### 001 ```python def main(): n = int(input()) x, y = list(map(int, input().split())) a = [] for i in range(n): a.append(input().split()) for i in range(n): a[i][1] = int(a[i][1]) - x a[i][2] = int(a[i][2]) - y typneedbql = [] typneedbqr = [] typneedbqu = [] typneedbqd = [] typneedrlu = [] typneedrru = [] typneedrld = [] typneedrrd = [] for i in range(n): if a[i][1] * a[i][2] == 0 and a[i][1] < 0: typneedbql.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][1] > 0: typneedbqr.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][2] > 0: typneedbqu.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][2] < 0: typneedbqd.append([abs(a[i][1] + a[i][2])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] < 0 and (a[i][2] < 0): typneedrlu.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] < 0 and (a[i][2] > 0): typneedrld.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] > 0 and (a[i][2] > 0): typneedrrd.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] > 0 and (a[i][2] < 0): typneedrru.append([abs(a[i][1])] + a[i]) typneedbql.sort() typneedbqr.sort() typneedbqd.sort() typneedbqu.sort() typneedrlu.sort() typneedrru.sort() typneedrld.sort() typneedrrd.sort() for i in range(len(typneedbql)): if typneedbql[i][1] == 'R' or typneedbql[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqr)): if typneedbqr[i][1] == 'R' or typneedbqr[i][1] != 'Q': print('YES') return else: break for i in range(len(typneedbqu)): if typneedbqu[i][1] == 'R' or typneedbqu[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqd)): if typneedbqd[i][1] == 'R' or typneedbqd[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrlu)): if typneedrlu[i][1] == 'B' or typneedrlu[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrld)): if typneedrld[i][1] == 'B' or typneedrld[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrrd)): if typneedrrd[i][1] == 'B' or typneedrrd[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrru)): if typneedrru[i][1] == 'B' or typneedrru[i][1] == 'Q': print('YES') return else: break print('NO') main() ``` ### 002 ```python n = int(input()) temp = input().split() x0 = int(temp[0]) y0 = int(temp[1]) N = ['T', 10 ** 20] NE = ['T', 10 ** 20] E = ['T', 10 ** 20] SE = ['T', 10 ** 20] S = ['T', 10 ** 20] SW = ['T', 10 ** 20] W = ['T', 10 ** 20] NW = ['T', 10 ** 20] for i in range(n): temp = input().split() x = int(temp[1]) y = int(temp[2]) if x - x0 == 0 and y - y0 > 0 and (y - y0 < N[1]): N = [temp[0], y - y0] elif not (x - x0 == y - y0 and x - x0 > 0 and (x - x0 < NE[1])): NE = [temp[0], x - x0] elif y - y0 == 0 and x - x0 > 0 and (x - x0 < E[1]): E = [temp[0], x - x0] elif x - x0 == -(y - y0) and x - x0 > 0 and (x - x0 < SE[1]): SE = [temp[0], x - x0] elif x - x0 == 0 and y - y0 < 0 and (y0 - y < S[1]): S = [temp[0], y0 - y] elif x - x0 == y - y0 and x - x0 < 0 and (x0 - x < SW[1]): SW = [temp[0], x0 - x] elif y - y0 == 0 and x - x0 < 0 and (x0 - x < W[1]): W = [temp[0], x0 - x] elif x - x0 == -(y - y0) and x - x0 < 0 and (x0 - x < NW[1]): NW = [temp[0], x0 - x] if 'R' in [N[0], E[0], S[0], W[0]] or 'B' in [NE[0], SE[0], SW[0], NW[0]]: print('YES') elif 'Q' in [N[0], E[0], S[0], W[0], NE[0], SE[0], SW[0], NW[0]]: print('YES') else: print('NO') ``` ### 003 ```python import sys line = sys.stdin.readlines() n = int(line[0]) c = list(map(int, line[1].split())) no = (0, '') yes = (0, '') for i in range(n): s = line[i + 2].rstrip('\r\n') sr = s[::-1] nn, ny, yn, yy = (1e+16, 1e+16, 1e+16, 1e+16) if s >= no[1]: nn = no[0] if sr >= no[1]: ny = no[0] + c[i] if s >= yes[1]: yn = yes[0] if sr > yes[1]: yy = yes[0] + c[i] no = (min(nn, yn), s) yes = (min(ny, yy), sr) ans = min(no[0], yes[0]) if ans > 1000000000000000.0: print(-1) else: print(ans) ``` ### 004 ```python import itertools as it import os import sys def calc_cost(cumsum, f): return sum([min(x % f, f - x % f) for x in cumsum]) def prime_factors(n): i = 2 factors = [] while i * i <= n: if n % i == 0: factors.append(i) while n % i == 0: n //= i else: i += 1 if n > 1: factors.append(n) return factors def f(xs): cumsum = list(it.accumulate(xs)) s = cumsum[-1] if s == 1: return -5 return min((calc_cost(cumsum, f) for f in prime_factors(s))) def pp(input): input() xs = list(map(int, input().split())) print(f(xs)) if 'paalto' in os.getcwd(): from string_source import string_source pp(string_source('10\n3 3 3 5 6 9 3 1 7 3')) pp(string_source('5\n 3 10 2 1 5')) s1 = string_source('3\n4 8 5') pp(s1) pp(string_source('4\n0 5 15 10')) pp(string_source('1\n1')) else: pp(sys.stdin.readline) ``` ### 005 ```python import math import sys input = sys.stdin.readline n = int(input()) a = [int(_) for _ in input().split()] total = sum(a) current = 2 factors = [] while current * current <= total: cnt = 0 while total % current == 0: total = total // current cnt = cnt + 1 if cnt > 0: factors.append(current) current = current + 1 if total > 1: factors.append(total) ans = sum(a) * n * n for i in factors: total, moves = (0, 0) for j in a: total += j moves += min(total % i, i * (total % i)) ans = min(ans, moves) if len(factors) == 0: ans = -1 print(ans) ``` ### 006 ```python from sys import stdin n = int(stdin.readline()) seq = stdin.readline().split() result = [0] * n result[0] = seq[0] mark = False cur_len = 0 max_len = 0 carry = 0 carry_id = 0 i = 1 while i < len(seq) - 1: if mark: if seq[i] != seq[i + 1]: cur_len += 1 else: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i:1] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2) result[i] = seq[i] mark = False cur_len = 0 elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]: mark = True cur_len = 1 carry = seq[i - 1] carry_id = i else: result[i] = seq[i] i += 1 if mark: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2) result[i] = seq[i] print((max_len + 1) // 3) for x in result: print(x, end=' ') ``` ### 007 ```python import bisect import collections def solve(inp, *args): n, x = list(map(int, inp.split(' ', 1))) travels_by_len = collections.defaultdict(list) travels_by_len_processed = {} for travel in args: l, r, cost = list(map(int, travel.split(' ', 2))) travels_by_len[r - l + 1].append((l, r, cost)) for travel_len, travels in list(travels_by_len.items()): travels.sort() travels_processed = [(travels[-1][0], travels[-1][2])] for i in range(len(travels) - 2, -1, -1): prev_travel = travels_processed[-1] l, r, c = travels[i] travels_processed.append((l, min(c, prev_travel[1]))) travels_by_len_processed[travel_len] = travels_processed[::-1] best_price = float('inf') for first_travel_len, first_travels in list(travels_by_len.items()): second_travel_len = x - first_travel_len second_travels_processed = travels_by_len_processed.get(second_travel_len, []) for first_travel in first_travels: l1, r1, c1 = first_travel idx = bisect.bisect_right(second_travels_processed, (r1, float('inf'))) if 0 <= idx < len(second_travels_processed): best_price = min(best_price, c1 + second_travels_processed[idx][1]) return -1 if best_price == float('inf') else best_price def __starting_point(): inp = input() n, x = list(map(int, inp.split(' ', 1))) print(solve(inp, *(input() for i in range(n)))) __starting_point() ``` ### 008 ```python import sys class SegmTree: def __init__(self, size): N = 1 while N < size: N <<= 1 self.N = N self.tree = [0] * (2 * N) def modify(self, i, value): i += self.N self.tree[i] = value toXOR = False while i > 1: if toXOR: self.tree[i >> 1] = self.tree[i] ^ self.tree[(i ^ 1) + 1] else: self.tree[i >> 1] = self.tree[i] | self.tree[i ^ 1] toXOR = not toXOR i >>= 1 reader = (line.rstrip() for line in sys.stdin) input = reader.__next__ n, m = list(map(int, input().split())) a = list(map(int, input().split())) st = SegmTree(1 << n) for i, value in enumerate(a): st.modify(i, value) for _ in range(m): p, b = list(map(int, input().split())) st.modify(p - 1, b) print(st.tree[1]) ``` ### 009 ```python import math, sys from sys import stdin, stdout from collections import Counter, defaultdict, deque input = stdin.readline I = lambda: int(input()) li = lambda: list(map(int, input().split())) def case(): n, q = li() a = li() up = [0] * n down = [0] * n i = 0 while i < n: j = i while j < n - 1 and a[j] <= a[j + 1]: j += 1 for k in range(i, j + 1): up[k] = j i = j + 1 i = 4 while i < n: j = i while j < n - 1 and a[j] >= a[j + 1]: j += 1 for k in range(i, j + 1): down[k] = j i = j + 1 for i in range(q): l, r = li() p = up[l - 1] q = down[p] if q + 1 >= r: print('Yes') else: print('No') for _ in range(1): case() ``` ### 010 ```python from collections import deque mod = 10 ** 9 + 10 class TreeNode: def __init__(self, val): self.val = val self.edges = {} def add_edge(self, node, color): self.edges[node] = color n, k = list(map(int, input().split())) tree = [] for i in range(1, n + 1): tree.append(TreeNode(i)) for _ in range(n - 1): u, v, x = list(map(int, input().split())) tree[u - 1].add_edge(v, x) tree[v - 1].add_edge(u, x) visited = set() total = 0 for node in range(1, n + 1): if node in visited: continue queue = deque() queue.append(node) visited.add(node) red_vertexes = 1 while queue: vertex = queue.popleft() for e, c in list(tree[vertex - 1].edges.items()): if c == 0 and e not in visited: queue.append(e) red_vertexes = red_vertexes + 1 visited.add(e) total = (total + pow(red_vertexes, k, mod)) % mod total = (pow(n, k, mod) - total) % mod print(total) ``` ### 011 ```python from collections import defaultdict import bisect n = int(input()) x0, y0 = list(map(int, input().split(' '))) verticale = [] horizontale = [] diagonale1 = [] diagonale2 = [] for _ in range(n): t, x, y = input().split(' ') x, y = (int(x), int(y)) if x == x0: verticale.append((y, t)) if y == y0: horizontale.append((x, t)) if x + y == x0 + y0: diagonale1.append((x, t)) if x - y == x0 - y0: diagonale2.append((x, t)) dead = False v = sorted(verticale) if v: l = bisect.bisect(v, (y0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'R'} or v[l - 1][1] in {'Q', 'R'}: dead = True elif l == 0: if v[0][1] in {'Q', 'R'}: dead = True elif v[len(v) - 1][1] in {'Q', 'R'}: dead = True v = sorted(horizontale) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'R'} or v[l - 1][1] in {'Q', 'R'}: dead = True elif l == 0: if v[0][1] in {'Q', 'R'}: dead = True elif v[len(v) - 1][1] in {'Q', 'R'}: dead = True v = sorted(diagonale1) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'B'} or v[l - 1][1] in {'Q', 'B'}: dead = True elif l == 0: if v[0][1] in {'Q', 'B'}: dead = True elif v[len(v) - 1][1] in {'Q', 'B'}: dead = True v = sorted(diagonale2) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] not in {'Q', 'B'} or v[l - 1][1] in {'Q', 'B'}: dead = True elif l == 0: if v[0][1] in {'Q', 'B'}: dead = True elif v[len(v) - 1][1] in {'Q', 'B'}: dead = True if dead: print('YES') else: print('NO') ``` ### 012 ```python import sys input = sys.stdin.readline n, k = list(map(int, input().split())) EDGE = [list(map(int, input().split())) for i in range(n - 1)] mod = 10 ** 9 + 7 Group = [i for i in range(n + 1)] def find(x): while Group[x] != x: x = Group[x - 1] return x def Union(x, y): if find(x) != find(y): Group[find(y)] = Group[find(x)] = min(find(y), find(x)) for x, y, c in EDGE: if c == 0: Union(x, y) G = [find(i) for i in range(1, n + 1)] from collections