) { if (ini % 2 == 0) second++; if (second > N) first++, second = first + 1; ini++; } while (ini <= R && ini < N * (N - 1) + 1) { if (ini % 2) cout << first << " "; else cout << second << " "; if (ini % 2 == 0) second++; if (second > N) first++, second = first + 1; ini++; } if (R == N * (N - 1) + 1) cout << "1 "; cout << "\n"; } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
/** * @author Finn Lidbetter */ import java.util.*; import java.io.*; import java.awt.geom.*; public class TaskD { public static void main(String[] args) throws IOException { BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); StringBuilder sb = new StringBuilder(); int nTests = Integer.parseInt(br.readLine()); for (int test=0; test<nTests; test++) { String[] s = br.readLine().split(" "); long n = Integer.parseInt(s[0]); long l = Long.parseLong(s[1]); long r = Long.parseLong(s[2]); if (l==r && l==n*(n-1)+1) { sb.append("1\n"); continue; } int section = 1; long end = 2*(n-section); while (l>end) { section++; end += 2*(n-section); } long[] ends = new long[(int)n]; ends[0] = 0; for (int i=1; i<n; i++) { ends[i] = ends[i-1] + 2*(n-i); } long upper = r; if (r==n*(n-1)+1) { upper = r-1; } for (long i=l; i<=upper; i++) { if (i!=l) sb.append(" "); if (i%2==1) { sb.append(section); } else { long offset = i-ends[section-1]; sb.append(section + (offset/2)); } if (i==ends[section]) section++; } if (r==n*(n-1)+1) { sb.append(" 1"); } sb.append("\n"); } System.out.print(sb); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
from sys import stdin input = stdin.buffer.readline for _ in range(int(input())): n, l, r = map(int, input().split()) l -= 1 r -= 1 flag, tmp, s = 1, 0, 0 ans = [] x, y = n, n - 1 for i in range(1, n): s += 2 * (n - i) if l < s and flag: x, tmp = i, (i > 1) * (s - 2 * (n - i)) l -= tmp flag = 0 if r < s: y = i r -= tmp break if x > y: l, r = 0, 0 for i in range(x, y + 1): for j in range(i + 1, n + 1): ans.append(i) ans.append(j) #if r >= len(ans) and y != n - 1: # print(0/0) ans.append(1) print(*ans[l : r + 1])
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; long long power(long long x, long long y, long long md = 1000000007LL) { long long res = 1; x %= md; while (y > 0) { if (y & 1) res = (res * x) % md; x *= x; if (x >= md) x %= md; y >>= 1; } return res; } signed main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); ; long long t = 1; cin >> t; while (t--) { long long n, l, r; cin >> n >> l >> r; vector<long long> ans; long long prev = 1; for (long long i = 1; i <= n; i++) { long long st = prev; long long end = prev + 2 * (n - i) - 1; if (l > end) { prev = end + 1; continue; } if (r < st) break; long long st1 = max(l, st); long long en1 = min(r, end); for (long long j = st1; j <= en1; j++) { if ((j - st) % 2 == 0) ans.emplace_back(i); else { long long ex = (j - st + 1) / 2; ans.emplace_back(i + ex); } } prev = end + 1; } if (r == prev) ans.emplace_back(1); for (auto &x : ans) cout << x << " "; cout << '\n'; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.*; import java.math.BigInteger; import java.util.*; /* ΠŸΡ€ΠΎΠΊΡ€Π°ΡΡ‚ΠΈΠ½ΠΈΡ€ΡƒΡŽ */ public class Main { static FastReader in; static PrintWriter out; static Random rand = new Random(); static final int INF = (int) (1e9 + 10), MOD = (int) (1e9 + 7), LOGN = 20; static final long IINF = (long) (2e18 + 10); static final int N = (int) (1e5 + 5); static int find(long[] arr, long x) { int l = 0, r = N - 5; while (l < r) { int m = (l + r) / 2; if (arr[m] < x) { l = m + 1; } else { r = m; } } return l; } static void solve() { int t = in.nextInt(); long[] pre = new long[N]; pre[0] = 1; for (int i = 1; i < N; i++) { pre[i] = pre[i - 1] + i * 2; } for (int tt = 0; tt < t; tt++) { int n = in.nextInt(); long l = in.nextLong(); long r = in.nextLong(); long nn = (long) n * (n - 1) + 1; long l1 = nn + 1 - l; int bl = find(pre, l1); int lol1 = n - bl; int lol2 = lol1 + 1 + (int) ((pre[bl] - l1) / 2); int turn = 1; if ((pre[bl] - l1) % 2 == 1) { turn ^= 3; } for (long i = l; i <= Math.min(nn - 1, r); i++) { if (turn == 1) { out.print(lol1 + " "); } else { out.print(lol2 + " "); lol2++; if (lol2 > n) { lol1++; lol2 = lol1 + 1; } } turn ^= 3; } if (r == nn) { out.print(1 + " "); } out.println(); } } public static void main(String[] args) throws FileNotFoundException, InterruptedException { in = new FastReader(System.in); // in = new FastReader(new FileInputStream("input.txt")); out = new PrintWriter(System.out); // out = new PrintWriter(new FileOutputStream("output.txt")); Thread thread = new Thread(null, () -> { int tests = 1; // tests = in.nextInt(); while (tests-- > 0) { solve(); } }, "Go", 1 << 28); thread.start(); thread.join(); // out.flush(); out.close(); } static class FastReader { BufferedReader br; StringTokenizer st; FastReader(InputStream is) { br = new BufferedReader(new InputStreamReader(is)); } Integer nextInt() { return Integer.parseInt(next()); } Long nextLong() { return Long.parseLong(next()); } Double nextDouble() { return Double.parseDouble(next()); } String next() { while (st == null || !st.hasMoreTokens()) { st = new StringTokenizer(nextLine()); } return st.nextToken(); } String nextLine() { String s = ""; try { s = br.readLine(); } catch (IOException e) { e.printStackTrace(); } return s; } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
// Problem : D. Minimum Euler Cycle // Contest : Educational Codeforces Round 85 (Rated for Div. 2) // URL : https://codeforces.com/contest/1334/problem/D // Memory Limit : 256 MB // Time Limit : 2000 ms // Powered by CP Editor (https://github.com/cpeditor/cpeditor) import java.io.*; import java.util.*; public class a { public static void main(String[] args) throws Exception { FastReader scan = new FastReader(); PrintWriter out = new PrintWriter(System.out); //PrintWriter out = new PrintWriter("file.out"); Task solver = new Task(); int t = scan.nextInt(); //int t = 1; for(int i = 1; i <= t; i++) solver.solve(i, scan, out); out.close(); } static class Task { static final int inf = Integer.MAX_VALUE; public void solve(int testNumber, FastReader sc, PrintWriter pw) { int n = sc.nextInt(); long sum =1; long l = sc.nextLong(); long r = sc.nextLong(); long c = 2*n-2; int start = 1; while(sum+c<l){ sum+=c;c-=2; if(c==0)c++; start++; } //pw.println(sum); ArrayList<Long> arr= new ArrayList<Long>(); c= start; long curr = c+1; while(sum<=Math.min(1l*n*(n-1),r)){ if(curr == n+1){ c++; curr = c+1; } if(sum>=l&&sum<=r){ arr.add(c); } sum++; if(sum>=l&&sum<=r){ arr.add(curr); } curr++; //pw.println(curr); sum++; } if(r==1l*n*(n-1)+1)arr.add(1l); for(long x : arr){ pw.print(x+" "); } pw.println(); } } long binpow(long a, long b, long m) { a %= m; long res = 1; while (b > 0) { if ((b & 1) == 1) res = res * a % m; a = a * a % m; b >>= 1; } return res; } static class tup implements Comparable<tup>{ int a, b; tup(int a,int b){ this.a=a; this.b=b; } @Override public int compareTo(tup o){ return Integer.compare(o.b,b); } } static void shuffle(int[] a) { Random get = new Random(); for (int i = 0; i < a.length; i++) { int r = get.nextInt(a.length); int temp = a[i]; a[i] = a[r]; a[r] = temp; } } static void shuffle(long[] a) { Random get = new Random(); for (int i = 0; i < a.length; i++) { int r = get.nextInt(a.length); long temp = a[i]; a[i] = a[r]; a[r] = temp; } } static class FastReader { BufferedReader br; StringTokenizer st; public FastReader() { br = new BufferedReader(new InputStreamReader(System.in)); } public FastReader(String s) throws FileNotFoundException { br = new BufferedReader(new FileReader(new File(s))); } String next() { while (st == null || !st.hasMoreElements()) { try { st = new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } } return st.nextToken(); } int nextInt() { return Integer.parseInt(next()); } long nextLong() { return Long.parseLong(next()); } double nextDouble() { return Double.parseDouble(next()); } String nextLine() { String str = ""; try { str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } return str; } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.*; import java.math.BigInteger; import java.util.*; public class Main { BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); PrintWriter pw = new PrintWriter(System.out); static int MOD = 1000000007; public static void main(String[] args) throws IOException { Main m = new Main(); m.solve(); m.close(); } void close() throws IOException { pw.flush(); pw.close(); br.close(); } int ri() throws IOException { return Integer.parseInt(br.readLine()); } long rl() throws IOException { return Long.parseLong(br.readLine()); } int[] ril(int n) throws IOException { int[] nums = new int[n]; int c = 0; for (int i = 0; i < n; i++) { int sign = 1; c = br.read(); int x = 0; if (c == '-') { sign = -1; c = br.read(); } while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = br.read(); } nums[i] = x * sign; } while (c != '\n' && c != -1) c = br.read(); return nums; } long[] rll(int n) throws IOException { long[] nums = new long[n]; int c = 0; for (int i = 0; i < n; i++) { int sign = 1; c = br.read(); long x = 0; if (c == '-') { sign = -1; c = br.read(); } while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = br.read(); } nums[i] = x * sign; } while (c != '\n' && c != -1) c = br.read(); return nums; } void solve() throws IOException { int t = ri(); for (int ti = 0; ti < t; ti++) { long[] nlr = rll(3); long n = nlr[0]; long l = nlr[1]; long r = nlr[2]; long sector = 1; long idx = 1; while (idx + (n - sector) * 2 < l) { idx = idx + (n - sector) * 2; sector++; } boolean left; // j represents the value in the pair that isn't the sector value long j = sector + (l - idx) / 2 + 1; if ((l - idx) % 2 == 0) { left = true; } else { left = false; } idx = l; while (idx <= r) { if (idx == n * (n - 1) + 1) { pw.print("1 "); break; } long val = left ? sector : j; pw.print(val + " "); if (j == n && !left) { sector++; j = sector + 1; } else if (!left) { j++; } left = !left; idx++; } pw.println(); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.util.ArrayList; import java.util.Collections; import java.util.List; import java.util.Scanner; public class MinimumEulerCycle { static long getValue(long n, long input, long i) { long head; if (input == n * (n - 1) + 1) { return 1; } if (i == 1) { head = 0; } else head = (i - 1) * (4 * n - 2 * i) / 2; long offset = (input - head); long value = offset % 2 != 0 ? i : i + offset / 2; return value; } static long getBlock(long n, long input) { if ((2 * n - 2) >= input) { return 1; } double a = Math.ceil((-Math.sqrt(Math.pow(n, 2) * 4 - 4 * n - 4 * input + 1) + 2 * n - 1) / 2); // double b = Math.floor((-Math.sqrt(Math.pow(n, 2) * 4 - 4 * n - 4 * input + 1) + 2 * n + 1) / 2); return (long)a; } static void check(long n, long l, long r) { for (long i = l; i <= r; i++) { long block = getBlock(n, i); long value = getValue(n, i, block); System.out.print(value + " "); } } public static void main(String[] args) { int n; Scanner sc = new Scanner(System.in); n = sc.nextInt(); long k, l, r; sc.nextLine(); for (int i = 0; i < n; i++) { k = sc.nextLong(); l = sc.nextLong(); r = sc.nextLong(); check(k, l, r); sc.nextLine(); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.*; import java.util.*; /** * A simple template for competitive programming problems. */ public class Solution { //final InputReader in = new InputReader("input.txt"); final InputReader in = new InputReader(System.in); final PrintWriter out = new PrintWriter(System.out); static final int MOD = 1000000007; void solve() { int T = in.nextInt(); while(T-->0) { int n = in.nextInt(); long l = in.nextLong(); long r = in.nextLong(); long start = 1L; int i = 1; while(i<=n) { start += 2*(n-i); i++; if(start>l) { i--; start -= 2*(n-i); break; } } long firstStart = start; List<Integer> ans = new ArrayList<>(); while(start<=r) { for(int j=i; j<n; j++) { for(int k=j+1; k<=n; k++) { ans.add(j); start++; ans.add(k); start++; } if(start>r) break; } if(start>r) break; ans.add(1); start++; } for(int j=(int)(l-firstStart); j<=r-firstStart; j++) { out.print(ans.get(j) + " "); } out.println(); } } public static void main(String[] args) throws FileNotFoundException { Solution s = new Solution(); Long t1 = System.currentTimeMillis(); s.solve(); System.err.println(System.currentTimeMillis() - t1 + " ms"); s.out.close(); } public Solution() throws FileNotFoundException { } private static class InputReader { private final InputStream stream; private final byte[] buf = new byte[1024]; private int curChar; private int numChars; InputReader(InputStream stream) { this.stream = stream; } InputReader(String fileName) { InputStream stream = null; try { stream = new FileInputStream(fileName); } catch (FileNotFoundException e) { e.printStackTrace(); } this.stream = stream; } int[] nextArray(int n) { int[] arr = new int[n]; for (int i = 0; i < n; i++) arr[i] = nextInt(); return arr; } int[][] nextMatrix(int n, int m) { int[][] matrix = new int[n][m]; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) matrix[i][j] = nextInt(); return matrix; } String nextLine() { int c = read(); while (isSpaceChar(c)) c = read(); StringBuilder res = new StringBuilder(); do { res.appendCodePoint(c); c = read(); } while (!isEndOfLine(c)); return res.toString(); } String nextString() { int c = read(); while (isSpaceChar(c)) c = read(); StringBuilder res = new StringBuilder(); do { res.appendCodePoint(c); c = read(); } while (!isSpaceChar(c)); return res.toString(); } long nextLong() { int c = read(); while (isSpaceChar(c)) c = read(); int sgn = 1; if (c == '-') { sgn = -1; c = read(); } long res = 0; do { if (c < '0' || c > '9') throw new InputMismatchException(); res *= 10; res += c - '0'; c = read(); } while (!isSpaceChar(c)); return res * sgn; } int nextInt() { int c = read(); while (isSpaceChar(c)) c = read(); int sgn = 1; if (c == '-') { sgn = -1; c = read(); } int res = 0; do { if (c < '0' || c > '9') throw new InputMismatchException(); res *= 10; res += c - '0'; c = read(); } while (!isSpaceChar(c)); return res * sgn; } double nextDouble() { return Double.parseDouble(nextString()); } private int read() { if (numChars == -1) throw new InputMismatchException(); if (curChar >= numChars) { curChar = 0; try { numChars = stream.read(buf); } catch (IOException e) { throw new InputMismatchException(); } if (numChars <= 0) return -1; } return buf[curChar++]; } private boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } private boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; using namespace std; inline int qpow(int b, int e, int m = 998244353) { int a = 1; for (; e; e >>= 1, b = (long long)b * b % m) if (e & 1) a = (long long)a * b % m; return a; } int n, m, q, k; int a[300005], b[300005], c[300005]; const int pp[11] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31}; void solve() { long long n, l, r; cin >> n >> l >> r; vector<long long> v(n + 1); v[1] = 1; for (long long i = 2; i < n; i++) { v[i] = v[i - 1] + 2 * (n - (i - 1)); } v[n] = v[n - 1] + 2; auto itr1 = upper_bound(v.begin(), v.end(), l); auto itr2 = upper_bound(v.begin(), v.end(), r); if (itr1 == v.end()) { cout << 1 << endl; } else { int in1 = -1; int in2 = -1; auto k1 = itr1; auto k2 = itr2; int st1; st1 = (--k1) - v.begin(); int st2; st2 = k2 - v.begin(); long long i = v[st1]; while (i <= r && i < v[n]) { for (int j = 0; j < n - st1; j++) { if (i >= l && i <= r) cout << st1 << " "; i++; if (i >= l && i <= r) cout << st1 + j + 1 << " "; i++; } st1++; } if (r == v[n]) cout << 1 << endl; else cout << endl; } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long t; cin >> t; while (t--) solve(); return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
t = int(input()) for y in range(t): n,l,r = list(map(int,input().split())) if(l == n*(n-1)+1): print(1) continue ind = 1 ct = 1 while(1): if(l < ct): break ct += (n-ind)*2 ind += 1 ind -= 1 if (ct-l)%2 == 0: st = ind print(st,end = " ") l += 1 st = n+1 for i in range(ct-1,l-1,-2): st -= 1 for i in range(l,r+1): if(i%2 == 1): print(ind,end = " ") else: print(st,end = " ") st += 1 if(st == n+1): ind += 1 if(ind == n): ind = 1 st = ind+1 print()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
/* D A R K L _ _ O R D D A K / | | \ L O R D A R _ / | | \ _ K L O R D A R K _ / | _ | \ _ L O R D D R K L _ / _ | _ | \\ | _ \ O R D D R K _ / _ | _ | \ \ | _ \ L O R D A R _ / _ / | / / \ \ | \ _ \ _ K L O D D _ / _ / | / / \ \ | \ _ \ _ A K _ / _ / | / / _ \ \ | \ _ \ _ L O R D A _ / _ / | / / _ \ \ | \ _ \ _ R K _ / _ / | | | | \ (O) / | | \ _ \ _ O D _ / _ / | | | | \ / | | \ _ \ _ D A / _ / | | | \ | \ _ \|/ / | | | \ _ \ K / _ / | | | \ | \ _ V / | | | \ _ \ L / / | | | \ _ / \ _ _ / | | | \ \ / / | | | | | | | \ \ / / | | | \ \ ROWECHEN / / | | | \ \ / / _ _ | | | \ \ ZHONG / / | | | _ _ \ \ / / _ / \ | | | | \ / \ \ / / \ / | | | | / \ _ \ \ / / _ / \ | | | | \ \ / / | | | | / \ _ \ \ / / / \ \ \ \ / / \ \ / / / / \ \ \ \ / / \ \ \ \ / / \ \ / / / / \ \ / \|/ \|/ | | | \|/ \|/ L O \|/ | | | | \|/ R D A R K L / _ | | | _ \ O R D D A R L O R / _ | | | _ \ D D A R L O R D / / / _ | _ | | \ _ \ D A R K O R D / / / _ | | _ | | \ _ \ D A R K L R D D A R | / / | | / | | \ / | | \ | K L O R D A R K | / / | | / | | \ / | | \ | L O R D A R / \ / | | | / | | / \ / K L O R D D A / \ / | | | / | | / \/ R K L O R D D / | / \ | \ / A R K L O R D A R K L / | / \ | \/ O R D D R K L O R D \ / | D A R K L O R D A R \/ | K L O R D D */ //TEMPLATE V2 import java.io.*; import java.util.*; import java.math.*; public class Main { //Solution goes below: ------------------------------------ public static void solution() throws IOException{ int T = nextInt(); for(int test=0;test<T;test++){ long n = nextLong(); long l = nextLong()-1; long r = nextLong(); boolean end = false; long total = n*n-n+1; if(r==total){ r--; end = true; } for(long level=1;level<n;level++){ long len = 2*(n-level); for(long i=l;i<Math.min(len,r);i++){ /*print(len); print(" "); print(i); print(" "); print(l); print(" "); print(r); print(" "); print(level); print(" ");*/ if(i%2==0){ print(level); }else{ print(i/2+1+level); } print(" ");//println(" "); } l = Math.max(l-len,0); r = Math.max(r-len,0); } if(end){ println("1 "); }else{ println(); } } } //Solution goes above: ------------------------------------ public static final String IN_FILE = ""; public static final String OUT_FILE = ""; //-------------------- ------------------------------------ //IO public static BufferedReader br; public static StringTokenizer st; public static BufferedWriter bw; public static void main(String[] args) throws IOException{ if(IN_FILE==""){ br = new BufferedReader(new InputStreamReader(System.in)); }else{ try { br = new BufferedReader(new FileReader(IN_FILE)); } catch (FileNotFoundException e) { br = new BufferedReader(new InputStreamReader(System.in)); } } if (OUT_FILE==""){ bw = new BufferedWriter(new OutputStreamWriter(System.out)); }else{ try { bw = new BufferedWriter (new FileWriter(OUT_FILE) ); } catch (FileNotFoundException e) { bw = new BufferedWriter(new OutputStreamWriter(System.out)); } } solution(); bw.close();//Flushes too. } public static String nextToken() { while (st == null || !st.hasMoreElements()) { try { st = new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } } return st.nextToken(); } public static String nextLine() { st = null; try { return br.readLine(); } catch (IOException e) { e.printStackTrace(); } return null; } public static int nextInt() { return Integer.parseInt(nextToken()); } public static long nextLong() { return Long.parseLong(nextToken()); } public static double nextDouble() { return Double.parseDouble(nextToken()); } public static void println(Object s) throws IOException{ bw.write(s.toString()+"\n"); } public static void println() throws IOException{ bw.newLine(); } public static void print(Object s) throws IOException{ bw.write(s.toString()); } public static void flush() throws IOException{//Useful for debug bw.flush(); } //Other public static class Arr<T> extends ArrayList<T> {} //I hate typing ArrayList }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
from sys import stdin, gettrace def input(): return stdin.buffer.readline() t = int(input()) for _ in range(t): n, l, r = list(map(int, input().split())) count = 0 i = 1 while count < l: if i == n: i = 1 count += (n - i) * 2 i += 1 i -= 1 count -= (n - i) * 2 j = i + (l - count + 1) // 2 length = r - l + 1 if (l % 2) == 0: print(j, end=' ') j += 1 length -= 1 if j > n: i += 1 j = i + 1 # print("before while i: {}, j: {}, length is {}".format(i, j, length)) while length > 0: if i == n: i = 1 print(i, end=' ') length -= 1 if length <= 0: break print(j, end=' ') length -= 1 j += 1 if j > n: i += 1 j = i + 1 print() # 1 2 1 3 1 4 1 5 ... 1 n 2 3 2 4 2 5 ... 2 n 3 1 ... 3 n ... n-1 1 ... n-1 n 1 # 1 2 1 3 1 4 1 5. 2 3 2 4 2 5. 3 4 3 5. 4 5. 1
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