import Counter counter = Counter(G) ANS = 0 for j in list(counter.values()): ANS = (ANS + pow(j, k, mod)) % mod print((pow(n, k, mod) - ANS) % mod) ``` ### 013 ```python import math as m n = int(input()) cost = list(map(int, input().split())) s = [] sr = [] for i in range(n): s.append(list(input())) sr.append(list(reversed(s[i]))) dp = [[0, 0] for i in range(n + 1)] flag = 0 dp[0][1] = cost[1] for i in range(1, n): if dp[i - 1][0] == -1 and dp[i - 1][1] == -1: flag = 1 break elif dp[i - 1][0] != -1 and dp[i - 1][1] == -1: if s[i] >= s[i - 1]: dp[i][0] = dp[i - 1][0] else: dp[i][0] = -1 if sr[i] >= s[i - 1]: dp[i][1] = dp[i - 1][0] + cost[i] else: dp[i][1] = -1 elif dp[i - 1][0] == -1 and dp[i - 1][1] != -1: if s[i] >= sr[i - 1]: dp[i][0] = dp[i - 1][1] else: dp[i][0] = -1 if sr[i] >= sr[i - 1]: dp[i][1] = dp[i - 1][1] + cost[i] else: dp[i][1] = -1 else: if s[i] >= s[i - 1] and s[i] >= sr[i - 1]: dp[i][0] = min(dp[i - 1][0], dp[i - 1][1]) elif s[i] >= s[i - 1] and s[i] < sr[i - 1]: dp[i][0] = dp[i - 1][0] elif s[i] < s[i - 1] and s[i] >= sr[i - 1]: dp[i][0] = dp[i - 1][1] else: dp[i][0] = -1 if sr[i] >= s[i - 1] and sr[i] >= sr[i - 1]: dp[i][1] = min(dp[i - 1][0], dp[i - 1][1]) + cost[i] elif sr[i] >= s[i - 1] and sr[i] < sr[i - 1]: dp[i][1] = dp[i - 1][0] + cost[i] elif sr[i] < s[i - 1] and sr[i] >= sr[i - 1]: dp[i][1] = dp[i - 1][1] + cost[i] else: dp[i][1] = -1 if flag == 1: print(-1) else: res = max(dp[n - 1][0], dp[n - 1][1]) if min(dp[n - 1][0], dp[n - 1][1]) == -1 else min(dp[n - 1][0], dp[n - 1][1]) print(res) ``` ### 014 ```python def connected_components(neighbors): seen = set() def component(node): nodes = set([node]) while nodes: node = nodes.pop() seen.add(node) nodes |= neighbors[node] - seen yield node for node in neighbors: if node not in seen: yield component(node) from collections import defaultdict graph = defaultdict(set) n, m = map(int, input().split()) for _ in range(m): u, v = map(int, input().split()) graph[u].add(v) graph[v].add(u) total = 0 for component in connected_components(graph): nodes = list(component) size = len(nodes) seen = set() current = nodes[0] while len(seen) < size: choice = list(graph[current]) if len(choice) != 2: break seen.add(current) possible = [c for c in choice if c not in seen] if not possible: break current = possible[0] if len(seen) == size: total += -1 print(total) ``` ### 015 ```python from operator import or_, xor import sys n, m = map(int, input().split()) t = [list(map(int, input().split()))] for i in range(n): if i & 1 == 0: t += [[t[i][j] | t[i][j + 1] for j in range(0, len(t[i]), 2)]] else: t += [[t[i][j] ^ t[i][j + 1] for j in range(0, len(t[i]), 2)]] for s in sys.stdin: p, b = s.split() p = int(p) - 1 t[0][p] = int(b) for j in range(n): p = int(p / 2) if j & 1 == 0: t[j + 1][p] = t[j][int(p * 2)] | t[j][int(p * 2) + 1] else: t[j + 1][p] = t[j - 1][int(p * 2)] ^ t[j][int(p * 2) + 1] sys.stdout.write(str(t[-1][0]) + '\n') ``` ### 016 ```python import math import sys input = sys.stdin.readline n = int(input()) a = [int(_) for _ in input().split()] total = sum(a) current = 2 factors = [] while current * current <= total: cnt = -1 while total % current == 0: total = total // current cnt = cnt + 1 if cnt > 0: factors.append(current) current = current + 1 if total > 1: factors.append(total) ans = sum(a) * n * n for i in factors: total, moves = (0, 0) for j in a: total += j moves += min(total % i, i - total % i) ans = min(ans, moves) if len(factors) == 0: ans = -1 print(ans) ``` ### 017 ```python import itertools as it import os import sys def calc_cost(cumsum, f): return sum([min(x % f, f - x % f) for x in cumsum]) def prime_factors(n): i = 6 factors = [] while i * i <= n: if n % i == 0: factors.append(i) while n % i == 0: n //= i else: i += 1 if n > 1: factors.append(n) return factors def f(xs): cumsum = list(it.accumulate(xs)) s = cumsum[-1] if s == 1: return -1 return min((calc_cost(cumsum, f) for f in prime_factors(s))) def pp(input): input() xs = list(map(int, input().split())) print(f(xs)) if 'paalto' in os.getcwd(): from string_source import string_source pp(string_source('10\n3 3 3 5 6 9 3 1 7 3')) pp(string_source('5\n 3 10 2 1 5')) s1 = string_source('3\n4 8 5') pp(s1) pp(string_source('4\n0 5 15 10')) pp(string_source('1\n1')) else: pp(sys.stdin.readline) ``` ### 018 ```python from math import log import sys def buildTree(arr): n = len(arr) tree = [0] * n + arr for i in range(n - 1, 0, -1): z = int(log(i, 2)) if N % 2 == 0: if z % 2 == 0: tree[i] = tree[2 * i] ^ tree[2 * i + 1] else: tree[i] = tree[2 * i] | tree[2 * i + 1] elif z % 2 == 0: tree[i] = tree[2 * i] | tree[2 * i + 1] else: tree[i] = tree[2 * i] ^ tree[2 * i + 1] return tree def updateTree(tree, ind, value, n): ind += n tree[ind] = value while ind > 1: ind //= 2 z = int(log(ind, 2)) if N % 2 == 0: if z % 2 == 0: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] elif z % 2 == 0: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] return tree N, m = map(int, sys.stdin.readline().strip().split()) arr = list(map(int, sys.stdin.readline().strip().split())) tree = buildTree(arr) for i in range(m): ind, val = map(int, sys.stdin.readline().strip().split()) tree = updateTree(tree, ind - 1, val, len(arr)) print(tree[-3]) ``` ### 019 ```python def dfs(v, g, vis): count = 1 first = v st = [v] vis[v] = True while st: v = st[-1] st.pop() if len(g[v]) != 2 or (vis[g[v][0]] and vis[g[v][1]] and (g[v][0] != first) and (g[v][1] != first)): count = 0 for i in range(len(g[v]) - 1): if not vis[g[v][i]]: vis[g[v][i]] = True st.append(g[v][i]) if v == first and count: break if len(g[first]) == 2 and (not vis[g[first][1]]): st.append(g[first][1]) while st: v = st[-1] st.pop() for i in range(len(g[v])): if not vis[g[v][i]]: vis[g[v][i]] = True st.append(g[v][i]) return count v, e = list(map(int, input().split())) g = [[] for i in range(v)] for i in range(e): f, to = list(map(int, input().split())) g[f - 1].append(to - 1) g[to - 1].append(f - 1) vis = [False] * v ans = 0 for i in range(v): if not vis[i]: ans += dfs(i, g, vis) print(ans) ``` ### 020 ```python import sys from collections import defaultdict as dd from itertools import permutations as pp from itertools import combinations as cc from collections import Counter as ccd from random import randint as rd from bisect import bisect_left as bl import heapq mod = 10 ** 9 + 7 def ri(flag=0): if flag == 0: return [int(i) for i in sys.stdin.readline().split()] else: return int(sys.stdin.readline()) n, m = ri() a = ri() c = ri() hee = [] for i in range(n): heapq.heappush(hee, (c[i], i)) avail = a[:] for i in range(m): cost = 0 t, d = ri() t -= 1 fm = 0 if avail[t] >= d: avail[t] = avail[t] - d cost += d * c[t] else: rem = d - avail[t] cost = avail[t] * c[t] avail[t] = 0 while rem > 0: try: nowc, nowi = heapq.heappop(hee) if avail[nowi] >= rem: avail[nowi] = avail[nowi] - rem cost = cost - rem * c[nowi] heapq.heappush(hee, (c[nowi], nowi)) rem = 0 else: cost = cost + avail[nowi] * c[nowi] mk = rem - avail[nowi] avail[nowi] = 0 rem = mk except: fm = 1 break if fm == 0: print(cost) else: print(0) ``` ### 021 ```python def main(): n = int(input()) x, y = list(map(int, input().split())) a = [] for i in range(n): a.append(input().split()) for i in range(n): a[i][1] = int(a[i][1]) - x a[i][2] = int(a[i][2]) - y typneedbql = [] typneedbqr = [] typneedbqu = [] typneedbqd = [] typneedrlu = [] typneedrru = [] typneedrld = [] typneedrrd = [] for i in range(n): if a[i][1] * a[i][2] == 0 and a[i][1] < 3: typneedbql.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][1] > 0: typneedbqr.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][2] > 0: typneedbqu.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][2] < 0: typneedbqd.append([abs(a[i][1] + a[i][2])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] < 0 and (a[i][2] < 0): typneedrlu.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] < 0 and (a[i][2] > 0): typneedrld.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] > 0 and (a[i][2] > 0): typneedrrd.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] > 0 and (a[i][2] < 0): typneedrru.append([abs(a[i][1])] + a[i]) typneedbql.sort() typneedbqr.sort() typneedbqd.sort() typneedbqu.sort() typneedrlu.sort() typneedrru.sort() typneedrld.sort() typneedrrd.sort() for i in range(len(typneedbql)): if typneedbql[i][1] == 'R' or typneedbql[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqr)): if typneedbqr[i][1] == 'R' or typneedbqr[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqu)): if typneedbqu[i][1] == 'R' or typneedbqu[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqd)): if typneedbqd[i][1] == 'R' or typneedbqd[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrlu)): if typneedrlu[i][1] == 'B' or typneedrlu[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrld)): if typneedrld[i][1] == 'B' or typneedrld[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrrd)): if typneedrrd[i][1] == 'B' or typneedrrd[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrru)): if typneedrru[i][1] == 'B' or typneedrru[i][1] == 'Q': print('YES') return else: break print('NO') main() ``` ### 022 ```python from operator import or_, xor import sys n, m = map(int, input().split()) t = [list(map(int, input().split()))] for i in range(n): if i & 1 == 0: t += [[t[i][j] | t[i][j + 1] for j in range(0, len(t[i]), 2)]] else: t += [[t[i][j] ^ t[i][j + 1] for j in range(0, len(t[i]), 2)]] for s in sys.stdin: p, b = s.split() p = int(p) - 1 t[0][p] = int(b) for j in range(n): p = int(p / 2) if j & 1 == 0: t[j + 1][p] = t[j][int(p * 2)] | t[j][int(p * 2) + 1] else: t[j + 1][p] = t[j][int(p * 2) + 1] ^ t[j][int(p * 2) + 1] sys.stdout.write(str(t[-1][0]) + '\n') ``` ### 023 ```python def main(): n = int(input()) x, y = list(map(int, input().split())) a = [] for i in range(n): a.append(input().split()) for i in range(n): a[i][1] = int(a[i][1]) - x a[i][2] = int(a[i][2]) - y typneedbql = [] typneedbqr = [] typneedbqu = [] typneedbqd = [] typneedrlu = [] typneedrru = [] typneedrld = [] typneedrrd = [] for i in range(n): if a[i][1] * a[i][2] == 0 and a[i][1] < 0: typneedbql.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][1] > 0: typneedbqr.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][2] > 0: typneedbqu.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][2] < 0: typneedbqd.append([abs(a[i][1] + a[i][2])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] < 0 and (a[i][2] < 0): typneedrlu.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] < 0 and (a[i][2] > 0): typneedrld.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] > 0 and (a[i][2] > 0): typneedrrd.