import math import sys A = 1 B = 1 C = 1 K = 0 def LFromI(I): return I*I*A + I*B + C def IFromL(L): return math.floor((-B+math.sqrt(B*B - 4*A*(C-L)))/(2*A)) def Out(l, R): curint = IFromL(l) curpos = LFromI(curint) while curpos <= R: if curint == K: print(1, end=' ') break for i in range(2*(K-curint)): if curpos+i > R: break if curpos+i < l: continue if i % 2 == 0: print(curint, end=' ') else: print(curint + (i+1)//2, end=' ' ) curint += 1 curpos = LFromI(curint) return 1; t = int(input()) for _ in range(t): K, l, r = map(int, input().split()) A = -1 B = 2*K+1 C = -2*K Out(l-1, r-1) print()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.util.*; import java.io.*; import java.text.*; public class D1334 { public static void main(String[] args) throws IOException { Scanner sc = new Scanner(System.in); PrintWriter pw = new PrintWriter(System.out); int t = sc.nextInt(); while (t-- > 0) { int n = sc.nextInt(); long l = sc.nextLong(); long r = sc.nextLong(); int curl = 0; int curr = 0; boolean uu = r == 1l * n * (n - 1) + 1; Queue<Long> ans = new LinkedList<Long>(); for (int i = 1; i <= n-1; i++) { int len = 2 * (n - i); curl = 1; curr = len; long intl = Math.max(curl, l); long intr = Math.min(curr, r); if (intl <= intr) { for (long j = intl; j <= intr; j++) { // pw.println(intl+" "+intr +" "+i+" "+l+" "+r+" "+curl+" "+curr); ans.add(j % 2 == 1 ? i : j / 2 + i); } } l -= len; r -= len; } if (uu) ans.add(1l); while (!ans.isEmpty()) { pw.print(ans.poll() + " "); } pw.println(); } pw.close(); } static class Scanner { StringTokenizer st; BufferedReader br; public Scanner(InputStream s) { br = new BufferedReader(new InputStreamReader(s)); } public Scanner(FileReader r) { br = new BufferedReader(r); } public String next() throws IOException { while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine()); return st.nextToken(); } public int nextInt() throws IOException { return Integer.parseInt(next()); } public long nextLong() throws IOException { return Long.parseLong(next()); } public String nextLine() throws IOException { return br.readLine(); } public double nextDouble() throws IOException { return Double.parseDouble(next()); } public int[] nextIntArr(int n) throws IOException { int[] arr = new int[n]; for (int i = 0; i < arr.length; i++) arr[i] = nextInt(); return arr; } public boolean ready() throws IOException { return br.ready(); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.*; import java.util.*; public class C { public static void main(String[] args) { FastScanner in = new FastScanner(); PrintWriter out = new PrintWriter(System.out); int t = in.nextInt(); while(t-->0) { long n = in.nextInt(), l = in.nextLong(), r = in.nextLong(); long x = 1; long sum = 1; while(sum+(n-x)*2<l){ sum += (n-x)*2; x++; } StringBuilder sb = new StringBuilder(); while(sum<=r){ if(sum>n*(n-1)){ sb.append(1); break; } for(long i=x+1;i<=n;i++){ if(sum>=l&&sum<=r) sb.append(x+" "); sum++; if(sum>=l&&sum<=r) sb.append(i+" "); sum++; } x++; } out.println(sb); } out.flush(); } static class FastScanner { BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); StringTokenizer st = new StringTokenizer(""); String next() { while(!st.hasMoreTokens()) try { st = new StringTokenizer(br.readLine()); } catch(IOException e) {} return st.nextToken(); } String nextLine(){ try{ return br.readLine(); } catch(IOException e) { } return ""; } int nextInt() { return Integer.parseInt(next()); } long nextLong() { return Long.parseLong(next()); } int[] readArray(int n) { int a[] = new int[n]; for(int i=0;i<n;i++) a[i] = nextInt(); return a; } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.util.*; import java.io.*; public class Solution { public static void main(String[] args) throws IOException{ Scanner in = new Scanner(System.in); BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); StringBuffer out = new StringBuffer(); int t=in.nextInt(); label: while(t--!=0) { long n=in.nextLong(); long l=in.nextLong(), r=in.nextLong(); long cnt=0; long i; for(i=1L; i<=n; i++) { if(l<=cnt+((n-i)<<1)) break; cnt+=((n-i)<<1); } for(; i<=n && cnt<=r; i++) { for(long j=i+1; j<=n && cnt<=r; j++) { cnt+=1; if(l<=cnt && cnt<=r) out.append(i+" "); cnt+=1; if(l<=cnt && cnt<=r) out.append(j+" "); } } cnt+=1; if(l<=cnt && cnt<=r) out.append(1+" "); out.append("\n"); } System.out.println(out); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(0); int t = 1; cin >> t; while (t--) { long long n, l, r; cin >> n >> l >> r; bool f = 0; if (r == (n * (n - 1) + 1)) { r--; f = 1; } long long ans1 = (n - 1) * 2; long long sum = ans1, pos = 0; for (long long i = 1; i < n; i++) { if (l <= ans1) { pos = i; break; } l -= ans1; r -= ans1; ans1 -= 2; } long long pos2 = (l + 1) / 2 + pos; while (l <= r) { if (l % 2 == 0) { cout << pos2 << " "; pos2++; } else cout << pos << " "; if (pos2 == n + 1) { pos++; pos2 = pos + 1; } l++; } if (f == 1) cout << 1 << " "; cout << endl; } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.OutputStream; import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintWriter; import java.io.BufferedWriter; import java.io.Writer; import java.io.OutputStreamWriter; import java.util.InputMismatchException; import java.io.IOException; import java.io.InputStream; /** * Built using CHelper plug-in * Actual solution is at the top * * @author sumit */ public class Main { public static void main(String[] args) { InputStream inputStream = System.in; OutputStream outputStream = System.out; InputReader in = new InputReader(inputStream); OutputWriter out = new OutputWriter(outputStream); DMinimumEulerCycle solver = new DMinimumEulerCycle(); solver.solve(1, in, out); out.close(); } static class DMinimumEulerCycle { public void solve(int testNumber, InputReader in, OutputWriter out) { int t = in.nextInt(); while (t-- > 0) { int n = in.nextInt(); long l = in.nextLong(); long r = in.nextLong(); StringBuilder str = new StringBuilder(); long[] sum = new long[n]; sum[0] = 2 * (n - 1); int mm = 2; for (int i = 1; i < n; i++) { int xx = n - mm; sum[i] = sum[i - 1] + 2 * xx; mm++; } while (l <= r) { if (l == (1L * n * (n - 1) + 1)) { str.append("1 "); } else { int start = 0; int end = n - 1; int ans = -1; while (start <= end) { int mid = (start + end) / 2; if (sum[mid] < l) { start = mid + 1; } else if (sum[mid] >= l) { ans = mid; end = mid - 1; } } long l1 = l; if (ans > 0) l = l - sum[ans - 1]; String ss = ""; if (l % 2 == 1) { ss = (1 + ans) + " "; } else { ss = (1 + ans + l / 2) + " "; } str.append(ss); l = l1; } l++; } out.printLine(str.toString()); } } } static class OutputWriter { private final PrintWriter writer; public OutputWriter(OutputStream outputStream) { writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream))); } public OutputWriter(Writer writer) { this.writer = new PrintWriter(writer); } public void print(Object... objects) { for (int i = 0; i < objects.length; i++) { if (i != 0) { writer.print(' '); } writer.print(objects[i]); } } public void printLine(Object... objects) { print(objects); writer.println(); } public void close() { writer.close(); } } static class InputReader { private InputStream stream; private byte[] buf = new byte[1024]; private int curChar; private int numChars; public InputReader(InputStream stream) { this.stream = stream; } public int read() { if (numChars == -1) throw new InputMismatchException(); if (curChar >= numChars) { curChar = 0; try { numChars = stream.read(buf); } catch (IOException e) { throw new InputMismatchException(); } if (numChars <= 0) return -1; } return buf[curChar++]; } public int nextInt() { int c = read(); while (isSpaceChar(c)) c = read(); int sgn = 1; if (c == '-') { sgn = -1; c = read(); } int res = 0; do { if (c < '0' || c > '9') throw new InputMismatchException(); res *= 10; res += c & 15; c = read(); } while (!isSpaceChar(c)); return res * sgn; } public long nextLong() { int c = read(); while (isSpaceChar(c)) c = read(); int sign = 1; if (c == '-') { sign = -1; c = read(); } long result = 0; do { if (c < '0' || c > '9') throw new InputMismatchException(); result *= 10; result += c & 15; c = read(); } while (!isSpaceChar(c)); return result * sign; } public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.*; import java.io.*; import java.math.*; public class Main { InputStream is; PrintWriter out; String INPUT = ""; //class Declaration static class pair implements Comparable < pair > { long x; long y; pair(long i, long j) { x = i; y = j; } public int compareTo(pair p) { if (this.x != p.x) { return (int)(this.x-p.x); } else { return (int)(this.y - p.y); } } public int hashCode() { return (x + " " + y).hashCode(); } public String toString() { return x + " " + y; } public boolean equals(Object o) { pair x = (pair) o; return (x.x == this.x && x.y == this.y); } } // int[] dx = {0,0,1,-1}; // int[] dy = {1,-1,0,0}; // int[] ddx = {0,0,1,-1,1,-1,1,-1}; // int[] ddy = {1,-1,0,0,1,-1,-1,1}; int inf = (int) 1e9 + 5; long mod = (long)1e9 + 7 ; void solve() throws Exception { int tt=ni(); while(tt-->0){ long n=nl(),l=nl(),r=nl(); long end = n*(n-1) + 1 ; if(l==end){ pn("1"); } else{ long segRightLimit = 2*(n-1); long segver = 1 ; long prevSegEnd = 0 ; while(l>segRightLimit){ segver ++ ; prevSegEnd = segRightLimit ; segRightLimit += 2*(n-segver); } // pn(segver); // pn(prevSegEnd); for(long j= prevSegEnd+1,segel=0;j<=r;++j){ long content = 0; if(segel == (n-segver)){ segel =0; segver++; } if(j%2==1){ content = segver ; } else{ segel++; content = segver + segel; } if(l<=j && j<=r){ if(j==end) p(1+" "); else p(content+" "); } } pn(""); } } } long pow(long a, long b) { long result = 1; while (b > 0) { if (b % 2 == 1) result = (result * a) % mod; b /= 2; a = (a * a) % mod; } return result; } void print(Object o) { System.out.println(o); System.out.flush(); } long gcd(long a, long b) { if (b == 0) return a; return gcd(b, a % b); } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms"); } public static void main(String[] args) throws Exception { new Main().run(); } //output methods private void pn(Object o) { out.println(o); } private void p(Object o) { out.print(o); } private ArrayList < ArrayList < Integer >> ng(int n, int e) { ArrayList < ArrayList < Integer >> g = new ArrayList < > (); for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ()); for (int i = 0; i < e; ++i) { int u = ni(), v = ni(); g.get(u).add(v); g.get(v).add(u); } return g; } private ArrayList < ArrayList < pair >> nwg(int n, int e) { ArrayList < ArrayList < pair >> g = new ArrayList < > (); for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ()); for (int i = 0; i < e; ++i) { int u = ni(), v = ni(), w = ni(); g.get(u).add(new pair(w, v)); g.get(v).add(new pair(w, u)); } return g; } //input methods private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if (lenbuf == -1) throw new InputMismatchException(); if (ptrbuf >= lenbuf) { ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if (lenbuf <= 0) return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while ((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char) skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while (p < n && !