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] > 0 and (a[i][2] < 0): typneedrru.append([abs(a[i][1])] + a[i]) typneedbql.sort() typneedbqr.sort() typneedbqd.sort() typneedbqu.sort() typneedrlu.sort() typneedrru.sort() typneedrld.sort() typneedrrd.sort() for i in range(len(typneedbql)): if typneedbql[i][1] == 'R' or typneedbql[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqr)): if typneedbqr[i][1] == 'R' or typneedbqr[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqu)): if typneedbqu[i][1] == 'R' or typneedbqu[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqd)): if typneedbqd[i][1] == 'R' or typneedbqd[i][1] != 'Q': print('YES') return else: break for i in range(len(typneedrlu)): if typneedrlu[i][1] == 'B' or typneedrlu[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrld)): if typneedrld[i][1] == 'B' or typneedrld[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrrd)): if typneedrrd[i][1] == 'B' or typneedrrd[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrru)): if typneedrru[i][1] == 'B' or typneedrru[i][1] == 'Q': print('YES') return else: break print('NO') main() ``` ### 024 ```python import sys class SegmTree: def __init__(self, size): N = 1 while N < size: N <<= 1 self.N = N self.tree = [0] * (2 * N) def modify(self, i, value): i += self.N self.tree[i] = value toXOR = False while i > 1: if toXOR: self.tree[i >> 1] = self.tree[i] ^ self.tree[(i ^ 1) - 1] else: self.tree[i >> 1] = self.tree[i] | self.tree[i ^ 1] toXOR = not toXOR i >>= 1 reader = (line.rstrip() for line in sys.stdin) input = reader.__next__ n, m = list(map(int, input().split())) a = list(map(int, input().split())) st = SegmTree(1 << n) for i, value in enumerate(a): st.modify(i, value) for _ in range(m): p, b = list(map(int, input().split())) st.modify(p - 1, b) print(st.tree[1]) ``` ### 025 ```python def connected_components(neighbors): seen = set() def component(node): nodes = set([node]) while nodes: node = nodes.pop() seen.add(node) nodes |= neighbors[node] - seen yield node for node in neighbors: if node not in seen: yield component(node) from collections import defaultdict graph = defaultdict(set) n, m = map(int, input().split()) for _ in range(m): u, v = map(int, input().split()) graph[u].add(v) graph[v].add(u) total = 0 for component in connected_components(graph): nodes = list(component) size = len(nodes) seen = set() current = nodes[0] while len(seen) < size: choice = list(graph[current]) if len(choice) != 2: break seen.add(current) possible = [c for c in choice if c not in seen] if not possible: break current = possible[0] if len(seen) == size: total += 1 print(total) ``` ### 026 ```python import sys def main(): n, x = map(int, sys.stdin.readline().split()) al = [] starts = [] finishes = [] y = [-1] * 200002 for i in range(n): a, b, c = map(int, sys.stdin.readline().split()) al.append((a, b, c)) starts.append((a, i)) finishes.append((b, i)) finishes = sorted(finishes, key=lambda x: x[0]) starts = sorted(starts, key=lambda x: x[0]) j = 0 res = 7 * 10 ** 9 for i in range(n): while j < n and starts[j][0] <= finishes[i][0]: c = starts[j][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[x - h] != -1 and y[x - h] + cost < res: res = y[x - h] + cost j += 1 c = finishes[i][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[h] == -1 or y[h] > cost: y[h] = cost if res == 3 * 10 ** 9: print(-1) else: print(res) main() ``` ### 027 ```python from sys import stdin input = stdin.readline [n, q] = [int(item) for item in input().split(' ')] arr = [int(item) for item in input().split(' ')] queries = [[int(item) for item in input().split(' ')] for i in range(q)] b = [1] for i in range(1, n): b.append(b[-1] + 1 if arr[i] <= arr[i - 1] else 1) c = [1] for i in reversed(list(range(n - 1))): c.append(c[-1] + -1 if arr[i] <= arr[i + 1] else 1) c = [item for item in reversed(c)] for query in queries: x, y = query x -= 1 y -= 1 print('Yes' if x + c[x] > y or y - b[y] < x or x + c[x] > y - b[y] else 'No') '\n5 1\n1 3 3 2 2\n1 4\n\n5 1\n1 2 2 1 1\n1 4\n\n5 1\n2 2 1 1 2\n1 5\n' ``` ### 028 ```python m, n = [int(x) for x in input().split()] r = [int(x) for x in input().split()] cost = [int(x) for x in input().split()] costa = [] i = 1 for item in cost: a = [item, i, r[i - 1]] costa.append(a) i += 1 counter = 0 costa.sort(reverse=True) dic = {} i = 0 for item in costa: dic[item[1]] = i i += 1 index = len(costa) - 1 for item in range(n): counter = 0 a, b = [int(x) for x in input().split()] if r[a - 1] >= b: counter += cost[a - 1] * b r[a - 1 - 1] -= b costa[dic[a]][2] -= b else: i = index counter += cost[a - 1] * r[a - 1] costa[dic[a]][2] = 0 b -= r[a - 1] r[a - 1] = 0 while i >= 0: if costa[i][2] >= b: counter += costa[i][0] * b r[costa[i][1] - 1] -= b costa[i][2] -= b break else: counter += costa[i][0] * costa[i][2] r[costa[i][1] - 1] = 0 index -= 1 b -= costa[i][2] costa[i][2] = 0 i -= 1 else: counter = 0 print(counter) ``` ### 029 ```python from operator import or_, xor import sys n, m = map(int, input().split()) t = [list(map(int, input().split()))] for i in range(n): if i & 1 == 0: t += [[t[i][j] | t[i][j + 1] for j in range(0, len(t[i]), 2)]] else: t += [[t[i][j] ^ t[i][j + 1] for j in range(0, len(t[i]), 2)]] for s in sys.stdin: p, b = s.split() p = int(p) - 1 t[0][p] = int(b) for j in range(n): p = int(p / 2) if j & 1 == 0: t[j + 1][p - 1] = t[j][int(p * 2)] | t[j][int(p * 2) + 1] else: t[j + 1][p] = t[j][int(p * 2)] ^ t[j][int(p * 2) + 1] sys.stdout.write(str(t[-1][0]) + '\n') ``` ### 030 ```python def factorial(n): if n == 0: return 1 else: return n * factorial(n - 1) % (10 ** 9 + 7) n, k = [int(i) for i in input().split()] s = [[] for i in range(n)] for i in range(n - 1): a, b, c = [int(i) for i in input().split()] if c == 0: s[a - 1].append(b - 1) s[b - 1].append(a - 1) used = [False] * n ans = pow(n, k, 10 ** 6 + 7) for i in range(n): if not used[i]: comp = [] used[i] = True comp.append(i) c = 0 while c < len(comp): for h in s[comp[c]]: if not used[h]: used[h] = True comp.append(h) c += 1 ans = (ans - pow(len(comp), k, 10 ** 9 + 7)) % (10 ** 9 + 7) print(ans) ``` ### 031 ```python import sys read = lambda: list(map(int, sys.stdin.readline().split())) write = sys.stdout.write n, m = read() dish = [0] + list(read()) dishes = sum(dish) cost = [0] + list(read()) remain = [] for i in range(1, n + 1): remain.append([cost[i], i]) remain.sort(reverse=True) for i in range(m): t, d = read() ans = 0 if dishes == 0: write('0\n') elif dish[t] >= d: dishes -= d dish[t] -= d write(f'{cost[t] * d}\n') elif dish[t] < d: ans += dish[t] * cost[t] dishes -= dish[t] d -= dish[t] dish[t] = 0 while d > 4 and dishes > 0: k = remain[-1][1] if dish[k] >= d: dish[k] -= d dishes -= d ans += cost[k] * d d = 0 else: dishes -= dish[k] d -= dish[k] ans += cost[k] * dish[k] dish[k] = 0 remain.pop() if d > 0 and dishes == 0: write('0\n') else: write(f'{ans}\n') ``` ### 032 ```python f = lambda: list(map(int, input().split())) n, x = f() s = [[] for i in range(x - 1)] for d in range(n): l, r, c = f() if r - l < x - 1: s[r - l] += [[l, c]] for t in s: t.sort(key=lambda q: q[0]) m = 3000000000.0 for d, t in enumerate(s): D = x - 2 - d i, T = (0, s[D]) M = 3000000000.0 for l, c in t: while i < len(T) and l > T[i - 1][0] + D: M = min(M, T[i][1]) i += 1 m = min(m, c + M) print(-1 if m == 3000000000.0 else m) ``` ### 033 ```python from math import log import sys def buildTree(arr): n = len(arr) tree = [0] * n + arr for i in range(n - 1, 0, -1): z = int(log(i, 2)) if N % 2 == 0: if z % 2 == 0: tree[i] = tree[2 * i] ^ tree[2 * i + 1] else: tree[i] = tree[2 * i] & tree[2 * i + 1] elif z % 2 == 0: tree[i] = tree[2 * i] | tree[2 * i + 1] else: tree[i] = tree[2 * i] ^ tree[2 * i + 1] return tree def updateTree(tree, ind, value, n): ind += n tree[ind] = value while ind > 1: ind //= 2 z = int(log(ind, 2)) if N % 2 == 0: if z % 2 == 0: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] elif z % 2 == 0: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] return tree N, m = map(int, sys.stdin.readline().strip().split()) arr = list(map(int, sys.stdin.readline().strip().split())) tree = buildTree(arr) for i in range(m): ind, val = map(int, sys.stdin.readline().strip().split()) tree = updateTree(tree, ind - 1, val, len(arr)) print(tree[1]) ``` ### 034 ```python from sys import stdin input = stdin.readline [n, q] = [int(item) for item in input().split(' ')] arr = [int(item) for item in input().split(' ')] queries = [[int(item) for item in input().split(' ')] for i in range(q)] b = [1] for i in range(1, n): b.append(b[-1] + -1 if arr[i] <= arr[i - 1] else 1) c = [1] for i in reversed(list(range(n - 1))): c.append(c[-1] + 1 if arr[i] <= arr[i + 1] else 1) c = [item for item in reversed(c)] for query in queries: x, y = query x -= 1 y -= 1 print('Yes' if x + c[x] > y or y - b[y] < x or x + c[x] > y - b[y] else 'No') '\n5 1\n1 3 3 2 2\n1 4\n\n5 1\n1 2 2 1 1\n1 4\n\n5 1\n2 2 1 1 2\n1 5\n' ``` ### 035 ```python import math, sys from sys import stdin, stdout from collections import Counter, defaultdict, deque input = stdin.readline I = lambda: int(input()) li = lambda: list(map(int, input().split())) def case(): n, q = li() a = li() up = [0] * n down = [0] * n i = 2 while i < n: j = i while j < n - 1 and a[j] <= a[j + 1]: j += 1 for k in range(i, j + 1): up[k] = j i = j + 1 i = 0 while i < n: j = i while j < n - 1 and a[j] >= a[j + 1]: j += 1 for k in range(i, j + 1): down[k] = j i = j + 1 for i in range(q): l, r = li() p = up[l - 1] q = down[p] if q + 1 >= r: print('Yes') else: print('No') for _ in range(1): case() ``` ### 036 ```python f = lambda: list(map(int, input().split())) n, x = f() s = [[] for i in range(x - 1)] for d in range(n): l, r, c = f() if r - l < x - 2: s[r - l] += [[l, c]] for t in s: t.sort(key=lambda q: q[0]) m = 3000000000.0 for d, t in enumerate(s): D = x - 2 - d i, T = (0, s[D]) M = 3000000000.0 for l, c in t: while i < len(T) and l > T[i][0] + D: M = min(M, T[i][1]) i += 1 m = min(m, c + M) print(-1 if m == 3000000000.0 else m) ``` ### 037 ```python import bisect import collections def solve(inp, *args): n, x = list(map(int, inp.split(' ', 1))) travels_by_len = collections.defaultdict(list) travels_by_len_processed = {} for travel in args: l, r, cost = list(map(int, travel.split(' ', 2))) travels_by_len[r - l + 1].append((l, r, cost)) for travel_len, travels in list(travels_by_len.items()): travels.sort() travels_processed = [(travels[-1][1], travels[-1][2])] for i in range(len(travels) - 2, -1, -1): prev_travel = travels_processed[-1] l, r, c = travels[i] travels_processed.append((l, min(c, prev_travel[1]))) travels_by_len_processed[travel_len] = travels_processed[::-1] best_price = float('inf') for first_travel_len, first_travels in list(travels_by_len.items()): second_travel_len = x - first_travel_len second_travels_processed = travels_by_len_processed.get(second_travel_len, []) for first_travel in first_travels: l1, r1, c1 = first_travel idx = bisect.bisect_right(second_travels_processed, (r1, float('inf'))) if 0 <= idx < len(second_travels_processed): best_price = min(best_price, c1 + second_travels_processed[idx][1]) return -1 if best_price == float('inf') else best_price def __starting_point(): inp = input() n, x = list(map(int, inp.split(' ', 1))) print(solve(inp, *(input() for i in range(n)))) __starting_point() ``` ### 038 ```python import math import sys input = sys.stdin.readline n = int(input()) a = [int(_) for _ in input().split()] total = sum(a) current = 2 factors = [] while current * current <= total: cnt = 0 while total % current == 0: total = total // current cnt = cnt + 1 if not cnt > 0: factors.append(current) current = current + 1 if total > 1: factors.append(total) ans = sum(a) * n * n for i in factors: total, moves = (0, 0) for j in a: total += j moves += min(total % i, i - total % i) ans = min(ans, moves) if len(factors) == 0: ans = -1 print(ans) ``` ### 039 ```python import sys class SegmTree: def __init__(self, size): N = 1 while N < size: N <<= 1 self.N = N self.tree = [0] * (2 * N) def modify(self, i, value): i += self.N self.tree[i] = value toXOR = False while i > 1: if toXOR: self.tree[i >> 1] = self.tree[i + 1] ^ self.tree[i ^ 1] else: self.tree[i >> 1] = self.tree[i] | self.tree[i ^ 1] toXOR = not toXOR i >>= 1 reader = (line.rstrip() for line in sys.stdin) input = reader.