(isSpaceChar(b))) { buf[p++] = (char) b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for (int i = 0; i < n; i++) map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for (int i = 0; i < n; i++) a[i] = ni(); return a; } private int ni() { int num = 0, b; boolean minus = false; while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if (b == '-') { minus = true; b = readByte(); } while (true) { if (b >= '0' && b <= '9') { num = num * 10 + (b - '0'); } else { return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if (b == '-') { minus = true; b = readByte(); } while (true) { if (b >= '0' && b <= '9') { num = num * 10 + (b - '0'); } else { return minus ? -num : num; } b = readByte(); } } private void tr(Object...o) { if (INPUT.length() > 0) System.out.println(Arrays.deepToString(o)); } void watch(Object...a) throws Exception { int i = 1; print("watch starts :"); for (Object o: a) { //print(o); boolean notfound = true; if (o.getClass().isArray()) { String type = o.getClass().getName().toString(); //print("type is "+type); switch (type) { case "[I": { int[] test = (int[]) o; print(i + " " + Arrays.toString(test)); break; } case "[[I": { int[][] obj = (int[][]) o; print(i + " " + Arrays.deepToString(obj)); break; } case "[J": { long[] obj = (long[]) o; print(i + " " + Arrays.toString(obj)); break; } case "[[J": { long[][] obj = (long[][]) o; print(i + " " + Arrays.deepToString(obj)); break; } case "[D": { double[] obj = (double[]) o; print(i + " " + Arrays.toString(obj)); break; } case "[[D": { double[][] obj = (double[][]) o; print(i + " " + Arrays.deepToString(obj)); break; } case "[Ljava.lang.String": { String[] obj = (String[]) o; print(i + " " + Arrays.toString(obj)); break; } case "[[Ljava.lang.String": { String[][] obj = (String[][]) o; print(i + " " + Arrays.deepToString(obj)); break; } case "[C": { char[] obj = (char[]) o; print(i + " " + Arrays.toString(obj)); break; } case "[[C": { char[][] obj = (char[][]) o; print(i + " " + Arrays.deepToString(obj)); break; } default: { print(i + " type not identified"); break; } } notfound = false; } if (o.getClass() == ArrayList.class) { print(i + " al: " + o); notfound = false; } if (o.getClass() == HashSet.class) { print(i + " hs: " + o); notfound = false; } if (o.getClass() == TreeSet.class) { print(i + " ts: " + o); notfound = false; } if (o.getClass() == TreeMap.class) { print(i + " tm: " + o); notfound = false; } if (o.getClass() == HashMap.class) { print(i + " hm: " + o); notfound = false; } if (o.getClass() == LinkedList.class) { print(i + " ll: " + o); notfound = false; } if (o.getClass() == PriorityQueue.class) { print(i + " pq : " + o); notfound = false; } if (o.getClass() == pair.class) { print(i + " pq : " + o); notfound = false; } if (notfound) { print(i + " unknown: " + o); } i++; } print("watch ends "); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
// Imports import java.util.*; import java.io.*; public class D { /** * @param args the command line arguments * @throws IOException, FileNotFoundException */ public static void main(String[] args) throws IOException, FileNotFoundException { // TODO UNCOMMENT WHEN ALGORITHM CORRECT BufferedReader f = new BufferedReader(new InputStreamReader(System.in)); /* BufferedReader f = new BufferedReader(new StringReader("3\n" + "2 1 3\n" + "3 3 6\n" + "99995 9998900031 9998900031")); */ // TODO code application logic here int T = Integer.parseInt(f.readLine()); for(int i = 0; i < T; i++) { StringTokenizer st = new StringTokenizer(f.readLine()); int N = Integer.parseInt(st.nextToken()); long L = Long.parseLong(st.nextToken()); long R = Long.parseLong(st.nextToken()); int tempN = N - 1; long count = 1; int actual = 0; while(count < L && tempN > 0) { count += 2*tempN; tempN--; } // System.out.println("COUNT: " + count); // System.out.println(tempN); if(tempN == 0 && count == L) { System.out.println("1"); } else { actual = N - tempN - 1; if(count == 1) { actual++; } else { count -= 2*(tempN + 1); } // System.out.println("ACTUAL: " + actual); // System.out.println("COUNT: " + count); StringBuilder sb = new StringBuilder(); int x = actual; int y = actual + 1; while(count <= R) { // count if(count >= L) { // System.out.println("xy: " + x + " " + y); if(count % 2 == 1) { sb.append(x); sb.append(" "); } else { sb.append(y); sb.append(" "); } } if(count % 2 == 0) { if(y < N) { y++; } else if(x < N - 1) { x++; y = x + 1; } else { x = 1; } } count++; } System.out.println(sb.substring(0, sb.length() - 1)); } } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; long long int max(long long int a, long long int b) { if (a >= b) return a; else return b; } long long int min(long long int a, long long int b) { if (a <= b) return a; else return b; } void solve() { long long int n, l, r; cin >> n >> l >> r; if (l == (1LL * n * (n - 1)) + 1) { cout << 1 << endl; return; } long long int sum = 0; long long int i; for (i = n - 1; i >= 1; i--) { sum += 1LL * 2 * i; if (sum >= l) { break; } } vector<long long int> ans; long long int total = r - l + 1; if (r == (1LL * n * (n - 1)) + 1) total--; long long int count = sum - l + 1; long long int a, b; if ((count % 2) == 0) { a = n - i; b = n - (count / 2) + 1; } else { ans.push_back(n - ((count) / 2)); a = n - i; b = n - (count / 2) + 1; total--; } if (count == 1) { a++; b = a + 1; } while (total > 0) { if (b == n + 1) { a++; b = a + 1; } ans.push_back(a); total--; if (total == 0) break; ans.push_back(b); total--; b++; } if (r == (1LL * n * (n - 1)) + 1) ans.push_back(1); for (auto it : ans) { cout << it << " "; } cout << endl; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); long long int t; cin >> t; while (t--) { solve(); } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.util.*; import java.util.stream.Collectors; import java.util.stream.IntStream; import java.util.stream.LongStream; public class Solution { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int t = scanner.nextInt(); scanner.nextLine(); for (int i = 0; i < t; i++) { solve(scanner, i + 1); } } public static void solve(Scanner in, int id) { int n = in.nextInt(); long l = in.nextLong(); long r = in.nextLong(); long visits = 0; for(int i = 1; i <= n-1; i++) { //Calculate visits long visits_i = 2*(n - i); if(visits + visits_i < l) { visits += visits_i; continue; } print(++visits, l, r, i); for(int j = i+1; j <= n-1; j++) { print(++visits, l, r, j); print(++visits, l, r, i); } print(++visits, l, r, n); if(visits > r) { System.out.println(); return; } } print(++visits, l, r, 1); System.out.println(); } private static void print(long next_id, long l, long r, int num) { if(next_id >= l && next_id <= r) { System.out.print(num + " "); } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
from bisect import bisect_left def get(x, n): if x==n: return [1] return [a for i in range(x+1,n+1) for a in [x,i]] def solve(): n,l,r = map(int,input().split()) cum = [0]*(n+1) for i in range(1,n): cum[i] = cum[i-1] + 2*(n-i) cum[n] = cum[n-1] + 1 xL = bisect_left(cum, l) xR = bisect_left(cum, r) hL = l - cum[xL-1] - 1 hR = r - cum[xR-1] - 1 if xL==xR: u = get(xL, n) print(*u[hL:hR+1]) return uL, uR = get(xL, n), get(xR, n) print(*uL[hL:], end=" ") for x in range(xL+1, xR): print(*get(x, n), end=" ") print(*uR[:hR+1]) return for _ in range(int(input())): solve()
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.util.*; import java.io.*; public class Main{ static int repow(int b,int p){ long a = b; long res=1; while(p>0){ if(p%2==1){ res*=a; } a*=a; p/=2; } return (int)res; } static int repow(int b,int p,int modder){ long a = b%modder; long res=1; while(p>0){ if(p%2==1){ res=(res*a)%modder; } a=(a*a)%modder; p/=2; } return (int)res; } static long repow(long b,long p){ long a = b; long res=1; while(p>0){ if(p%2==1){ res*=a; } a*=a; p/=2; } return res; } static long repow(long b,long p,long modder){ long a = b%modder; long res=1; while(p>0){ if(p%2==1){ res=(res*a)%modder; } a=(a*a)%modder; p/=2; } return res; } static long gcd(long c,long d){ while(true){ long f=c%d; if(f==0){ return d; } c=d; d=f; } } static long lcm(long c,long d){ return c/gcd(c,d)*d; } static ArrayList<Integer> divList(int n){ ArrayList<Integer> div=new ArrayList<Integer>(); for(int i=1;i*i<=n;i++){ if(n%i==0){ div.add(i); if(i*i!=n){ div.add((int)(n/i)); } } } return div; } static ArrayList<Long> divList(long n){ ArrayList<Long> div=new ArrayList<Long>(); for(long i=1;i*i<=n;i++){ if(n%i==0){ div.add(i); if(i*i!=n){ div.add(n/i); } } } return div; } static HashSet<Integer> divSet(int n){ HashSet<Integer> div=new HashSet<Integer>(); for(int i=1;i*i<=n;i++){ if(n%i==0){ div.add(i); div.add((int)(n/i)); } } return div; } static Map<Long,Integer> pFacMap(long x){ Map<Long,Integer> mp=new HashMap<>(); long t=x; for(long i=2;i*i<=x&&i<=t;i++){ if(t%i==0){ int num=0; while(t%i==0){ t/=i; num++; } mp.put(i,num); } } if(t!=1){ mp.put(t,1); } return mp; } static boolean iP(long n){ if(n==2){ return true; } if((n&1)==0||n==1){ return false; } // if(n>3037007383L){ if(n>Integer.MAX_VALUE){ return tameshiwari(n); } long d=n-1; int s=0; while((d&1)==0){ d/=2; s++; } int[] aa = {2,3,5,7,11,13,17}; for(int i=0;i<7&&aa[i]<n;i++){ int a = aa[i]; long t = d; long y=repow(a,t,n); while(t!=n-1&&y!=1&&y!=n-1){ y = (y*y)%n; t=t<<1; } if(y!=n-1&&(t&1)==0){ return false; } } return true; } static boolean tameshiwari(long n){ for(long i=2;i*i<=n;i++){ if(n%i==0){ return false; } } return true; } static class NCK{ int max; int mod; long[] fac; long[] finv; long[] inv; NCK(){ this(510000,1000000007); } NCK(int max,int mod){ this.max=max; this.mod=mod; pre(max,mod); } void pre(int nmax,int nmod){ fac = new long[nmax]; finv = new long[nmax]; inv = new long[nmax]; fac[0]=fac[1]=1; finv[0]=finv[1]=1; inv[1]=1; for(int i=2;i<nmax;i++){ fac[i]=fac[i-1]*i%nmod; inv[i]=nmod-inv[nmod%i]*(nmod/i)%nmod; finv[i]=finv[i-1]*inv[i]%nmod; } } long nCk(int n,int k){ if(n<k){return 0;} if(n<0||k<0){return 0;} return fac[n]*(finv[k]*finv[n-k]%mod)%mod; } } static int kmp(String t,String p){ int[] f=new int[p.length()+1]; int i=0; int j=1; f[1]=0; while(j<p.length()){ if(i==0||p.charAt(i-1)==p.charAt(j-1)){ i++; j++; f[j]=i; }else{ i=f[i]; } } i=1; j=1; while(i<=p.length()&&j<=t.length()){ if(i==0||p.charAt(i-1)==t.charAt(j-1)){ i++; j++; }else{ i=f[i]; } } return i==(p.length()+1)?j-i:-1; } static String StSort(String s){ StringBuilder sb = new StringBuilder(s); int lg = sb.length(); int l; int r; int gaze; for(int i=1;i<lg;i++){ l=0; r=i-1; while(l<=r){ gaze=(l+r)/2; if(sb.charAt(gaze)<=sb.charAt(i)){ l=gaze+1; }else if(sb.charAt(gaze)>sb.charAt(i)){ r=gaze-1; } } sb.insert(l,sb.charAt(i)); sb.deleteCharAt(i+1); } return sb.toString(); } static class Xy{ int x; int y; Xy(int x,int y){ this.x=x; this.y=y; } public int manht(Xy o){ return Math.abs(x-o.x)+Math.abs(y-o.y); } public String toString(){ return "["+x+","+y+"]"; } public double henkaku(){ return Math.atan2(y,x); } public static int hencom(Xy s1,Xy s2){ return (int)Math.signum(s1.henkaku()-s2.henkaku()); } public boolean equals(Object o){ return x==((Xy)o).x&&y==((Xy)o).y; } } static class Zip1{ Map<Long,Integer> zip=new HashMap<>(); long[] unzip; Zip1(long[] a){ Arrays.sort(a); long mae=0;int zure=0; for(int i=0;i<a.length;i++){ if(i==0||mae!