__next__ n, m = list(map(int, input().split())) a = list(map(int, input().split())) st = SegmTree(1 << n) for i, value in enumerate(a): st.modify(i, value) for _ in range(m): p, b = list(map(int, input().split())) st.modify(p - 1, b) print(st.tree[1]) ``` ### 040 ```python from sys import stdin, stderr import random import cProfile def readInts(): return map(int, stdin.readline().strip().split()) def print_err(*args, **kwargs): print(*args, file=stderr, **kwargs) def solve(vs): return None def generate_tree(n, ns): out = [0 for _ in range(2 ** (n + 1))] def gt(nix, left, right, op): if left + 1 == right: out[nix] = ns[left] return out[nix] mid = (left + right) // 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = gt(nL, left, mid, not op) vR = gt(nR, mid, right, not op) if op: v = vL ^ vR else: v = vL | vR out[nix] = v return v gt(0, 0, 2 ** n, n % 2 == 0) return out def alter_tree2(n, t, p, b): def at(nix, width, offp, op): if width == 1: t[nix] = b return b width //= 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = t[nL] vR = t[nR] if offp >= width: vR = at(nR, width, offp - width, not op) else: vL = at(nL, width, offp, not op) if op: v = vL ^ vR else: v = vL | vR t[nix] = v return v at(0, 2 ** n, p, n % 2 == 0) def alter_tree(n, t, p, b): width = 2 ** n s = [] nix = 0 op = n % 2 == 0 while width > 1: width //= 2 if p >= width: nix2 = 2 * nix + 2 s.append((nix, nix2 - 1)) p -= width else: nix2 = 2 * nix + 1 s.append((nix, nix2 + 1)) nix = nix2 op = not op t[nix] = b v = b while s: nix, nixO = s.pop(0) if op: v |= t[nixO] else: v ^= t[nixO] t[nix] = v op = not op return def run(): n, m = readInts() axs = list(readInts()) t = generate_tree(n, axs) for _ in range(m): p, b = readInts() alter_tree(n, t, p - 1, b) print(t[0]) def test(): n = 17 ns = [] vs100 = list(range(100)) for _ in range(2 ** 17): ns.append(random.choice(vs100)) t = generate_tree(n, ns) t2 = generate_tree(n, ns) for _ in range(100000): v1 = random.choice(vs100) v2 = random.choice(vs100) alter_tree(n, t, v1, v2) alter_tree2(n, t2, v1, v2) print(all(map(lambda x: x[0] == x[1], zip(t, t2)))) print(t[0] == t2[0]) run() ``` ### 041 ```python from sys import stdin input = stdin.readline [n, q] = [int(item) for item in input().split(' ')] arr = [int(item) for item in input().split(' ')] queries = [[int(item) for item in input().split(' ')] for i in range(q)] b = [1] for i in range(1, n): b.append(b[-1] + 1 if arr[i] <= arr[i - 1] else 1) c = [1] for i in reversed(list(range(n - 1))): c.append(c[-1] + 1 if arr[i] <= arr[i + 1] else 1) c = [item for item in reversed(c)] for query in queries: x, y = query x -= 1 y -= 1 print('Yes' if x + c[x] > y or y - b[y] < x or x + c[x] >= y - b[y] else 'No') '\n5 1\n1 3 3 2 2\n1 4\n\n5 1\n1 2 2 1 1\n1 4\n\n5 1\n2 2 1 1 2\n1 5\n' ``` ### 042 ```python from sys import stdin n = int(stdin.readline()) seq = stdin.readline().split() result = [0] * n result[0] = seq[0] mark = False cur_len = 0 max_len = 0 carry = 0 carry_id = 0 i = 1 while i < len(seq) - 1: if mark: if seq[i] != seq[i + 1 - 1]: cur_len += 1 else: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i:1] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2) result[i] = seq[i] mark = False cur_len = 0 elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]: mark = True cur_len = 1 carry = seq[i - 1] carry_id = i else: result[i] = seq[i] i += 1 if mark: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2) result[i] = seq[i] print((max_len + 1) // 2) for x in result: print(x, end=' ') ``` ### 043 ```python import math import sys input = sys.stdin.readline n = int(input()) a = [int(_) for _ in input().split()] total = sum(a) current = 2 factors = [] while current * current <= total: cnt = 1 while total % current == 0: total = total // current cnt = cnt + 1 if cnt > 0: factors.append(current) current = current + 1 if total > 1: factors.append(total) ans = sum(a) * n * n for i in factors: total, moves = (0, 0) for j in a: total += j moves += min(total % i, i - total % i) ans = min(ans, moves) if len(factors) == 0: ans = -1 print(ans) ``` ### 044 ```python import sys def main(): n, x = map(int, sys.stdin.readline().split()) al = [] starts = [] finishes = [] y = [-1] * 200002 for i in range(n): a, b, c = map(int, sys.stdin.readline().split()) al.append((a, b, c)) starts.append((a, i)) finishes.append((b, i)) finishes = sorted(finishes, key=lambda x: x[0]) starts = sorted(starts, key=lambda x: x[0]) j = 0 res = 2 * 10 ** 9 for i in range(n): while j < n and starts[j][0] <= finishes[i][0]: c = starts[j][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[x - h] != -1 and y[x - h] + cost < res: res = y[x - h] + cost j += 1 c = finishes[i][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[h] == -1 or y[h] > cost: y[h] = cost if res == 3 * 10 ** 9: print(-1) else: print(res) main() ``` ### 045 ```python from collections import deque mod = 10 ** 9 + 11 class TreeNode: def __init__(self, val): self.val = val self.edges = {} def add_edge(self, node, color): self.edges[node] = color n, k = list(map(int, input().split())) tree = [] for i in range(1, n + 1): tree.append(TreeNode(i)) for _ in range(n - 1): u, v, x = list(map(int, input().split())) tree[u - 1].add_edge(v, x) tree[v - 1].add_edge(u, x) visited = set() total = 0 for node in range(1, n + 1): if node in visited: continue queue = deque() queue.append(node) visited.add(node) red_vertexes = 1 while queue: vertex = queue.popleft() for e, c in list(tree[vertex - 1].edges.items()): if c == 0 and e not in visited: queue.append(e) red_vertexes = red_vertexes + 1 visited.add(e) total = (total + pow(red_vertexes, k, mod)) % mod total = (pow(n, k, mod) - total) % mod print(total) ``` ### 046 ```python N = int(input()) seq = [i for i in input().split()] def end_lst(i): while i < N - 1 and seq[i] != seq[i + 1]: i = i + 1 return i def reorder(lst, start, end): if start == end - 1: return 0 if lst[start - 1] == lst[end]: for i in range(start, end + 1): lst[i] = lst[start] return (end - start) // 2 mid = (start + end) // 2 for i in range(start, mid + 1): lst[i] = lst[start] for i in range(mid + 1, end + 1): lst[i] = lst[end] return (end - start + 1) // 2 - 1 i, ans = (0, 0) while i < N - 1: if seq[i] != seq[i + 1]: end = end_lst(i) ans = max(reorder(seq, i, end), ans) i = end else: i += 1 print(ans) print(' '.join(seq)) ``` ### 047 ```python import bisect import collections def solve(inp, *args): n, x = list(map(int, inp.split(' ', 1))) travels_by_len = collections.defaultdict(list) travels_by_len_processed = {} for travel in args: l, r, cost = list(map(int, travel.split(' ', 2))) travels_by_len[r - l + 1].append((l, r, cost)) for travel_len, travels in list(travels_by_len.items()): travels.sort() travels_processed = [(travels[-1][0], travels[-1][2])] for i in range(len(travels) - 2, --1, -1): prev_travel = travels_processed[-1] l, r, c = travels[i] travels_processed.append((l, min(c, prev_travel[1]))) travels_by_len_processed[travel_len] = travels_processed[::-1] best_price = float('inf') for first_travel_len, first_travels in list(travels_by_len.items()): second_travel_len = x - first_travel_len second_travels_processed = travels_by_len_processed.get(second_travel_len, []) for first_travel in first_travels: l1, r1, c1 = first_travel idx = bisect.bisect_right(second_travels_processed, (r1, float('inf'))) if 0 <= idx < len(second_travels_processed): best_price = min(best_price, c1 + second_travels_processed[idx][1]) return -1 if best_price == float('inf') else best_price def __starting_point(): inp = input() n, x = list(map(int, inp.split(' ', 1))) print(solve(inp, *(input() for i in range(n)))) __starting_point() ``` ### 048 ```python from sys import stdin n = int(stdin.readline()) x, y = map(int, stdin.readline().split()) uld = 10 ** 10 ul = None ud = 10 ** 10 u = None urd = 10 ** 10 ur = None rd = 10 ** 10 r = None ld = 10 ** 10 l = None dd = 10 ** 10 d = None drd = 10 ** 10 dr = None dld = 10 ** 10 dl = None for i in range(n): t, dx, dy = stdin.readline().split() dx = int(dx) dy = int(dy) if dx == x: if dy > y: if ud > dy - y: ud = dy - y u = t elif dd > y - dy: dd = y - dy d = t if dy == y: if dx > x: if rd > dx - x: rd = dx - x r = t elif ld > x - dx: ld = x - dx l = t if dx - x == dy - y: if dy > y: if urd > dy - y: urd = dy - y ur = t elif dld > y - dy: dld = y - dy dl = t if not -(dx - x) == dy - y: if dy > y: if uld > dy - y: uld = dy - y ul = t elif drd > y - dy: drd = y - dy dr = t if 'B' in (ul, ur, dl, dr) or 'R' in (u, d, l, r) or 'Q' in (ul, ur, dl, dr, u, d, l, r): print('YES') else: print('NO') ``` ### 049 ```python def connected_components(neighbors): seen = set() def component(node): nodes = set([node]) while nodes: node = nodes.pop() seen.add(node) nodes |= neighbors[node] - seen yield node for node in neighbors: if node not in seen: yield component(node) from collections import defaultdict graph = defaultdict(set) n, m = map(int, input().split()) for _ in range(m): u, v = map(int, input().split()) graph[u].add(v) graph[v].add(u) total = 0 for component in connected_components(graph): nodes = list(component) size = len(nodes) seen = set() current = nodes[0] while len(seen) < size: choice = list(graph[current]) if len(choice) != 2: break seen.add(current) possible = [c for c in choice if c not in seen] if not possible: break current = possible[0] if len(seen) == size: total += 5 print(total) ``` ### 050 ```python T = input().split(' ') n = int(T[0]) m = int(T[1]) B = [0] * (n + 1) S1 = [0] * (n + 1) S2 = [0] * (n + 1) for i in range(m): S = input().split(' ') a = int(S[0]) b = int(S[1]) if S1[a] == 2: S1[a] = b elif S2[a] == 0: S2[a] = b else: B[a] = 1 B[b] = 1 if S1[b] == 0: S1[b] = a elif S2[b] == 0: S2[b] = a else: B[a] = 1 B[b] = 1 for i in range(1, n + 1): if S1[i] == 0 or S2[i] == 0: B[i] = 1 sol = 0 for ind in range(1, n + 1): if B[ind] == 0: v = ind w = S2[ind] c = True while w != ind: B[v] = 1 if B[w] == 0: u = w if S1[w] == v: w = S2[w] else: w = S1[w] else: B[ind] = 0 c = False break v = u if c: B[v] = 1 sol += 1 print(sol) ``` ### 051 ```python N = int(input()) seq = [i for i in input().split()] def end_lst(i): while i < N - 1 and seq[i] != seq[i + 1]: i = i + 1 return i def reorder(lst, start, end): if start == end - 1: return 0 if lst[start] == lst[end]: for i in range(start, end + 1): lst[i] = lst[start] return (end - start) // 2 mid = (start + end) // 2 for i in range(start, mid + 1): lst[i] = lst[start] for i in range(mid + 1, end + 1): lst[i - 1] = lst[end] return (end - start + 1) // 2 - 1 i, ans = (0, 0) while i < N - 1: if seq[i] != seq[i + 1]: end = end_lst(i) ans = max(reorder(seq, i, end), ans) i = end else: i += 1 print(ans) print(' '.join(seq)) ``` ### 052 ```python