=a[i]){ zip.put(a[i],i-zure); mae=a[i]; }else{ zure++; } } unzip=new long[size()]; for(Map.Entry<Long,Integer> me:zip.entrySet()){ unzip[me.getValue()]=me.getKey(); } } int zip(long t){ return zip.get(t); } long unzip(int i){ return unzip[i]; } int size(){ return zip.size(); } } static class UnFd{ int[] parent; int[] size; int forest; UnFd(int n){ parent=new int[n]; size=new int[n]; forest=n; for(int i=0;i<n;i++){ parent[i]=i; size[i]=1; } } private boolean isRoot(int i){ return parent[i]==i; } private int rootOf(int i){ if(isRoot(i)){ return i; } return parent[i]=rootOf(parent[i]); } public boolean same(int i,int j){ return rootOf(i)==rootOf(j); } public void merge(int i,int j){ i=rootOf(i); j=rootOf(j); if(i==j){ return; } size[Integer.min(i,j)]+=size[Integer.max(i,j)]; parent[Integer.max(i,j)]=Integer.min(i,j); forest--; } public int sizeOf(int i){ return size[rootOf(i)]; } public int[] parents(){ return parent; } public int forest(){ return forest; } public String toString(){ return Arrays.toString(parent); } } static class SegTree<T>{ int n; int m; java.util.function.BinaryOperator<T> op; int[] l; int[] r; T[] a; T ident; SegTree(int n,java.util.function.BinaryOperator<T> op,T ident){ this.n=n; this.op=op; this.ident=ident; int ii=n-1; int p=0; while(ii>0){ ii/=2; p++; } m=repow(2,p+1)-1; @SuppressWarnings("unchecked") T[] b=(T[])(new Object[m]); a=b; Arrays.fill(a,ident); l=new int[m]; r=new int[m]; for(int i=0;i<=m/2;i++){ l[m/2+i]=i; r[m/2+i]=i+1; } for(int i=m/2-1;i>=0;i--){ l[i]=l[lch(i)]; r[i]=r[rch(i)]; } } SegTree(int n,java.util.function.BinaryOperator<T> op,T ident,T[] ary){ this.n=n; this.op=op; this.ident=ident; int ii=n-1; int p=0; while(ii>0){ ii/=2; p++; } m=repow(2,p+1)-1; @SuppressWarnings("unchecked") T[] b=(T[])(new Object[m]); a=b; for(int i=0;i<n;i++){ a[m/2+i]=ary[i]; } for(int i=m/2+n;i<m;i++){ a[i]=ident; } for(int i=m/2-1;i>=0;i--){ a[i]=op.apply(a[lch(i)],a[rch(i)]); } l=new int[m]; r=new int[m]; for(int i=0;i<=m/2;i++){ l[m/2+i]=i; r[m/2+i]=i+1; } for(int i=m/2-1;i>=0;i--){ l[i]=l[lch(i)]; r[i]=r[rch(i)]; } } public T getAll(){ return a[0]; } public T get(int from,int to){ if(from<0||n<to||from>=to){ throw new IllegalArgumentException(String.valueOf(from)+","+String.valueOf(to)); } return get(from,to,0); } private T get(int from,int to,int node){ if(from==l[node]&&to==r[node]){ return a[node]; }else{ if(to<=l[node]+(r[node]-l[node])/2){ return get(from,to,lch(node)); }else if(l[node]+(r[node]-l[node])/2<=from){ return get(from,to,rch(node)); }else{ return op.apply(get(from,l[node]+(r[node]-l[node])/2,lch(node)),get(l[node]+(r[node]-l[node])/2,to,rch(node))); } } } public void set(T ob,int i){ if(i<0||n<=i){ throw new IndexOutOfBoundsException(String.valueOf(i)+"isOutFromLength "+String.valueOf(n)); } int j=m/2+i; a[j]=ob; while(true){ if(j==0){ break; } j=prt(j); a[j]=op.apply(a[lch(j)],a[rch(j)]); } } static private int prt(int node){ return (node-1)/2; } static private int lch(int node){ return 2*node+1; } static private int rch(int node){ return 2*node+2; } public String toString(){ return Arrays.toString(a); } } static boolean next_permutation(int[] per){ if(per.length<2){ return false; } int i; for(i=per.length-1;i>0;i--){ if(per[i-1]<per[i]){ break; } } if(0<i){ i--; int tmp; int j; for(j=per.length-1;j>i;j--){ if(per[j]>per[i]){ break; } } //swap(i,j) tmp=per[i]; per[i]=per[j]; per[j]=tmp; for(int k=i+1;k<(i+1+per.length)/2;k++){ //swap(k,per.length-k+i) tmp=per[k]; per[k]=per[per.length-k+i]; per[per.length-k+i]=tmp; } return true; } int tmp; for(int k=0;k<per.length;k++){ //swap(k,per.length-k-1) tmp=per[k]; per[k]=per[per.length-k-1]; per[per.length-k-1]=tmp; } return false; } static boolean next_bits(boolean[] b){ for(int i=0;i<b.length;i++){ if(b[i]){ b[i]=false; }else{ b[i]=true; return true; } } return false; } static class Scnr{ private final InputStream ins; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int buflen = 0; Scnr(){ this(System.in); } Scnr(InputStream in){ ins = in; } private boolean hasNextByte(){ if(ptr<buflen){ return true; }else{ ptr = 0; try{ buflen = ins.read(buffer); }catch(IOException e){ e.printStackTrace(); } if(buflen<=0){ return false; } } return true; } private int readByte(){ if(hasNextByte()){ return buffer[ptr++]; }else{ return -1; } } private static boolean isPrintableChar(int c){ return 33<=c&&c<=126; } public boolean hasNext(){ while(hasNextByte()&&!isPrintableChar(buffer[ptr])){ ptr++; } return hasNextByte(); } public String next(){ return nextBuilder().toString(); } public StringBuilder nextBuilder(){ if(!hasNext()){ throw new NoSuchElementException(); } StringBuilder sb = new StringBuilder(); int b = readByte(); while(isPrintableChar(b)){ sb.appendCodePoint(b); b = readByte(); } return sb; } public double nextDouble(){ return Double.parseDouble(next()); } public long nextLong(){ if(!hasNext()){ throw new NoSuchElementException(); } long n = 0; boolean minus = false; int b = readByte(); if(b=='-'){ minus=true; b=readByte(); } if(b<'0'||'9'<b){ throw new NumberFormatException(); } while(true){ if('0'<=b&&b<='9'){ n*=10; n+=b-'0'; }else if(b==-1||!isPrintableChar(b)){ return minus?-n:n; }else{ throw new NumberFormatException(); } b=readByte(); } } public int nextInt(){ long nl=nextLong(); if(nl<Integer.MIN_VALUE||Integer.MAX_VALUE<nl){ throw new NumberFormatException(); } return (int) nl; } public String[] nextA(int n){ String[] a = new String[n]; nextA(a,n); return a; } public void nextA(String[] a,int n){ nextA(a,0,n); } public void nextA(String[] a,int off,int len){ for(int i=off;i<off+len;i++){ a[i]=next(); } } public int[] nextAInt(int n){ int[] a = new int[n]; nextAInt(a,n); return a; } public void nextAInt(int[] a,int n){ nextAInt(a,0,n); } public void nextAInt(int[] a,int off,int len){ for(int i=off;i<off+len;i++){ a[i] = nextInt(); } } public long[] nextALong(int n){ long[] a = new long[n]; nextALong(a,n); return a; } public void nextALong(long[] a,int n){ nextALong(a,0,n); } public void nextALong(long[] a,int off,int len){ for(int i=off;i<off+len;i++){ a[i] = nextLong(); } } public double[] nextADouble(int n){ double[] a = new double[n]; nextADouble(a,n); return a; } public void nextADouble(double[] a,int n){ nextADouble(a,0,n); } public void nextADouble(double[] a,int off,int len){ for(int i=off;i<off+len;i++){ a[i] = nextDouble(); } } public List<Integer> nextLInt(int n){ List<Integer> l = new ArrayList<>(n); for(int i=0;i<n;i++){ l.add(sc.nextInt()); } return l; } public List<Long> nextLLong(int n){ List<Long> l = new ArrayList<>(n); for(int i=0;i<n;i++){ l.add(sc.nextLong()); } return l; } public List<Double> nextLDouble(int n){ List<Double> l = new ArrayList<>(n); for(int i=0;i<n;i++){ l.add(sc.nextDouble()); } return l; } } static Scnr sc = new Scnr(); static PrintWriter out = new PrintWriter(System.out); public static void main(String args[]){ for(int i=sc.nextInt();i>0;i--) solve(); out.flush(); } static long n; static void solve(){ n=sc.nextLong(); long l=sc.nextLong(); long r=sc.nextLong(); long len=r-l+1; long[] ku=dokoku(l); System.err.println(ku[0]+":"+ku[1]); Kubun kubun; while(len>0){ kubun=new Kubun((int)(ku[0])); kubun.setPos((int)(ku[1])); ku[1]=1; while(len>0&&kubun.hasNext()){ out.print(kubun.next()+" "); len--; } ku[0]++; } out.println(); } static long[] dokoku(long l){ long zo=2*(n-1); int res=0; while(1<l){ l-=zo; zo-=2; res++; } zo+=2; l+=zo; return new long[]{res,l}; } static class Kubun{ int ku; long pos; Kubun(int ku){ this.ku=ku; } void setPos(int pos){ this.pos=pos; } long next(){ if(ku==n){ return 1; } if((pos&1)==1){ pos++; return ku; }else{ pos++; return ku+pos/2; } } boolean hasNext(){ if(ku==n){ return true; } return pos<=(n-ku)*2; } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; long long t, n, l, r; void stampa(int x, int y) { if (r == 0) return; cout << x << " "; r--; if (x == n && y >= n) return; int succ; if (y > x) { succ = x + (y == n); } else { if (x == n) { succ = y + 1; } else { succ = x + 1; } } stampa(y, succ); } int main() { cin >> t; while (t--) { cin >> n >> l >> r; r = (r - l + 1); for (long long i = 1; i <= n; i++) { if (l > ((n - i) * 2ll)) { l -= ((n - i) * 2ll); } else { if (l % 2 == 0) stampa(i + l / 2, i + ((i + l / 2 == n))); else stampa(i, i + (l + 1) / 2); break; } } if (r > 0) cout << "1"; cout << "\n"; } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; long long n; void prnt(long long a, long long b, long long cnt) { if (cnt) printf("%d ", a); if (cnt < 2) return; printf("%d ", b); if (b != n) prnt(a, b + 1, cnt - 2); else if (a != n - 1) prnt(a + 1, a + 2, cnt - 2); else if (cnt > 2) printf("1"); } long long arth(long long st, long long en, long long n) { return n * (st + en) / 2; } long long clc(long long m) { return arth((n - 1) * 2, (n - m) * 2, m); } long long bs(long long lft) { long long l = 1, r = n - 1, m; while (l < r) { m = (l + r) / 2; long long c = clc(m); if (lft > c) l = m + 1; else r = m; } return l; } void fnd(long long lft, long long rit) { long long l1 = bs(lft); long long l2 = bs(lft + 1); if (l1 == l2) { long long nl = lft; if (l1 > 1) nl -= clc(l1 - 1); long long k = nl / 2; if (nl % 2 == 0) cout << k + l1 << " ", lft++; prnt(l1, k + l1 + 1, rit - lft + 1); } else { cout << n << " "; prnt(l2, l2 + 1, rit - lft); } } int main() { long long t; scanf("%lld", &t); while (t--) { scanf("%lld", &n); long long lft, rit; scanf("%lld%lld", &lft, &rit); long long mx = n * (n - 1) + 1; if (lft == mx) cout << 1 << endl; else if (lft + 1 == mx) { cout << n; if (rit == mx) cout << " " << 1 << endl; } else { fnd(lft, rit); cout << endl; } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; void file() {} signed main() { ios::sync_with_stdio(false), cin.tie(0), cout.tie(0); ; long long t; cin >> t; while (t--) { long long n, l, r; cin >> n >> l >> r; vector<long long> a; long long cnt = 0, flag = 0; for (long long i = 1; i <= n && cnt < r; i++) { if (cnt < l && l <= cnt + (n - i) * 2) { flag = 1; } if (flag) { for (long long j = i + 1; j <= n; j++) { a.push_back(i); cnt++; if (cnt == r) break; a.push_back(j); cnt++; if (cnt == r) break; } } else cnt += (n - i) * 2; } if (r == n * (n - 1) + 1) a.push_back(1); long long len = a.size(); for (long long i = len - (r - l + 1); i < len; i++) cout << a[i] << " "; cout << "\n"; } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; int T, n; long long l, r; int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> T; while (T > 0) { --T; cin >> n >> l >> r; long long s = 0; for (int i = 1; i <= n; ++i) { long long t = s + 1ll * 2 * (n - i); if (t < l) { s = t; continue; } if (s < l && t >= l) { if (l % 2 == 1) { int L = (l - s) / 2 + 1 + i; if (t >= r) { int R = (r - s) / 2 + i; for (int j = L; j <= R; ++j) { cout << i << " " << j << " "; } if ((r - s) % 2 == 1) cout << i << " "; s = t; break; } for (int j = L; j <= n; ++j) { cout << i << " " << j << " "; } } else { int L = (l - s) / 2 + i; cout << L << " "; if (t >= r) { int R = (r - s) / 2 + i; for (int j = L + 1; j <= R; ++j) { cout << i << " " << j << " "; } if ((r - s) % 2 == 1) cout << i << " "; s = t; break; } for (int j = L + 1; j <= n; ++j) { cout << i << " " << j << " "; } } s = t; continue; } if (t < r) { for (int j = i + 1; j <= n; ++j) { cout << i << " " << j << " "; } s = t; continue; } if (s < r && t >= r) { int R = (r - s) / 2 + i; for (int j = i + 1; j <= R; ++j) { cout << i << " " << j << " "; } if ((r - s) % 2 == 1) cout << i << " "; s = t; } } if (s < r) cout << 1; cout << '\n'; } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; long long arr[200005]; long long solve(long long x, long long n) { long long ind = lower_bound(arr + 1, arr + n, x) - arr; x -= arr[ind - 1]; if (x & 1) return ind; return x / 2 + ind; } int main() { long long t; cin >> t; while (t--) { long long n, l, r; cin >> n >> l >> r; arr[0] = 0; for (long long i = 1; i <= n; i++) { arr[i] = arr[i - 1] + (n - i) * 2; } for (long long i = l; i <= r; i++) { if (i == n * (n - 1) + 1) cout << 1 << " "; else cout << solve(i, n) << " "; } cout << endl; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; const long long N = 500005; const long long M = 1000000007; int main() { long long t; cin >> t; while (t--) { long long n, l, r; cin >> n >> l >> r; vector<long long> v; v.push_back(1); for (long long i = 1; i < n; i++) { v.push_back(2 * i); } reverse(v.begin(), v.end()); vector<long long> v1; v1.push_back(v[0]); long long sum = v[0]; for (long long i = 1; i < n; i++) { sum += v[i]; v1.push_back(sum); } vector<long long>::iterator it = lower_bound(v1.begin(), v1.end(), l); vector<long long>::iterator it1 = lower_bound(v1.begin(), v1.end(), r); long long z = it - v1.begin(); long long z1 = it1 - v1.begin(); long long num = v1[z]; long long num1 = v1[z1]; if (z == n - 1) { cout << 1; } else { long long chk = 0; long long a, b, c, d; long long w = num - l; b = n - w / 2; a = z + 1; if (z1 == n - 1) { chk = 1; } else { c = z1 + 1; long long w = num1 - r; d = n - w / 2; } if (chk == 1) { if (l % 2 == 0) { cout << b << " "; long long nu = b + 1; while (nu <= n) { cout << a << " " << nu << " "; nu++; } } else { long long nu = b; while (nu <= n) { cout << a << " " << nu << " "; nu++; } } for (long long j = a + 1; j < n; j++) { long long nu = j + 1; while (nu <= n) { cout << j << " " << nu << " "; nu++; } } cout << 1 << " "; } else if (a == c) { if (l % 2 == 0 && r % 2 == 0) { cout << b << " "; long long nu = b + 1; while (nu <= d) { cout << a << " " << nu << " "; nu++; } } else if (l % 2 == 0 && r % 2 != 0) { cout << b << " "; long long nu = b + 1; while (nu < d) { cout << a << " " << nu << " "; nu++; } cout << a << " "; } else if (l % 2 != 0 && r % 2 == 0) { long long nu = b; while (nu <= d) { cout << a << " " << nu << " "; nu++; } } else { long long nu = b; while (nu < d) { cout << a << " " << nu << " "; nu++; } cout << a << " "; } } else { if (l % 2 == 0) { cout << b << " "; long long nu = b + 1; while (nu <= n) { cout << a << " " << nu << " "; nu++; } } else { long long nu = b; while (nu <= n) { cout << a << " " << nu << " "; nu++; } } if (a + 1 < c) { for (long long j = a + 1; j < c; j++) { long long nu = j + 1; while (nu <= n) { cout << j << " " << nu << " "; nu++; } } } if (r % 2 == 0) { long long nu = c + 1; while (nu <= d) { cout << c << " " << nu << " "; nu++; } } else { long long nu = c + 1; while (nu < d) { cout << c << " " << nu << " "; nu++; } cout << c << " "; } } } cout << endl; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
def solve(): n, l, r = [int(i) for i in input().split()] seq = [] i = 1 while l <= r: while l > 2 * n - 2: if l == 3: i = 1 break l -= 2 * n - 2 r -= 2 * n - 2 n -= 1 i += 1 if l%2 == 0: seq.append(l // 2 + i) else: seq.append(i) l += 1 return " ".join(str(i) for i in seq) T = int(input()) for _ in range(T): print(solve())
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
t = int(input()) def query(i, n, x): if (x % 2 == 1): return i else: return (i + x // 2) for _ in range(t): n, l, r = map(int, input().split()) i = 1 s = 0 includeOne = False if r == n * (n - 1) + 1: includeOne = True r -= 1 if l == n * (n - 1) + 1: print(1) continue while s + 2 * (n - i) < l: s += 2 * (n - i) i += 1 newS = s allIs = [i] while newS + 2 * (n - i) < r: newS += 2 * (n - i) i += 1 allIs.append(i) allIin = 0 answer = [] i = allIs[0] for x in range(l, r + 1): r = query(i, n, x - s) if r == n: s += 2 * (n - i) i += 1 answer.append(r) if includeOne: answer.append(1) print(*answer)
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; #pragma comment(linker, "/stack:200000000") #pragma GCC optimize("Ofast") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") const int MAXN = 0; const int MAXK = 0; void solve() { long long n, l, r; cin >> n >> l >> r; long long sum = 0; for (int i = (1); i < (n); ++i) { sum += 2 * (n - i); if (sum >= l) { sum -= 2 * (n - i); long long var = i, cnt = 0; while (cnt < 2 * (n - i) && sum < r) { ++sum, ++cnt, var += !(cnt & 1); if (sum >= l) if (cnt & 1) cout << i << " "; else cout << var << " "; } if (sum != r) l = sum + 1; else break; } } if (r == n * (n - 1LL) + 1LL) cout << 1 << '\n'; else cout << '\n'; } int main() { ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); int t; cin >> t; while (t--) solve(); return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; void fun(long long start, long long end, long long l, long long r) { long long n = end - start + 1; for (long long i = max(1ll, l); i <= min(2 * (n - 1), r); i++) { if (i % 2 == 0) { cout << start + i / 2 << " "; } else { cout << start << " "; } } if (r > 2 * (n - 1) && start + 1 != end) { fun(start + 1, end, max(1ll, l - 2 * (n - 1)), r - 2 * (n - 1)); } } int main() { ios::sync_with_stdio(false); cin.tie(0); int t; cin >> t; while (t--) { long long n, l, r; cin >> n >> l >> r; bool flag = 0; if (r == n * (n - 1) + 1) { flag = 1; r--; } if (l <= r) { fun(1, n, l, r); } if (flag) { cout << 1 << " "; } cout << endl; } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; void _print(long long int t) { cerr << t; } void _print(int t) { cerr << t; } void _print(string t) { cerr << t; } void _print(char t) { cerr << t; } void _print(long double t) { cerr << t; } void _print(double t) { cerr << t; } void _print(long long unsigned t) { cerr << t; } template <class T, class V> void _print(pair<T, V> p); template <class T> void _print(vector<T> v); template <class T> void _print(set<T> v); template <class T, class V> void _print(map<T, V> v); template <class T> void _print(multiset<T> v); template <class T, class V> void _print(pair<T, V> p) { cerr << "{"; _print(p.first); cerr << ","; _print(p.second); cerr << "}"; } template <class T> void _print(vector<T> v) { cerr << "[ "; for (T i : v) { _print(i); cerr << " "; } cerr << "]"; } template <class T> void _print(set<T> v) { cerr << "[ "; for (T i : v) { _print(i); cerr << " "; } cerr << "]"; } template <class T> void _print(multiset<T> v) { cerr << "[ "; for (T i : v) { _print(i); cerr << " "; } cerr << "]"; } template <class T, class V> void _print(map<T, V> v) { cerr << "[ "; for (auto i : v) { _print(i); cerr << " "; } cerr << "]"; } template <class a> void printarr(a arr[], int n) { for (int i = 0; i < n; i++) cout << arr[i] << ' '; cout << '\n'; } template <class c> void printarr(vector<c> v) { for (auto i : v) { cout << i << ' '; } cout << '\n'; } template <class c> void printarr(set<c> s) { for (auto i : s) { cout << i << ' '; } cout << '\n'; } template <class t> t extended_gcd(t a, t b, t &x, t &y) { t x1, y1; if (b == 0) { x = 1, y = 0; return a; } t g = extended_gcd(b, a % b, x1, y1); x = y1; y = x1 - (a / b) * y1; return g; } template <class a> a powmod(a t1, a t2, a mod) { a res = 1; t1 = t1 % mod; if (t1 == 0) return 0; while (t2) { if (t2 & 1) res = (res * t1) % mod; t1 = (t1 * t1) % mod; t2 = t2 >> 1; } return res; } template <class a> a powmod(a t1, a t2) { a res = 1; if (t1 == 0) return 0; while (t2) { if (t2 & 1) res = (res * t1); t1 = (t1 * t1); t2 = t2 >> 1; } return res; } const long long int MOD = 1e9 + 7; const int N = 1e2 + 5; void run() { long long int n, l, r; cin >> n >> l >> r; long long int p = n - 1, last = 0; while (p * 2 + last < l) { last += p * 2; p--; if (p == 0) { cout << 1 << '\n'; return; } } long long int t = n - p; ; long long int tt = t + ceil((l - last) / 2.0); tt = (tt == t) ? tt + 1 : tt; ; last = ((l - last) % 2) ? t : tt; while (l <= r) { cout << last << ' '; if (last == tt) { tt++; if (tt > n) { t++; if (t == n) t = 1; tt = t + 1; } last = t; } else { last = tt; } l++; } cout << '\n'; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); ; cout << setprecision(15) << fixed; int test; cin >> test; while (test--) { run(); } cerr << "time taken : " << (float)clock() / CLOCKS_PER_SEC << " secs" << '\n'; return 0; ; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.util.*; import java.lang.*; import java.io.*; public class Main { PrintWriter out = new PrintWriter(System.out); BufferedReader in = new BufferedReader(new InputStreamReader(System.in)); StringTokenizer tok = new StringTokenizer(""); String next() throws IOException { if (!tok.hasMoreTokens()) { tok = new StringTokenizer(in.readLine()); } return tok.nextToken(); } int ni() throws IOException { return Integer.parseInt(next()); } long nl() throws IOException { return Long.parseLong(next()); } void solve() throws IOException { for (int tc=ni();tc>0;tc--) { long n=nl(),a=nl(),b=nl(); long curr=1; long p=0; for (long x=1;x<=n;x++) { long nc=curr+2*(n-x); if (nc>a) { p=x; break; } curr=nc; } if (p==0) { out.println(1); continue; } long q=p+1; while (curr<a) { curr+=2; q++; } if (curr>a) { out.print((q-1)+" "); } while (curr<b-1 && q<=n) { out.print(p+" "+q+" "); q++; curr+=2; } if (curr==b) { if (q>n) if (p+2>n) out.println(1); else out.println(p+1); else out.println(p); continue; } if (curr==b-1) { if (q>n) { if (p+2>n) out.println(n+"1"); else out.println((p+1)+" "+(p+2)); } else out.println(p+" "+q); continue; } p++; while (p<n) { q=p+1; while (curr<b-1 && q<=n) { out.print(p+" "+q+" "); q++; curr+=2; } if (curr>=b-1) break; p++; } if (p==n) { if (curr==b) out.println(n); else out.println(n+" 1"); } else { if (curr==b) { if (q>n) if (p+2>n) out.println(1); else out.println(p+1); else out.println(p); continue; } if (curr==b-1) { if (q>n) { if (p+2>n) out.println(n+"1"); else out.println((p+1)+" "+(p+2)); } else out.println(p+" "+q); } } } out.flush(); } public static void main(String[] args) throws IOException { new Main().solve(); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.math.BigDecimal; import java.math.RoundingMode; import java.util.*; import java.util.logging.Logger; public class Main { public static void main(String[] args){ PrintWriter out = new PrintWriter(System.out); InputReader sc=new InputReader(System.in); int t=sc.nextInt(); for (int i = 0; i < t; i++) { long N=sc.nextInt(); long l=sc.nextLong(); long r=sc.nextLong(); long indexl=0; for (long k = 1; k <= N; k++) { if (k==N) { if (N*(N-1)+1>=l) { indexl=(int) k; } }else { if (2*k*N-k*(k+1)>=l) { indexl=(int) k; break; } } } long indexr=0; for (long k = 1; k <= N; k++) { if (k==N) { if (N*(N-1)+1>=r) { indexr=(int) k; } }else { if (2*k*N-k*(k+1)>=r) { indexr=(int) k; break; } } } ArrayList<Integer> arrayList=new ArrayList<>(); for (int j = (int) indexl; j <= (int)indexr; j++) { if (j==N) { arrayList.add(1); } for (int j2 = 1; j+j2 <= N; j2++) { arrayList.add(j); arrayList.add(j+j2); } } int start=(int) (l-((indexl-1)*2*N-(indexl-1)*(indexl)+1)); int end=(int) (r-((indexl-1)*2*N-(indexl-1)*(indexl)+1)); for (int j = start; j <= end; j++) { out.println(arrayList.get(j)); } } out.flush(); } static class InputReader { private InputStream in; private byte[] buffer = new byte[1024]; private int curbuf; private int lenbuf; public InputReader(InputStream in) { this.in = in; this.curbuf = this.lenbuf = 0; } public boolean hasNextByte() { if (curbuf >= lenbuf) { curbuf = 0; try { lenbuf = in.read(buffer); } catch (IOException e) { throw new InputMismatchException(); } if (lenbuf <= 0) return false; } return true; } private int readByte() { if (hasNextByte()) return buffer[curbuf++]; else return -1; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private void skip() { while (hasNextByte() && isSpaceChar(buffer[curbuf])) curbuf++; } public boolean hasNext() { skip(); return hasNextByte(); } public String next() { if (!hasNext()) throw new NoSuchElementException(); StringBuilder sb = new StringBuilder(); int b = readByte(); while (!isSpaceChar(b)) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } public int nextInt() { if (!hasNext()) throw new NoSuchElementException(); int c = readByte(); while (isSpaceChar(c)) c = readByte(); boolean minus = false; if (c == '-') { minus = true; c = readByte(); } int res = 0; do { if (c < '0' || c > '9') throw new InputMismatchException(); res = res * 10 + c - '0'; c = readByte(); } while (!isSpaceChar(c)); return (minus) ? -res : res; } public long nextLong() { if (!hasNext()) throw new NoSuchElementException(); int c = readByte(); while (isSpaceChar(c)) c = readByte(); boolean minus = false; if (c == '-') { minus = true; c = readByte(); } long res = 0; do { if (c < '0' || c > '9') throw new InputMismatchException(); res = res * 10 + c - '0'; c = readByte(); } while (!isSpaceChar(c)); return (minus) ? -res : res; } public double nextDouble() { return Double.parseDouble(next()); } public int[] nextIntArray(int n) { int[] a = new int[n]; for (int i = 0; i < n; i++) a[i] = nextInt(); return a; } public long[] nextLongArray(int n) { long[] a = new long[n]; for (int i = 0; i < n; i++) a[i] = nextLong(); return a; } public char[][] nextCharMap(int n, int m) { char[][] map = new char[n][m]; for (int i = 0; i < n; i++) map[i] = next().toCharArray(); return map; } } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.PrintWriter; import java.util.Scanner; public class mineuler { public static void main(String[] args) { Scanner scan=new Scanner(System.in); PrintWriter out=new PrintWriter(System.out); int t=scan.nextInt(); for(int tt=0;tt<t;tt++) { int n=scan.nextInt(); long l=scan.nextLong()-1, r=scan.nextLong()-1; int startnum1=1; long id1=0L, ct=n-1; while(id1+ct*2<l) { id1+=ct*2; ct--; startnum1++; } int printed=0; int cur=startnum1, add=1; long dif=l-id1; while(printed<r-l+1) { if(dif<=0) { printed++; out.print(cur); out.print(" "); } if(cur==startnum1) { cur+=add; if(cur==n) { add=0; startnum1++; if(startnum1==n) startnum1=1; } } else { cur=startnum1; add++; } dif--; } out.println(); } out.close(); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.*; import java.util.*; public class Main{ static long MOD = 1000000007; static long dp[] = new long[1 << 21]; public static void main(String[] args) { MyScanner sc = new MyScanner(); out = new PrintWriter(new BufferedOutputStream(System.out)); // Start writing your solution here. ------------------------------------- long MOD = 1000000007; int t = sc.nextInt(); //int t = 1; while(t -- > 0) { boolean mod = false; long n = sc.nextInt(); long l = sc.nextLong(), r = sc.nextLong(); if(l == n * (n - 1) + 1) { out.println(1); } else { if (r == n * (n - 1) + 1) { r--; mod = true; } long[] res = solve(n, l, r); for (int i = 0; i < res.length; i++) out.print(res[i] + " "); if (mod) out.print(1); out.println(""); } //for(int ii = 0; ii <= n; ii++) System.out.println(Arrays.toString(dp[ii])); } out.close(); } private static long[] solve(long n, long l, long r) { long [] res = new long[(int)(r - l + 1)]; long sum = 0l, ind = 0l; while(sum < l) { sum += 2 * (n - ind - 1); ind++; } sum -= 2 * (n - ind); l -= sum + 1; r -= sum + 1; sum = 0; ArrayList <Long> list = new ArrayList(); for(; ind < n && sum <= r; ind++) { for(long j = ind + 1; j <= n; j++) { list.add(ind); list.add(j); } sum += 2 * (n - ind - 1); } int ll = (int) l; //System.out.println(l + " " + r + " " + sum + " " + list); for(int x = 0; x <= r - l; x++) { res[x] = list.get(x + ll); } return res; } private static int dfs(int[][] dp, int x, int st, boolean op, char[] c) { if (x >= c.length) return st == 11 ? 0 : 1; if (!op && dp[x][st] != -1) return dp[x][st]; int maxx = op ? c[x] - '0' : 9, res = 0; for(int i = 0; i <= maxx; i++) { if(st != 11 && Math.abs(st - i) >= 2) continue; if(st == 11 && i == 0) res += dfs(dp, x - 1, 11, op && (i == maxx), c); else res += dfs(dp, x - 1, i, op && (i == maxx), c); } if(!op) dp[x][st] = res; return res; } //-----------PrintWriter for faster output--------------------------------- public static PrintWriter out; //-----------MyScanner class for faster input---------- public static class MyScanner { BufferedReader br; StringTokenizer st; public MyScanner() { br = new BufferedReader(new InputStreamReader(System.in)); } String next() { while (st == null || !st.hasMoreElements()) { try { st = new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } } return st.nextToken(); } int nextInt() { return Integer.parseInt(next()); } long nextLong() { return Long.parseLong(next()); } double nextDouble() { return Double.parseDouble(next()); } String nextLine(){ String str = ""; try { str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } return str; } } //-------------------------------------------------------- }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
/* If you want to aim high, aim high Don't let that studying and grades consume you Just live life young ****************************** If I'm the sun, you're the moon Because when I go up, you go down ******************************* I'm working for the day I will surpass you https://www.a2oj.com/Ladder16.html */ import java.util.*; import java.io.*; import java.math.*; public class x1334D { public static void main(String omkar[]) throws Exception { BufferedReader infile = new BufferedReader(new InputStreamReader(System.in)); StringTokenizer st = new StringTokenizer(infile.readLine()); int T = Integer.parseInt(st.nextToken()); StringBuilder sb = new StringBuilder(); outer:while(T-->0) { st = new StringTokenizer(infile.readLine()); int N = Integer.parseInt(st.nextToken()); long L = Long.parseLong(st.nextToken()); long R = Long.parseLong(st.nextToken()); long val = 0L; for(int i=1; i < N; i++) { if(val+2*(N-i) >= L) { long startdex = val+1; R -= startdex; L -= startdex; ArrayList<Integer> ls = new ArrayList<Integer>(); ls.add(i); int next = i+1; for(int a=1; a < 2*(N-i); a++) { if(a%2 == 1) ls.add(next++); else ls.add(i); } int boof = i; while(boof+1 < N && ls.size() <= R) { ls.add(boof+1); next = boof+2; for(int a=1; a < 2*(N-boof-1); a++) { if(a%2 == 1) ls.add(next++); else ls.add(boof+1); } boof++; } if(boof+1 >= N) ls.add(1); //print for(int a = (int)L; a <= R; a++) sb.append(ls.get(a)+" "); sb.append("\n"); continue outer; } else val += 2*(N-i); } sb.append("1\n"); } System.out.print(sb); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
for t in range(int(input())): n,l,r=map(int,input().split()) b=1 for i in range(1,n): a=b b+=2*(n-i) if l<b: break x,y=i,(l-a)//2+i+1 b=(l-a)%2 for _ in range(r-l): if b: print(y,end=" ") y+=1 if y==n+1: x+=1 y=x+1 else: print(x,end=" ") b^=1 if r==n*(n-1)+1: print(1) else: print(y if b else x) #JSR
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; void print_pattern(long long row, long long col, long long count, long long elements) { if (elements == 0) { cout << 1 << " "; return; } long long x = row; long long next_x = row + 1; long long j = 0; bool flag = 1; while (j < elements && count > 0) { if (j >= col) { cout << x << " "; count--; } if (flag) { x = next_x; next_x++; } else { x = row; } flag = !flag; j++; } if (count > 0) { print_pattern(row + 1, 0, count, elements - 2); } } void solve() { long long n, l, r, count; cin >> n >> l >> r; count = r - l + 1; bool zero_flag = 0; long long i, j, row; long long to_subtract = 2 * (n - 1); row = 1; while (l - to_subtract > 0) { l -= to_subtract; to_subtract -= 2; row++; if (to_subtract == 0) { zero_flag = 1; break; } } if (zero_flag) { cout << 1 << endl; return; } if (l == 0) { row++; } else { l--; } print_pattern(row, l, count, to_subtract); cout << endl; } int main() { int t; cin >> t; while (t--) { solve(); } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
python3
#import math #from functools import lru_cache #import heapq #from collections import defaultdict #from collections import Counter #from sys import stdout #from sys import setrecursionlimit from sys import stdin input = stdin.readline for ti in range(int(input().strip())): n, l, r = [int(x) for x in input().strip().split()] cs, tc, cc = 1, 0, n - 1 ans = [] while(tc + 2*cc < l and cs<=n): tc += 2*cc cs += 1 cc -= 1 #print(tc) while(tc<=r and cs<=n): for cci in range(cs + 1, n+1): ne = cs tc += 1 if(l<=tc<=r): ans.append(ne) ne = cci tc += 1 if(l<=tc<=r): ans.append(ne) if(tc>r): break cs += 1 cc -= 1 if(tc<r): ans.append(1) print(*ans)