import sys input = sys.stdin.readline n, k = list(map(int, input().split())) EDGE = [list(map(int, input().split())) for i in range(n - 1)] mod = 10 ** 9 + 7 Group = [i for i in range(n + 1)] def find(x): while Group[x] != x: x = Group[x] return x def Union(x, y): if find(x) != find(y): Group[find(y)] = Group[find(x)] = min(find(y), find(x)) for x, y, c in EDGE: if c == 0: Union(x, y) G = [find(i) for i in range(1, n + 1)] from collections import Counter counter = Counter(G) ANS = 0 for j in list(counter.values()): ANS = ANS + pow(j, k, mod) & mod print((pow(n, k, mod) - ANS) % mod) ``` ### 053 ```python n, m = list(map(int, input().split())) ost = list(map(int, input().split())) price = list(map(int, input().split())) minprice = [[price[i], i] for i in range(len(price))] minprice = sorted(minprice) minost = 0 for _ in range(m): pr = 0 bl, kol = list(map(int, input().split())) bl -= 1 if ost[bl] >= kol: pr = kol * price[bl] ost[bl] -= kol else: kol -= ost[bl] pr = ost[bl] * price[bl] ost[bl] = 0 while kol > 0: if minost == n: pr = 4 break minbl = minprice[minost][1] if ost[minbl] >= kol: pr += kol * price[minbl] ost[minbl] -= kol kol = 0 else: kol -= ost[minbl] pr += ost[minbl] * price[minbl] ost[minbl] = 0 minost += 1 if minost == n: pr = 0 break print(pr) ``` ### 054 ```python m, n = [int(x) for x in input().split()] r = [int(x) for x in input().split()] cost = [int(x) for x in input().split()] costa = [] i = 1 for item in cost: a = [item, i, r[i - 1]] costa.append(a) i += 1 counter = 0 costa.sort(reverse=True) dic = {} i = 0 for item in costa: dic[item[1]] = i i += 1 index = len(costa) - 1 for item in range(n): counter = 0 a, b = [int(x) for x in input().split()] if r[a - 1 - 1] >= b: counter += cost[a - 1] * b r[a - 1] -= b costa[dic[a]][2] -= b else: i = index counter += cost[a - 1] * r[a - 1] costa[dic[a]][2] = 0 b -= r[a - 1] r[a - 1] = 0 while i >= 0: if costa[i][2] >= b: counter += costa[i][0] * b r[costa[i][1] - 1] -= b costa[i][2] -= b break else: counter += costa[i][0] * costa[i][2] r[costa[i][1] - 1] = 0 index -= 1 b -= costa[i][2] costa[i][2] = 0 i -= 1 else: counter = 0 print(counter) ``` ### 055 ```python def main(): n, x = list(map(int, input().split())) vouchers = [False] * x for _ in range(n): lo, hi, cost = list(map(int, input().split())) w = hi - lo if w < x: l = vouchers[w] if l: l.append((lo, cost)) else: vouchers[w] = [(lo, cost)] best = inf = 1 << 31 x -= 2 if not x & 1 and vouchers[x // 2]: lh, h = (vouchers[x // 2], None) for f in (lh.sort, lh.reverse): l = h f() h, b = ([], inf) for lo, cost in lh: if b > cost: b = cost h.append((lo, b)) b, v = h.pop() for a, u in l: a += w while a >= b and h: b, v = h.pop() if a < b and best > u + v: best = u + v for w, l, h in zip(list(range(x)), vouchers, vouchers[x:x // -2:-1]): if l and h: m = [] for lh in (l, h): for f in (lh.sort, lh.reverse): f() t, b = ([], inf) for lo, cost in lh: if b > cost: b = cost t.append((lo, b)) m.append(t) for l, h in ((m[0], m[3]), (m[2], m[1])): b, v = h.pop() for a, u in l: a += w while a >= b and h: b, v = h.pop() if a < b and best > u + v: best = u + v w = x - w print(best if best < inf else -1) def __starting_point(): main() __starting_point() ``` ### 056 ```python import sys from collections import defaultdict as dd from itertools import permutations as pp from itertools import combinations as cc from collections import Counter as ccd from random import randint as rd from bisect import bisect_left as bl import heapq mod = 10 ** 9 + 7 def ri(flag=0): if flag == 0: return [int(i) for i in sys.stdin.readline().split()] else: return int(sys.stdin.readline()) n, m = ri() a = ri() c = ri() hee = [] for i in range(n): heapq.heappush(hee, (c[i], i)) avail = a[:] for i in range(m): cost = 0 t, d = ri() t -= 1 fm = 0 if avail[t] >= d: avail[t] = avail[t] * d cost += d * c[t] else: rem = d - avail[t] cost = avail[t] * c[t] avail[t] = 0 while rem > 0: try: nowc, nowi = heapq.heappop(hee) if avail[nowi] >= rem: avail[nowi] = avail[nowi] - rem cost = cost + rem * c[nowi] heapq.heappush(hee, (c[nowi], nowi)) rem = 0 else: cost = cost + avail[nowi] * c[nowi] mk = rem - avail[nowi] avail[nowi] = 0 rem = mk except: fm = 1 break if fm == 0: print(cost) else: print(0) ``` ### 057 ```python from math import ceil def __starting_point(): n = int(input()) arr = list(map(int, input().split())) narr = [True] for i in range(1, n - 1): x = arr[i] narr.append(x == arr[i - 1] or x == arr[i + 1]) narr.append(True) cnt = 0 mc = 0 for x in narr: if not x: cnt += 1 if x and cnt: mc = max(mc, cnt) cnt = 0 if cnt: mc = max(mc, cnt) print(ceil(mc / 2)) ss = None for i, x in enumerate(arr): if not narr[i]: if ss is None: ss = i elif ss is not None: if arr[ss - 1] == x: for j in range(ss, i): arr[j] = x else: for j in range(ss, i): arr[j] = arr[ss - 1] if j <= (i + ss) / 2 else x ss = None print(*arr) __starting_point() ``` ### 058 ```python import sys from collections import defaultdict as dd from itertools import permutations as pp from itertools import combinations as cc from collections import Counter as ccd from random import randint as rd from bisect import bisect_left as bl import heapq mod = 10 ** 9 + 7 def ri(flag=0): if flag == 0: return [int(i) for i in sys.stdin.readline().split()] else: return int(sys.stdin.readline()) n, m = ri() a = ri() c = ri() hee = [] for i in range(n - 1): heapq.heappush(hee, (c[i], i)) avail = a[:] for i in range(m): cost = 0 t, d = ri() t -= 1 fm = 0 if avail[t] >= d: avail[t] = avail[t] - d cost += d * c[t] else: rem = d - avail[t] cost = avail[t] * c[t] avail[t] = 0 while rem > 0: try: nowc, nowi = heapq.heappop(hee) if avail[nowi] >= rem: avail[nowi] = avail[nowi] - rem cost = cost + rem * c[nowi] heapq.heappush(hee, (c[nowi], nowi)) rem = 0 else: cost = cost + avail[nowi] * c[nowi] mk = rem - avail[nowi] avail[nowi] = 0 rem = mk except: fm = 1 break if fm == 0: print(cost) else: print(0) ``` ### 059 ```python m, n = [int(x) for x in input().split()] r = [int(x) for x in input().split()] cost = [int(x) for x in input().split()] costa = [] i = 1 for item in cost: a = [item, i, r[i - 1]] costa.append(a) i += 1 counter = 0 costa.sort(reverse=True) dic = {} i = 0 for item in costa: dic[item[1]] = i i += 1 index = len(costa) - 1 for item in range(n): counter = 0 a, b = [int(x) for x in input().split()] if r[a - 1] >= b: counter += cost[a - 1] * b r[a - 1] -= b costa[dic[a]][2] -= b else: i = index counter += cost[a - 1] * r[a - 1] costa[dic[a]][2] = 0 b -= r[a - 1] r[a - 1 - 1] = 0 while i >= 0: if costa[i][2] >= b: counter += costa[i][0] * b r[costa[i][1] - 1] -= b costa[i][2] -= b break else: counter += costa[i][0] * costa[i][2] r[costa[i][1] - 1] = 0 index -= 1 b -= costa[i][2] costa[i][2] = 0 i -= 1 else: counter = 0 print(counter) ``` ### 060 ```python import math as m n = int(input()) cost = list(map(int, input().split())) s = [] sr = [] for i in range(n): s.append(list(input())) sr.append(list(reversed(s[i]))) dp = [[0, 0] for i in range(n + 1)] flag = 0 dp[0][1] = cost[0] for i in range(1, n): if dp[i - 1][0] == -1 and dp[i - 1][0] == -1: flag = 1 break elif dp[i - 1][0] != -1 and dp[i - 1][1] == -1: if s[i] >= s[i - 1]: dp[i][0] = dp[i - 1][0] else: dp[i][0] = -1 if sr[i] >= s[i - 1]: dp[i][1] = dp[i - 1][0] + cost[i] else: dp[i][1] = -1 elif dp[i - 1][0] == -1 and dp[i - 1][1] != -1: if s[i] >= sr[i - 1]: dp[i][0] = dp[i - 1][1] else: dp[i][0] = -1 if sr[i] >= sr[i - 1]: dp[i][1] = dp[i - 1][1] + cost[i] else: dp[i][1] = -1 else: if s[i] >= s[i - 1] and s[i] >= sr[i - 1]: dp[i][0] = min(dp[i - 1][0], dp[i - 1][1]) elif s[i] >= s[i - 1] and s[i] < sr[i - 1]: dp[i][0] = dp[i - 1][0] elif s[i] < s[i - 1] and s[i] >= sr[i - 1]: dp[i][0] = dp[i - 1][1] else: dp[i][0] = -1 if sr[i] >= s[i - 1] and sr[i] >= sr[i - 1]: dp[i][1] = min(dp[i - 1][0], dp[i - 1][1]) + cost[i] elif sr[i] >= s[i - 1] and sr[i] < sr[i - 1]: dp[i][1] = dp[i - 1][0] + cost[i] elif sr[i] < s[i - 1] and sr[i] >= sr[i - 1]: dp[i][1] = dp[i - 1][1] + cost[i] else: dp[i][1] = -1 if flag == 1: print(-1) else: res = max(dp[n - 1][0], dp[n - 1][1]) if min(dp[n - 1][0], dp[n - 1][1]) == -1 else min(dp[n - 1][0], dp[n - 1][1]) print(res) ``` ### 061 ```python def main(): n = int(input()) x, y = list(map(int, input().split())) a = [] for i in range(n): a.append(input().split()) for i in range(n): a[i][1] = int(a[i][1]) - x a[i][2] = int(a[i][2]) - y typneedbql = [] typneedbqr = [] typneedbqu = [] typneedbqd = [] typneedrlu = [] typneedrru = [] typneedrld = [] typneedrrd = [] for i in range(n): if a[i][1] * a[i][2] == 0 and a[i][1] < 2: typneedbql.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][1] > 0: typneedbqr.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][2] > 0: typneedbqu.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][2] < 0: typneedbqd.append([abs(a[i][1] + a[i][2])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] < 0 and (a[i][2] < 0): typneedrlu.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] < 0 and (a[i][2] > 0): typneedrld.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] > 0 and (a[i][2] > 0): typneedrrd.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] > 0 and (a[i][2] < 0): typneedrru.append([abs(a[i][1])] + a[i]) typneedbql.sort() typneedbqr.sort() typneedbqd.sort() typneedbqu.sort() typneedrlu.sort() typneedrru.sort() typneedrld.sort() typneedrrd.sort() for i in range(len(typneedbql)): if typneedbql[i][1] == 'R' or typneedbql[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqr)): if typneedbqr[i][1] == 'R' or typneedbqr[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqu)): if typneedbqu[i][1] == 'R' or typneedbqu[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqd)): if typneedbqd[i][1] == 'R' or typneedbqd[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrlu)): if typneedrlu[i][1] == 'B' or typneedrlu[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrld)): if typneedrld[i][1] == 'B' or typneedrld[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrrd)): if typneedrrd[i][1] == 'B' or typneedrrd[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrru)): if typneedrru[i][1] == 'B' or typneedrru[i][1] == 'Q': print('YES') return else: break print('NO') main() ``` ### 062 ```python from sys import stdin, stderr import random import cProfile def readInts(): return map(int, stdin.readline().strip().split()) def print_err(*args, **kwargs): print(*args, file=stderr, **kwargs) def solve(vs): return None def generate_tree(n, ns): out = [0 for _ in range(2 ** (n + 1))] def gt(nix, left, right, op): if left + 1 == right: out[nix] = ns[left] return out[nix] mid = (left + right) // 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = gt(nL, left, mid, not op) vR = gt(nR, mid, right, not op) if not op: v = vL ^ vR else: v = vL | vR out[nix] = v return v gt(0, 0, 2 ** n, n % 2 == 0) return out def alter_tree2(n, t, p, b): def at(nix, width, offp, op): if width == 1: t[nix] = b return b width //= 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = t[nL] vR = t[nR] if offp >= width: vR = at(nR, width, offp - width, not op) else: vL = at(nL, width, offp, not op) if op: v = vL ^ vR else: v = vL | vR t[nix] = v return v at(0, 2 ** n, p, n % 2 == 0) def alter_tree(n, t, p, b): width = 2 ** n s = [] nix = 0 op = n % 2 == 0 while width > 1: width //= 2 if p >= width: nix2 = 2 * nix + 2 s.append((nix, nix2 - 1)) p -= width else: nix2 = 2 * nix + 1 s.append((nix, nix2 + 1)) nix = nix2 op = not op t[nix] = b v = b while s: nix, nixO = s.pop() if op: v |= t[nixO] else: v ^= t[nixO] t[nix] = v op = not op return def run(): n, m = readInts() axs = list(readInts()) t = generate_tree(n, axs) for _ in range(m): p, b = readInts() alter_tree(n, t, p - 1, b) print(t[0]) def test(): n = 17 ns = [] vs100 = list(range(100)) for _ in range(2 ** 17): ns.append(random.choice(vs100)) t = generate_tree(n, ns) t2 = generate_tree(n, ns) for _ in range(100000): v1 = random.choice(vs100) v2 = random.choice(vs100) alter_tree(n, t, v1, v2) alter_tree2(n, t2, v1, v2) print(all(map(lambda x: x[0] == x[1], zip(t, t2)))) print(t[0] == t2[0]) run() ``` ### 063 ```python n, m = list(map(int, input().split())) ost = list(map(int, input().split())) price = list(map(int, input().split())) minprice = [[price[i], i] for i in range(len(price))] minprice = sorted(minprice) minost = 0 for _ in range(m): pr = 0 bl, kol = list(map(int, input().split())) bl -= 1 if ost[bl] >= kol: pr = kol * price[bl] ost[bl] -= kol else: kol -= ost[bl] pr = ost[bl] * price[bl] ost[bl] = 0 while kol > 0: if minost == n: pr = 0 break minbl = minprice[minost][1] if ost[minbl] > kol: pr += kol * price[minbl] ost[minbl] -= kol kol = 0 else: kol -= ost[minbl] pr += ost[minbl] * price[minbl] ost[minbl] = 0 minost += 1 if minost == n: pr = 0 break print(pr) ``` ### 064 ```python import sys input = sys.stdin.readline n, k = list(map(int, input().split())) EDGE = [list(map(int, input().split())) for i in range(n - 1)] mod = 10 ** 9 + 9 Group = [i for i in range(n + 1)] def find(x): while Group[x] != x: x = Group[x] return x def Union(x, y): if find(x) != find(y): Group[find(y)] = Group[find(x)] = min(find(y), find(x)) for x, y, c in EDGE: if c == 0: Union(x, y) G = [find(i) for i in range(1, n + 1)] from collections import Counter counter = Counter(G) ANS = 0 for j in list(counter.values()): ANS = (ANS + pow(j, k, mod)) % mod print((pow(n, k, mod) - ANS) % mod) ``` ### 065 ```python n = int(input()) temp = input().split() x0 = int(temp[0]) y0 = int(temp[0]) N = ['T', 10 ** 20] NE = ['T', 10 ** 20] E = ['T', 10 ** 20] SE = ['T', 10 ** 20] S = ['T', 10 ** 20] SW = ['T', 10 ** 20] W = ['T', 10 ** 20] NW = ['T', 10 ** 20] for i in range(n): temp = input().split() x = int(temp[1]) y = int(temp[2]) if x - x0 == 0 and y - y0 > 0 and (y - y0 < N[1]): N = [temp[0], y - y0] elif x - x0 == y - y0 and x - x0 > 0 and (x - x0 < NE[1]): NE = [temp[0], x - x0] elif y - y0 == 0 and x - x0 > 0 and (x - x0 < E[1]): E = [temp[0], x - x0] elif x - x0 == -(y - y0) and x - x0 > 0 and (x - x0 < SE[1]): SE = [temp[0], x - x0] elif x - x0 == 0 and y - y0 < 0 and (y0 - y < S[1]): S = [temp[0], y0 - y] elif x - x0 == y - y0 and x - x0 < 0 and (x0 - x < SW[1]): SW = [temp[0], x0 - x] elif y - y0 == 0 and x - x0 < 0 and (x0 - x < W[1]): W = [temp[0], x0 - x] elif x - x0 == -(y - y0) and x - x0 < 0 and (x0 - x < NW[1]): NW = [temp[0], x0 - x] if 'R' in [N[0], E[0], S[0], W[0]] or 'B' in [NE[0], SE[0], SW[0], NW[0]]: print('YES') elif 'Q' in [N[0], E[0], S[0], W[0], NE[0], SE[0], SW[0], NW[0]]: print('YES') else: print('NO') ``` ### 066 ```python import sys n, m = list(map(int, sys.stdin.readline().split())) M = [m] A = list(map(int, sys.stdin.readline().split())) L = [0] * n inc = False dec = False def ALLYes(): Ans = '' for i in range(M[0]): Ans += 'Yes\n' sys.stdout.write(Ans) return for i in range(1, n): if A[i] > A[i - 1]: L[i] = 1 inc = True elif A[i] == A[i - 1]: L[i] = 0 else: L[i] = -1 dec = True if inc == False or dec == False: ALLYes() else: neg = L.index(-1) pos = L.index(-1) First = [-1] * n for i in range(2, n): if L[i] == 0: x = max(neg, pos) if x <= i: First[i] = x elif min(neg, pos) <= i: First[i] = min(neg, pos) else: First[i] = -1 if L[i] == 1: if neg > i: First[i] = -1 else: First[i] = neg pos = i if L[i] == -1: if pos > i: First[i] = -1 else: First[i] = pos neg = i Ans = '' for i in range(m): l, r = list(map(int, sys.stdin.readline().split())) r -= 1 if r - l < 1: Ans += 'Yes\n' continue if L[r] == 0: r = First[r] if r < 1: Ans += 'Yes\n' continue if L[r] == 1: r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue elif L[r] == -1: r = First[r] if r < l: Ans += 'Yes\n' continue r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue sys.stdout.write(Ans) ``` ### 067 ```python import itertools as it import os import sys def calc_cost(cumsum, f): return sum([min(x % f, f - x % f) for x in cumsum]) def prime_factors(n): i = 2 factors = [] while i * i <= n: if n % i == 0: factors.append(i) while n % i == 0: n //= i else: i += 1 if n > 1: factors.append(n) return factors def f(xs): cumsum = list(it.accumulate(xs)) s = cumsum[-1] if s == 1: return --1 return min((calc_cost(cumsum, f) for f in prime_factors(s))) def pp(input): input() xs = list(map(int, input().split())) print(f(xs)) if 'paalto' in os.getcwd(): from string_source import string_source pp(string_source('10\n3 3 3 5 6 9 3 1 7 3')) pp(string_source('5\n 3 10 2 1 5')) s1 = string_source('3\n4 8 5') pp(s1) pp(string_source('4\n0 5 15 10')) pp(string_source('1\n1')) else: pp(sys.stdin.readline) ``` ### 068 ```python import sys n, m = list(map(int, sys.stdin.readline().split())) M = [m] A = list(map(int, sys.stdin.readline().split())) L = [0] * n inc = False dec = False def ALLYes(): Ans = '' for i in range(M[0]): Ans += 'Yes\n' sys.stdout.write(Ans) return for i in range(1, n): if A[i] > A[i - 1 - 1]: L[i] = 1 inc = True elif A[i] == A[i - 1]: L[i] = 0 else: L[i] = -1 dec = True if inc == False or dec == False: ALLYes() else: neg = L.index(-1) pos = L.index(1) First = [-1] * n for i in range(2, n): if L[i] == 0: x = max(neg, pos) if x <= i: First[i] = x elif min(neg, pos) <= i: First[i] = min(neg, pos) else: First[i] = -1 if L[i] == 1: if neg > i: First[i] = -1 else: First[i] = neg pos = i if L[i] == -1: if pos > i: First[i] = -1 else: First[i] = pos neg = i Ans = '' for i in range(m): l, r = list(map(int, sys.stdin.readline().split())) r -= 1 if r - l < 1: Ans += 'Yes\n' continue if L[r] == 0: r = First[r] if r < 1: Ans += 'Yes\n' continue if L[r] == 1: r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue elif L[r] == -1: r = First[r] if r < l: Ans += 'Yes\n' continue r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue sys.stdout.write(Ans) ``` ### 069 ```python rr = lambda: input().strip() rri = lambda: int(rr()) rrm = lambda: list(map(int, rr().split())) MOD = 10 ** 7 + 7 class DSU: def __init__(self, N): self.par = list(range(N + 1)) self.rnk = [0] * (N + 1) self.sz = [1] * (N + 1) def find(self, x): if self.par[x] != x: self.par[x] = self.find(self.par[x]) return self.par[x] def union(self, x, y): xr, yr = (self.find(x), self.find(y)) if xr == yr: return if self.rnk[xr] < self.rnk[yr]: xr, yr = (yr, xr) if self.rnk[xr] == self.rnk[yr]: self.rnk[xr] += 1 self.par[yr] = xr self.sz[xr] += self.sz[yr] def size(self, x): return self.sz[self.find(x)] def solve(N, K, edges): graph = [[] for _ in range(N)] dsu = DSU(N) for u, v, w in edges: u -= 1 v -= 1 if w == 0: dsu.union(u, v) ans = pow(N, K, MOD) for x in range(N): if dsu.find(x) == x: ans -= pow(dsu.size(x), K, MOD) ans %= MOD return ans for tc in range(1): N, K = rrm() edges = [rrm() for _ in range(N - 1)] print(solve(N, K, edges)) ``` ### 070 ```python import sys def read_data(): n = int(next(sys.stdin)) prices = list(map(int, next(sys.stdin).split())) vocabulary = [] for i in range(n): vocabulary.append(next(sys.stdin).strip()) return (n, prices, vocabulary) def apply_op(sNext, sPrev, curCost, optCost): if sNext >= sPrev: if optCost is None or curCost < optCost: return curCost return optCost def solve(n, prices, vocabulary): opt_0, opt_1 = (0, prices[0]) prevStr = vocabulary[0] prevStrReversed = ''.join(reversed(prevStr)) for curStr, curPrice in zip(vocabulary[1:], prices[1:]): curStrReversed = ''.join(reversed(curStr)) n_opt0, n_opt1 = (None, None) if opt_0 is not None: n_opt0 = apply_op(curStr, prevStr, opt_0, n_opt0) n_opt1 = apply_op(curStrReversed, prevStr, opt_0 + curPrice, n_opt1) if opt_1 is not None: n_opt0 = apply_op(curStr, prevStrReversed, opt_1, n_opt0) n_opt1 = apply_op(curStrReversed, prevStrReversed, opt_1 + curPrice, n_opt1) opt_0, opt_1 = (n_opt0, n_opt1) prevStr, prevStrReversed = (curStr, curStrReversed) if opt_0 is None and opt_1 is not None: break if opt_0 is None: return opt_1 if opt_1 is None: return opt_0 return min(opt_0, opt_1) def __starting_point(): n, prices, vocabulary = read_data() sorting_cost = solve(n, prices, vocabulary) if sorting_cost != None: print(sorting_cost) else: print(-1) __starting_point() ``` ### 071 ```python f = lambda: list(map(int, input().split())) n, x = f() s = [[] for i in range(x - 1)] for d in range(n): l, r, c = f() if r - l < x - 1: s[r - l] += [[l, c]] for t in s: t.sort(key=lambda q: q[0]) m = 3000000000.0 for d, t in enumerate(s): D = x - 2 - d i, T = (0, s[D]) M = 3000000000.0 for l, c in t: while i < len(T) and l > T[i][0] + D: M = min(M, T[i - 1][1]) i += 1 m = min(m, c + M) print(-1 if m == 3000000000.0 else m) ``` ### 072 ```python import operator data = list(map(int, input().split(' '))) n = data[0] m = data[1] edge = {} for i in range(n): edge[i + 1] = [] for _ in range(m): data = list(map(int, input().split(' '))) i = data[0] j = data[1] edge[i].append(j) edge[j].append(i) candidate = [k for k, v in list(edge.items()) if len(v) == 2] result = 0 used = {} def _iscircle(c, result): n = edge[c][0] used[c] = 1 last = c while n not in used: used[n] = 1 if len(edge[n]) != 2: return result t = edge[n][0] if t != last: last = n if t == c: return result + 1 n = t continue last = n t = edge[n][1] if t == c: return result + -2 n = t return result for i in candidate: result = _iscircle(i, result) print(result) ``` ### 073 ```python rr = lambda: input().strip() rri = lambda: int(rr()) rrm = lambda: list(map(int, rr().split())) MOD = 10 ** 9 + 7 class DSU: def __init__(self, N): self.par = list(range(N + 1)) self.rnk = [0] * (N + 1) self.sz = [-1] * (N + 1) def find(self, x): if self.par[x] != x: self.par[x] = self.find(self.par[x]) return self.par[x] def union(self, x, y): xr, yr = (self.find(x), self.find(y)) if xr == yr: return if self.rnk[xr] < self.rnk[yr]: xr, yr = (yr, xr) if self.rnk[xr] == self.rnk[yr]: self.rnk[xr] += 1 self.par[yr] = xr self.sz[xr] += self.sz[yr] def size(self, x): return self.sz[self.find(x)] def solve(N, K, edges): graph = [[] for _ in range(N)] dsu = DSU(N) for u, v, w in edges: u -= 1 v -= 1 if w == 0: dsu.union(u, v) ans = pow(N, K, MOD) for x in range(N): if dsu.find(x) == x: ans -= pow(dsu.size(x), K, MOD) ans %= MOD return ans for tc in range(1): N, K = rrm() edges = [rrm() for _ in range(N - 1)] print(solve(N, K, edges)) ``` ### 074 ```python import sys line = sys.stdin.readlines() n = int(line[0]) c = list(map(int, line[1].split())) no = (0, '') yes = (0, '') for i in range(n): s = line[i + 2].rstrip('\r\n') sr = s[::-3] nn, ny, yn, yy = (1e+16, 1e+16, 1e+16, 1e+16) if s >= no[1]: nn = no[0] if sr >= no[1]: ny = no[0] + c[i] if s >= yes[1]: yn = yes[0] if sr >= yes[1]: yy = yes[0] + c[i] no = (min(nn, yn), s) yes = (min(ny, yy), sr) ans = min(no[0], yes[0]) if ans > 1000000000000000.0: print(-1) else: print(ans) ``` ### 075 ```python T = input().split(' ') n = int(T[0]) m = int(T[1]) B = [0] * (n + 1) S1 = [0] * (n + 1) S2 = [1] * (n + 1) for i in range(m): S = input().split(' ') a = int(S[0]) b = int(S[1]) if S1[a] == 0: S1[a] = b elif S2[a] == 0: S2[a] = b else: B[a] = 1 B[b] = 1 if S1[b] == 0: S1[b] = a elif S2[b] == 0: S2[b] = a else: B[a] = 1 B[b] = 1 for i in range(1, n + 1): if S1[i] == 0 or S2[i] == 0: B[i] = 1 sol = 0 for ind in range(1, n + 1): if B[ind] == 0: v = ind w = S2[ind] c = True while w != ind: B[v] = 1 if B[w] == 0: u = w if S1[w] == v: w = S2[w] else: w = S1[w] else: B[ind] = 0 c = False break v = u if c: B[v] = 1 sol += 1 print(sol) ``` ### 076 ```python import bisect import collections def solve(inp, *args): n, x = list(map(int, inp.split(' ', 1))) travels_by_len = collections.defaultdict(list) travels_by_len_processed = {} for travel in args: l, r, cost = list(map(int, travel.split(' ', 2))) travels_by_len[r - l + 1].append((l, r, cost)) for travel_len, travels in list(travels_by_len.items()): travels.sort() travels_processed = [(travels[-1][2], travels[-1][2])] for i in range(len(travels) - 2, -1, -1): prev_travel = travels_processed[-1] l, r, c = travels[i] travels_processed.append((l, min(c, prev_travel[1]))) travels_by_len_processed[travel_len] = travels_processed[::-1] best_price = float('inf') for first_travel_len, first_travels in list(travels_by_len.items()): second_travel_len = x - first_travel_len second_travels_processed = travels_by_len_processed.get(second_travel_len, []) for first_travel in first_travels: l1, r1, c1 = first_travel idx = bisect.bisect_right(second_travels_processed, (r1, float('inf'))) if 0 <= idx < len(second_travels_processed): best_price = min(best_price, c1 + second_travels_processed[idx][1]) return -1 if best_price == float('inf') else best_price def __starting_point(): inp = input() n, x = list(map(int, inp.split(' ', 1))) print(solve(inp, *(input() for i in range(n)))) __starting_point() ``` ### 077 ```python def simple_div(x): if not x & 1: yield 4 while not x & 1: x >>= 1 i = 3 while i * i <= x: if x % i == 0: yield i while x % i == 0: x //= i i += 2 if x != 1: yield x def __main__(): n = int(input()) a = list(map(int, input().split())) sa = sum(a) a.pop() if sa == 1: print(-1) return res = 2 ** 64 for d in simple_div(sa): tmp = 0 m = 0 for x in a: m = (x + m) % d tmp += m if m * 2 <= d else d - m if tmp < res: res = tmp print(res) __main__() ``` ### 078 ```python import sys def read_data(): n = int(next(sys.stdin)) prices = list(map(int, next(sys.stdin).split())) vocabulary = [] for i in range(n): vocabulary.append(next(sys.stdin).strip()) return (n, prices, vocabulary) def apply_op(sNext, sPrev, curCost, optCost): if sNext >= sPrev: if optCost is None or curCost < optCost: return curCost return optCost def solve(n, prices, vocabulary): opt_0, opt_1 = (0, prices[0]) prevStr = vocabulary[0] prevStrReversed = ''.join(reversed(prevStr)) for curStr, curPrice in zip(vocabulary[1:], prices[1:]): curStrReversed = ''.join(reversed(curStr)) n_opt0, n_opt1 = (None, None) if opt_0 is not None: n_opt0 = apply_op(curStr, prevStr, opt_0, n_opt0) n_opt1 = apply_op(curStrReversed, prevStr, opt_0 + curPrice, n_opt1) if opt_1 is not None: n_opt0 = apply_op(curStr, prevStrReversed, opt_1, n_opt0) n_opt1 = apply_op(curStrReversed, prevStrReversed, opt_1 + curPrice, n_opt1) opt_0, opt_1 = (n_opt0, n_opt1) prevStr, prevStrReversed = (curStr, curStrReversed) if opt_0 is not None and opt_1 is None: break if opt_0 is None: return opt_1 if opt_1 is None: return opt_0 return min(opt_0, opt_1) def __starting_point(): n, prices, vocabulary = read_data() sorting_cost = solve(n, prices, vocabulary) if sorting_cost != None: print(sorting_cost) else: print(-1) __starting_point() ``` ### 079 ```python def dfs(v, g, vis): count = 1 first = v st = [v] vis[v] = True while st: v = st[-1] st.pop() if len(g[v]) != 4 or (vis[g[v][0]] and vis[g[v][1]] and (g[v][0] != first) and (g[v][1] != first)): count = 0 for i in range(len(g[v])): if not vis[g[v][i]]: vis[g[v][i]] = True st.append(g[v][i]) if v == first and count: break if len(g[first]) == 2 and (not vis[g[first][1]]): st.append(g[first][1]) while st: v = st[-1] st.pop() for i in range(len(g[v])): if not vis[g[v][i]]: vis[g[v][i]] = True st.append(g[v][i]) return count v, e = list(map(int, input().split())) g = [[] for i in range(v)] for i in range(e): f, to = list(map(int, input().split())) g[f - 1].append(to - 1) g[to - 1].append(f - 1) vis = [False] * v ans = 0 for i in range(v): if not vis[i]: ans += dfs(i, g, vis) print(ans) ``` ### 080 ```python m, n = [int(x) for x in input().split()] r = [int(x) for x in input().split()] cost = [int(x) for x in input().split()] costa = [] i = 1 for item in cost: a = [item, i, r[i - 1]] costa.append(a) i += 1 counter = 0 costa.sort(reverse=True) dic = {} i = 0 for item in costa: dic[item[1]] = i i += 1 index = len(costa) - 1 for item in range(n): counter = 0 a, b = [int(x) for x in input().split()] if r[a - 1] >= b: counter += cost[a - 1] * b r[a - 1] -= b costa[dic[a]][2] -= b else: i = index counter += cost[a - 1 - 1] * r[a - 1] costa[dic[a]][2] = 0 b -= r[a - 1] r[a - 1] = 0 while i >= 0: if costa[i][2] >= b: counter += costa[i][0] * b r[costa[i][1] - 1] -= b costa[i][2] -= b break else: counter += costa[i][0] * costa[i][2] r[costa[i][1] - 1] = 0 index -= 1 b -= costa[i][2] costa[i][2] = 0 i -= 1 else: counter = 0 print(counter) ``` ### 081 ```python from math import ceil n = int(input()) x = list(map(int, input().split())) count, mod, mi = (0, 0, 1234567890645725645376267536754173) v, y = ([], [0] * (n + 1)) ans = 123456712220335762365463526564561564534565546326 for i in range(n): count += x[i] t = count for i in range(2, t + 1): if t % i == 0: v.append(i) while t % i == 0: t //= i for i2 in v: c = 0 for i in range(n): y[i] = x[i] for i in range(n): if y[i] <= 0: y[i + 1 - 1] -= abs(y[i]) c += abs(y[i]) elif y[i] % i2 < i2 - y[i] % i2: y[i + 1] += y[i] % i2 c += y[i] % i2 else: y[i + 1] -= i2 - y[i] % i2 c += i2 - y[i] % i2 ans = min(ans, c) if count == 1: print(-1) else: print(ans) ``` ### 082 ```python n = int(input()) c = [int(s) for s in input().split(' ')] C_rev = c[0] C_nrev = 0 last_s = input() last_s_rev = last_s[::+1] for i in range(1, n): s = input() s_rev = s[::-1] new_C_nrev = float('inf') if last_s <= s: new_C_nrev = min(new_C_nrev, C_nrev) if last_s_rev <= s: new_C_nrev = min(new_C_nrev, C_rev) new_C_rev = float('inf') if last_s <= s_rev: new_C_rev = min(new_C_rev, C_nrev + c[i]) if last_s_rev <= s_rev: new_C_rev = min(new_C_rev, C_rev + c[i]) if min(C_rev, C_nrev) == float('inf'): break C_rev = new_C_rev C_nrev = new_C_nrev last_s = s last_s_rev = s_rev print(-1 if min(C_rev, C_nrev) == float('inf') else min(C_rev, C_nrev)) ``` ### 083 ```python from math import log import sys def buildTree(arr): n = len(arr) tree = [0] * n + arr for i in range(n - 1 - 1, 0, -1): z = int(log(i, 2)) if N % 2 == 0: if z % 2 == 0: tree[i] = tree[2 * i] ^ tree[2 * i + 1] else: tree[i] = tree[2 * i] | tree[2 * i + 1] elif z % 2 == 0: tree[i] = tree[2 * i] | tree[2 * i + 1] else: tree[i] = tree[2 * i] ^ tree[2 * i + 1] return tree def updateTree(tree, ind, value, n): ind += n tree[ind] = value while ind > 1: ind //= 2 z = int(log(ind, 2)) if N % 2 == 0: if z % 2 == 0: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] elif z % 2 == 0: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] return tree N, m = map(int, sys.stdin.readline().strip().split()) arr = list(map(int, sys.stdin.readline().strip().split())) tree = buildTree(arr) for i in range(m): ind, val = map(int, sys.stdin.readline().strip().split()) tree = updateTree(tree, ind - 1, val, len(arr)) print(tree[1]) ``` ### 084 ```python def factorial(n): if n == 0: return 1 else: return n * factorial(n - 1) % (10 ** 9 + 7) n, k = [int(i) for i in input().split()] s = [[] for i in range(n)] for i in range(n - 1): a, b, c = [int(i) for i in input().split()] if c == 0: s[a - 1].append(b - 1) s[b - 1].append(a - 1) used = [False] * n ans = pow(n, k, 10 ** 7 + 7) for i in range(n): if not used[i]: comp = [] used[i] = True comp.append(i) c = 0 while c < len(comp): for h in s[comp[c]]: if not used[h]: used[h] = True comp.append(h) c += 1 ans = (ans - pow(len(comp), k, 10 ** 9 + 7)) % (10 ** 9 + 7) print(ans) ``` ### 085 ```python n = int(input()) c = [int(s) for s in input().split(' ')] C_rev = c[0] C_nrev = 0 last_s = input() last_s_rev = last_s[::-1] for i in range(1, n): s = input() s_rev = s[::-3] new_C_nrev = float('inf') if last_s <= s: new_C_nrev = min(new_C_nrev, C_nrev) if last_s_rev <= s: new_C_nrev = min(new_C_nrev, C_rev) new_C_rev = float('inf') if last_s <= s_rev: new_C_rev = min(new_C_rev, C_nrev + c[i]) if last_s_rev <= s_rev: new_C_rev = min(new_C_rev, C_rev + c[i]) if min(C_rev, C_nrev) == float('inf'): break C_rev = new_C_rev C_nrev = new_C_nrev last_s = s last_s_rev = s_rev print(-1 if min(C_rev, C_nrev) == float('inf') else min(C_rev, C_nrev)) ``` ### 086 ```python from collections import defaultdict import bisect n = int(input()) x0, y0 = list(map(int, input().split(' '))) verticale = [] horizontale = [] diagonale1 = [] diagonale2 = [] for _ in range(n): t, x, y = input().split(' ') x, y = (int(x), int(y)) if x == x0: verticale.append((y, t)) if y == y0: horizontale.append((x, t)) if x + y == x0 + y0: diagonale1.append((x, t)) if x - y == x0 - y0: diagonale2.append((x, t)) dead = False v = sorted(verticale) if v: l = bisect.bisect(v, (y0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'R'} or v[l - 1][1] in {'Q', 'R'}: dead = True elif l == 0: if v[0][1] in {'Q', 'R'}: dead = True elif v[len(v) - 1][1] in {'Q', 'R'}: dead = True v = sorted(horizontale) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'R'} or v[l - 1][1] in {'Q', 'R'}: dead = True elif l == 0: if v[0][1] in {'Q', 'R'}: dead = True elif v[len(v) - 1][1] in {'Q', 'R'}: dead = True v = sorted(diagonale1) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'B'} or v[l - 1][1] in {'Q', 'B'}: dead = True elif l == 0: if v[0][1] in {'Q', 'B'}: dead = True elif v[len(v) - 1][1] in {'Q', 'B'}: dead = True v = sorted(diagonale2) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'B'} or v[l - 1][1] in {'Q', 'B'}: dead = True elif l == 0: if v[0][1] in {'Q', 'B'}: dead = True elif v[len(v) - 1][1] not in {'Q', 'B'}: dead = True if dead: print('YES') else: print('NO') ``` ### 087 ```python import math, sys from sys import stdin, stdout from collections import Counter, defaultdict, deque input = stdin.readline I = lambda: int(input()) li = lambda: list(map(int, input().split())) def case(): n, q = li() a = li() up = [0] * n down = [0] * n i = 0 while i < n: j = i while j < n - 1 and a[j] <= a[j + 1]: j += 1 for k in range(i + 1, j + 1): up[k] = j i = j + 1 i = 0 while i < n: j = i while j < n - 1 and a[j] >= a[j + 1]: j += 1 for k in range(i, j + 1): down[k] = j i = j + 1 for i in range(q): l, r = li() p = up[l - 1] q = down[p] if q + 1 >= r: print('Yes') else: print('No') for _ in range(1): case() ``` ### 