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.*; import java.util.*; public class D { static class FastReader { BufferedReader br; StringTokenizer st; public FastReader() { br = new BufferedReader(new InputStreamReader(System.in)); } String next() { while (st == null || !st.hasMoreElements()) { try { st = new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } } return st.nextToken(); } int nextInt() { return Integer.parseInt(next()); } long nextLong() { return Long.parseLong(next()); } double nextDouble() { return Double.parseDouble(next()); } String nextLine() { String str = ""; try { str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } return str; } } public static void main (String[] args) throws IOException{ FastReader s = new FastReader(); BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out)); int t = s.nextInt();//t: number of test cases for (int i = 0; i < t; i++) { int n = s.nextInt(); double l = s.nextDouble(); double r = s.nextDouble(); boolean islLast = l == 1.0 * n * (n-1) + 1; boolean isrLast = r == 1.0 * n * (n-1) + 1; if(!islLast){ double templ_01 = Math.ceil(((2*n-1)-Math.sqrt(4*Math.pow(n,2)-4*n+1-4*l))/2); double templ_02 = (templ_01 - 1) * (2*n - templ_01); int templ_11 = (int)(templ_01); int templ_12 = (int)((l - 1 - templ_02) / 2 + templ_11 + 1); if (isrLast) r--; boolean isrOdd = r%2==1; if (isrOdd) { r--; } double tempr_01 = Math.ceil(((2*n-1)-Math.sqrt(4*Math.pow(n,2)-4*n+1-4*r))/2); double tempr_02 = (tempr_01 - 1) * (2*n - tempr_01); int tempr_11 = (int) (tempr_01); int tempr_12 = (int)((r - 1 - tempr_02) / 2 + tempr_11 + 1); if (l%2==0) { bw.write(templ_12 + " "); templ_12++; if (templ_12 > n) { templ_11 ++; templ_12 = templ_11 + 1; } } while(templ_11 < tempr_11 || templ_11 == tempr_11 && templ_12 <= tempr_12){ bw.write(templ_11 + " "); bw.write(templ_12 + " "); templ_12++; if (templ_12 > n) { templ_11 ++; templ_12 = templ_11 + 1; } } if (isrOdd) { bw.write(templ_11 + " "); } if (isrLast) { bw.write("1"); } } else bw.write("1"); bw.write("\n"); } bw.flush(); bw.close(); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; void debug_out() { cerr << endl; } void clock_out() { cerr << "\nTime Elapsed : " << 1.0 * clock() / CLOCKS_PER_SEC << " s\n"; } void fileio() { freopen("/home/dwai/Desktop/cp/input.txt", "r", stdin); freopen("/home/dwai/Desktop/cp/output.txt", "w", stdout); freopen("/home/dwai/Desktop/cp/debug.txt", "w", stderr); } void ofileio() { freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); } template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) { cerr << " " << H; debug_out(T...); } int IT_MAX = 1 << 20; const long long MOD = 1000000007; const int INF = 0x3f3f3f3f; const long long LL_INF = 0x3f3f3f3f3f3f3f3f; const double PI = acos(-1); const double ERR = 1e-10; void solve() { long long n, l, r; cin >> n >> l >> r; long long lev = 1; long long cnt = 0; vector<long long> ans; while (cnt < r && lev < n) { long long x = (n - lev) * 2; if (cnt + x < l) { lev++; cnt += x; continue; } x = lev; while (cnt < r && x < n) { cnt++; if (cnt >= l && cnt <= r) { ans.emplace_back(lev); } cnt++; x++; if (cnt >= l && cnt <= r) { ans.emplace_back(x); } } lev++; } if (++cnt <= r) { ans.emplace_back(1); } for (long long x : ans) cout << x << " "; cout << "\n"; } int main() { 42; ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0); srand(time(NULL)); long long t = 1; cin >> t; while (t--) { solve(); } return 0; }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
java
import java.io.BufferedReader; import java.io.BufferedWriter; import java.io.FileNotFoundException; import java.io.IOException; import java.io.InputStream; import java.io.InputStreamReader; import java.io.OutputStreamWriter; import java.io.PrintWriter; import java.util.ArrayList; import java.util.Arrays; import java.util.StringTokenizer; public class Main { public static void main(String[] args) throws FileNotFoundException { InputReader in = new InputReader(System.in); PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out))); TaskB solver = new TaskB(); solver.solve(1, in, out); out.flush(); out.close(); } } class Pair { int first; int second; Pair(int first, int second) { this.first = first; this.second = second; } } class TaskB { int INF = (int) 1e9 + 7; int MAX_N = (int) 1e5 + 5; long mod = (long) 1e8; ArrayList<Integer> edges[]; ArrayList<Integer> rev_edges[]; boolean visited[]; ArrayList<Integer> topSort; int color[]; ArrayList<Integer> list; public void solve(int testNumber, InputReader in, PrintWriter pw) { int t = in.nextInt(); for (int j = 1; j <= t; j++) { int n = in.nextInt(); long l = in.nextLong(); long r = in.nextLong(); int index_l = -1; int index_r = -1; long sum1 = 0, sum2 = 0; for (int i = 1; i <= n; i++) { if (i != n) { index_l = i; if (sum1 + (2 * (n - i)) >= l) { break; } } else { index_l = i; if (sum1 + 1 >= l) { break; } } sum1 += (2 * (n - i)); } for (int i = 1; i <= n; i++) { if (i != n) { index_r = i; if (sum2 + (2 * (n - i)) >= r) { break; } } else { index_r = i; if (sum2 + 1 >= r) { break; } } sum2 += (2 * (n - i)); } // System.out.println(sum1 + " " + sum2); list = new ArrayList<Integer>(); if (index_l < index_r) { prepareList((int) (l - sum1), index_l == n ? 1 : 2 * (n - index_l), index_l, n); // System.out.println(list); for (int i = index_l + 1; i < index_r; i++) { prepareList(1, 2 * (n - i), i, n); } prepareList(1, (int) (r - sum2), index_r, n); // System.out.println(list); } else { prepareList((int) (l - sum1), (int) (r - sum2), index_l, n); } // System.out.println(list); for (int x : list) { pw.print(x + " "); } pw.println(); } } void prepareList(int l, int r, int id, int n) { for (int i = l; i <= r; i++) { if (i % 2 != 0) { if (id == n) { list.add(1); } else { list.add(id); } } else { int temp = i / 2; list.add(id + temp); } } } long gcd(long a, long b) { if (b == 0) { return a; } else { return gcd(b, a % b); } } int[] shrink(int a[]) { int n = a.length; long b[] = new long[n]; for (int i = 0; i < n; i++) { b[i] = ((long) (a[i] << 32)) | i; } Arrays.sort(b); int ret[] = new int[n]; int p = 0; for (int i = 0; i < n; i++) { if (i > 0 && (b[i] ^ b[i - 1]) >> 32 != 0) { p++; } ret[(int) b[i]] = p; } return ret; } int sum(int ft[], int i) { int sum = 0; for (int j = i; j >= 1; j -= (j & -j)) { sum += ft[j]; // System.out.println(sum); } return sum; } void add(int ft[], int i, int x) { for (int j = i; j < ft.length; j += (j & -j)) { // System.out.println(j); ft[j] += x; } } boolean isValid(int i, int j, char arr[][]) { if (i >= arr[0].length || j >= arr[0].length) { return false; } if (arr[i][j] == '*') { return false; } return true; } long pow(long m, long k) { long prod = 1; for (int i = 0; i < k; i++) { prod = (prod * m) % INF; } return prod % INF; } // int sum(int k) { // int sum=0; // for(int i=k;i>=1;i) { // sum+=ft[k]; // } // } long fib(int N) { long fib[] = new long[N + 1]; fib[0] = 1; fib[1] = 1; for (int i = 2; i <= N; i++) { fib[i] = (fib[i - 1] + fib[i - 2]) % mod; } return fib[N] % mod; } long sum(int i, int j, long arr[]) { long sum = 0; for (int k = i; k <= j; k++) { sum += arr[k]; } return sum; } boolean FirstRow_Col(Pair pair) { return pair.first == 0 || pair.second == 0; } int __gcd(int a, int b) { if (b == 0) return a; return __gcd(b, a % b); } public int getInt(int num) { int ret = -1; switch (num) { case 0: ret = 6; break; case 1: ret = 2; break; case 2: ret = 5; break; case 3: ret = 5; break; case 4: ret = 4; break; case 5: ret = 5; break; case 6: ret = 6; break; case 7: ret = 3; break; case 8: ret = 7; break; case 9: ret = 6; break; } return ret; } public int isPow(long num) { int count = 0; while (num > 0) { num /= 2; count++; } return count; } } class InputReader { BufferedReader br; StringTokenizer st; public InputReader(InputStream in) { br = new BufferedReader(new InputStreamReader(in)); st = null; } public String next() { while (st == null || !st.hasMoreTokens()) { try { st = new StringTokenizer(br.readLine()); } catch (IOException e) { throw new RuntimeException(e); } } return st.nextToken(); } public int nextInt() { return Integer.parseInt(next()); } public long nextLong() { return Long.parseLong(next()); } public double nextDouble() { return Double.parseDouble(next()); } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; long long z = 998244353; long long gcd(long long a, long long b) { if (a == 0) return b; if (b == 0) return a; return gcd(b, a % b); } long long power(long long a, long long b) { long long res = 1; while (b) { if (b & 1) { res = (res * a) % z; b--; } else { a = (a * a) % z; b = b >> 1; } } return res; } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); long long t; t = 1; cin >> t; while (t--) { long long n, l, r; cin >> n >> l >> r; long long s = 1, i = 1; long long len = r - l + 1; while (i < n) { if (l - 2 * (n - i) >= 0) { l -= 2 * (n - i); i++; s++; } else { break; } } vector<long long> v; len += l; long long p = 0; v.push_back(n); for (long long i = s; i <= n; i++) { for (long long j = i + 1; j <= n; j++) { v.push_back(i); p++; if (p == len) break; v.push_back(j); p++; if (p == len) break; } if (p == len) break; } v.push_back(1); for (long long i = l; i < len; i++) cout << v[i] << " "; cout << "\n"; } }
1334_D. Minimum Euler Cycle
You are given a complete directed graph K_n with n vertices: each pair of vertices u β‰  v in K_n have both directed edges (u, v) and (v, u); there are no self-loops. You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 β€” a visiting order, where each (v_i, v_{i + 1}) occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r. Input The first line contains the single integer T (1 ≀ T ≀ 100) β€” the number of test cases. Next T lines contain test cases β€” one per line. The first and only line of each test case contains three integers n, l and r (2 ≀ n ≀ 10^5, 1 ≀ l ≀ r ≀ n(n - 1) + 1, r - l + 1 ≀ 10^5) β€” the number of vertices in K_n, and segment of the cycle to print. It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5. Output For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once. Example Input 3 2 1 3 3 3 6 99995 9998900031 9998900031 Output 1 2 1 1 3 2 3 1 Note In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1. In the third test case, it's quite obvious that the cycle should start and end in vertex 1.
{ "input": [ "3\n2 1 3\n3 3 6\n99995 9998900031 9998900031\n" ], "output": [ "1 2 1 \n1 3 2 3 \n1 \n" ] }
{ "input": [ "1\n2 2 3\n", "1\n4 13 13\n", "1\n3 1 1\n", "10\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n2 1 3\n", "1\n3 7 7\n", "1\n25 30 295\n", "1\n4 12 13\n", "5\n3 7 7\n4 13 13\n5 21 21\n6 31 31\n7 42 43\n", "1\n5 4 4\n" ], "output": [ "2 1 \n", "1 \n", "1 \n", "1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n1 2 1 \n", "1 \n", "16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 5 23 5 24 5 25 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 8 \n", "4 1 \n", "1 \n1 \n1 \n1 \n7 1 \n", "3 \n" ] }
CORRECT
cpp
#include <bits/stdc++.h> using namespace std; const long long INF = (long long)2e9; const long long inf = (long long)2e18; const long double eps = (long double)1e-8; const long long mod = (long long)1e9 + 7; const long long MAXN = (long long)1e5 + 1; const long long MAXC = (long long)1e6 + 1; const long long MAXE = (long long)1000; const long long MAXLOG = 21; const long long maxlen = (long long)1e5; const long long asci = (long long)256; const long long block = 480; const long double PI = acos(-1); const long double e = 2.7182818284; template <class T> istream &operator>>(istream &in, vector<T> &arr) { for (T &cnt : arr) { in >> cnt; } return in; }; void solve() { long long n, l, r; cin >> n >> l >> r; l--, r--; vector<long long> a; long long i = 0; for (; i < n - 1; ++i) { if (l >= 2 * (n - i - 1)) l -= 2 * (n - i - 1), r -= 2 * (n - i - 1); else break; } while (a.size() <= r && i < n) { for (long long j = i + 1; j < n; ++j) { a.push_back(i); a.push_back(j); } ++i; } if (i == n) a.push_back(0); for (; l <= r; ++l) { cout << a[l] + 1 << " "; } cout << "\n"; } int main() { srand(time(0)); ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); cout.precision(30); long long t; cin >> t; while (t--) solve(); return 0; }