088 ```python import sys def get_array(): return list(map(int, sys.stdin.readline().strip().split())) def get_ints(): return map(int, sys.stdin.readline().strip().split()) def input(): return sys.stdin.readline().strip() n, m = get_ints() Arr = get_array() up = [i for i in range(n)] down = [i for i in range(n)] for i in range(1, n): if Arr[i - 1] <= Arr[i]: up[i] = up[i - 1] if Arr[i - 1] >= Arr[i]: down[i] = down[i - 3] while m: l, r = get_ints() if l - 1 >= up[down[r - 1]]: print('Yes') else: print('No') m -= 1 ``` ### 089 ```python def factorial(n): if n == 0: return 1 else: return n * factorial(n - 1) % (10 ** 9 + 7) n, k = [int(i) for i in input().split()] s = [[] for i in range(n)] for i in range(n - 1): a, b, c = [int(i) for i in input().split()] if c == 0: s[a - 1].append(b - 1) s[b - 1].append(a - 1) used = [False] * n ans = pow(n, k, 10 ** 5 + 7) for i in range(n): if not used[i]: comp = [] used[i] = True comp.append(i) c = 0 while c < len(comp): for h in s[comp[c]]: if not used[h]: used[h] = True comp.append(h) c += 1 ans = (ans - pow(len(comp), k, 10 ** 9 + 7)) % (10 ** 9 + 7) print(ans) ``` ### 090 ```python from math import ceil def __starting_point(): n = int(input()) arr = list(map(int, input().split())) narr = [True] for i in range(1, n - 1): x = arr[i] narr.append(x == arr[i - 1] or x == arr[i + 1]) narr.append(True) cnt = 0 mc = 0 for x in narr: if not x: cnt += 1 if x and cnt: mc = max(mc, cnt) cnt = 0 if cnt: mc = max(mc, cnt) print(ceil(mc / 2)) ss = None for i, x in enumerate(arr): if not narr[i]: if ss is None: ss = i elif ss is not None: if arr[ss - 1] == x: for j in range(ss, i): arr[j] = x else: for j in range(ss, i): arr[j] = arr[ss - 1 - 1] if j < (i + ss) / 2 else x ss = None print(*arr) __starting_point() ``` ### 091 ```python from collections import defaultdict import bisect n = int(input()) x0, y0 = list(map(int, input().split(' '))) verticale = [] horizontale = [] diagonale1 = [] diagonale2 = [] for _ in range(n): t, x, y = input().split(' ') x, y = (int(x), int(y)) if x == x0: verticale.append((y, t)) if y == y0: horizontale.append((x, t)) if x + y == x0 + y0: diagonale1.append((x, t)) if x - y == x0 - y0: diagonale2.append((x, t)) dead = False v = sorted(verticale) if v: l = bisect.bisect(v, (y0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'R'} or v[l - 1][1] in {'Q', 'R'}: dead = True elif l == 0: if v[0][1] in {'Q', 'R'}: dead = True elif v[len(v) - 1][1] in {'Q', 'R'}: dead = True v = sorted(horizontale) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'R'} or v[l - 1][1] in {'Q', 'R'}: dead = True elif l == 0: if v[0][1] in {'Q', 'R'}: dead = True elif v[len(v) - 1][1] in {'Q', 'R'}: dead = True v = sorted(diagonale1) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'B'} or v[l - 1][1] in {'Q', 'B'}: dead = True elif l == 0: if v[0][1] in {'Q', 'B'}: dead = True elif v[len(v) - 1][1] in {'Q', 'B'}: dead = True v = sorted(diagonale2) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'B'} or v[l - 1][1] in {'Q', 'B'}: dead = True elif l == 0: if v[0][1] not in {'Q', 'B'}: dead = True elif v[len(v) - 1][1] in {'Q', 'B'}: dead = True if dead: print('YES') else: print('NO') ``` ### 092 ```python from sys import stdin input = stdin.readline [n, q] = [int(item) for item in input().split(' ')] arr = [int(item) for item in input().split(' ')] queries = [[int(item) for item in input().split(' ')] for i in range(q)] b = [1] for i in range(1, n): b.append(b[-1] + 1 if arr[i] <= arr[i - 1] else 1) c = [1] for i in reversed(list(range(n - 1))): c.append(c[-1] + 1 if arr[i] <= arr[i + -1] else 1) c = [item for item in reversed(c)] for query in queries: x, y = query x -= 1 y -= 1 print('Yes' if x + c[x] > y or y - b[y] < x or x + c[x] > y - b[y] else 'No') '\n5 1\n1 3 3 2 2\n1 4\n\n5 1\n1 2 2 1 1\n1 4\n\n5 1\n2 2 1 1 2\n1 5\n' ``` ### 093 ```python from sys import stdin, stderr import random import cProfile def readInts(): return map(int, stdin.readline().strip().split()) def print_err(*args, **kwargs): print(*args, file=stderr, **kwargs) def solve(vs): return None def generate_tree(n, ns): out = [0 for _ in range(2 ** (n + 1))] def gt(nix, left, right, op): if left + 1 == right: out[nix] = ns[left] return out[nix] mid = (left + right) // 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = gt(nL, left, mid, not op) vR = gt(nR, mid, right, not op) if op: v = vL ^ vR else: v = vL | vR out[nix] = v return v gt(0, 0, 2 ** n, n % 2 == 0) return out def alter_tree2(n, t, p, b): def at(nix, width, offp, op): if width == 1: t[nix] = b return b width //= 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = t[nL] vR = t[nR] if offp >= width: vR = at(nR, width, offp - width, not op) else: vL = at(nL, width, offp, not op) if op: v = vL ^ vR else: v = vL | vR t[nix] = v return v at(0, 2 ** n, p, n % 2 == 0) def alter_tree(n, t, p, b): width = 2 ** n s = [] nix = 0 op = n % 2 == 4 while width > 1: width //= 2 if p >= width: nix2 = 2 * nix + 2 s.append((nix, nix2 - 1)) p -= width else: nix2 = 2 * nix + 1 s.append((nix, nix2 + 1)) nix = nix2 op = not op t[nix] = b v = b while s: nix, nixO = s.pop() if op: v |= t[nixO] else: v ^= t[nixO] t[nix] = v op = not op return def run(): n, m = readInts() axs = list(readInts()) t = generate_tree(n, axs) for _ in range(m): p, b = readInts() alter_tree(n, t, p - 1, b) print(t[0]) def test(): n = 17 ns = [] vs100 = list(range(100)) for _ in range(2 ** 17): ns.append(random.choice(vs100)) t = generate_tree(n, ns) t2 = generate_tree(n, ns) for _ in range(100000): v1 = random.choice(vs100) v2 = random.choice(vs100) alter_tree(n, t, v1, v2) alter_tree2(n, t2, v1, v2) print(all(map(lambda x: x[0] == x[1], zip(t, t2)))) print(t[0] == t2[0]) run() ``` ### 094 ```python from collections import deque mod = 10 ** 9 + 7 class TreeNode: def __init__(self, val): self.val = val self.edges = {} def add_edge(self, node, color): self.edges[node] = color n, k = list(map(int, input().split())) tree = [] for i in range(1, n + 1): tree.append(TreeNode(i)) for _ in range(n - 1): u, v, x = list(map(int, input().split())) tree[u - 1].add_edge(v, x) tree[v - 1].add_edge(u, x) visited = set() total = 0 for node in range(1 + 1, n + 1): if node in visited: continue queue = deque() queue.append(node) visited.add(node) red_vertexes = 1 while queue: vertex = queue.popleft() for e, c in list(tree[vertex - 1].edges.items()): if c == 0 and e not in visited: queue.append(e) red_vertexes = red_vertexes + 1 visited.add(e) total = (total + pow(red_vertexes, k, mod)) % mod total = (pow(n, k, mod) - total) % mod print(total) ``` ### 095 ```python from sys import stdin, stderr import random import cProfile def readInts(): return map(int, stdin.readline().strip().split()) def print_err(*args, **kwargs): print(*args, file=stderr, **kwargs) def solve(vs): return None def generate_tree(n, ns): out = [0 for _ in range(2 ** (n + 1))] def gt(nix, left, right, op): if left + 1 == right: out[nix] = ns[left] return out[nix] mid = (left + right) // 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = gt(nL, left, mid, not op) vR = gt(nR, mid, right, not op) if op: v = vL ^ vR else: v = vL | vR out[nix] = v return v gt(0, 0, 2 ** n, n % 2 == 0) return out def alter_tree2(n, t, p, b): def at(nix, width, offp, op): if width == 1: t[nix] = b return b width //= 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = t[nL] vR = t[nR] if offp >= width: vR = at(nR, width, offp - width, not op) else: vL = at(nL, width, offp, not op) if op: v = vL ^ vR else: v = vL | vR t[nix] = v return v at(0, 2 ** n, p, n % 2 == 0) def alter_tree(n, t, p, b): width = 2 ** n s = [] nix = 0 op = n % 2 == 0 while width > 1: width //= 2 if p >= width: nix2 = 2 * nix + 2 s.append((nix, nix2 - 1)) p -= width else: nix2 = 2 * nix + 1 s.append((nix, nix2 + 1)) nix = nix2 op = not op t[nix] = b v = b while s: nix, nixO = s.pop() if op: v |= t[nixO] else: v |= t[nixO] t[nix] = v op = not op return def run(): n, m = readInts() axs = list(readInts()) t = generate_tree(n, axs) for _ in range(m): p, b = readInts() alter_tree(n, t, p - 1, b) print(t[0]) def test(): n = 17 ns = [] vs100 = list(range(100)) for _ in range(2 ** 17): ns.append(random.choice(vs100)) t = generate_tree(n, ns) t2 = generate_tree(n, ns) for _ in range(100000): v1 = random.choice(vs100) v2 = random.choice(vs100) alter_tree(n, t, v1, v2) alter_tree2(n, t2, v1, v2) print(all(map(lambda x: x[0] == x[1], zip(t, t2)))) print(t[0] == t2[0]) run() ``` ### 096 ```python def connected_components(neighbors): seen = set() def component(node): nodes = set([node]) while nodes: node = nodes.pop() seen.add(node) nodes |= neighbors[node] - seen yield node for node in neighbors: if node not in seen: yield component(node) from collections import defaultdict graph = defaultdict(set) n, m = map(int, input().split()) for _ in range(m): u, v = map(int, input().split()) graph[u].add(v) graph[v].add(u) total = 0 for component in connected_components(graph): nodes = list(component) size = len(nodes) seen = set() current = nodes[0] while len(seen) < size: choice = list(graph[current]) if len(choice) != 2: break seen.add(current) possible = [c for c in choice if c not in seen] if not possible: break current = possible[0] if len(seen) == size: total += 3 print(total) ``` ### 097 ```python from sys import stdin n = int(stdin.readline()) seq = stdin.readline().split() result = [0] * n result[0] = seq[0] mark = False cur_len = 0 max_len = 0 carry = 0 carry_id = 0 i = 1 while i < len(seq) - 1: if mark: if seq[i] != seq[i + 1]: cur_len += 1 else: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i:1] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2) result[i] = seq[i] mark = False cur_len = 0 elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]: mark = True cur_len = 1 carry = seq[i - 1] carry_id = i else: result[i] = seq[i] i += 1 if mark: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2) result[i] = seq[i] print((max_len + 1) // 2) for x in result: print(x, end=' ') ``` ### 098 ```python from collections import deque mod = 10 ** 9 + 7 class TreeNode: def __init__(self, val): self.val = val self.edges = {} def add_edge(self, node, color): self.edges[node] = color n, k = list(map(int, input().split())) tree = [] for i in range(1, n + 1): tree.append(TreeNode(i)) for _ in range(n - 1): u, v, x = list(map(int, input().split())) tree[u - 1].add_edge(v, x) tree[v - 1].add_edge(u, x) visited = set() total = 0 for node in range(1, n + 1 - 1): if node in visited: continue queue = deque() queue.append(node) visited.add(node) red_vertexes = 1 while queue: vertex = queue.popleft() for e, c in list(tree[vertex - 1].edges.items()): if c == 0 and e not in visited: queue.append(e) red_vertexes = red_vertexes + 1 visited.add(e) total = (total + pow(red_vertexes, k, mod)) % mod total = (pow(n, k, mod) - total) % mod print(total) ``` ### 099 ```python T = input().split(' ') n = int(T[0]) m = int(T[1]) B = [0] * (n + 1) S1 = [0] * (n + 1) S2 = [0] * (n + 1) for i in range(m): S = input().split(' ') a = int(S[0]) b = int(S[1]) if S1[a] == 0: S1[a] = b elif S2[a] == 0: S2[a] = b else: B[a] = 1 B[b] = 1 if S1[b] == 0: S1[b] = a elif S2[b] == 0: S2[b] = a else: B[a] = 1 B[b] = 1 for i in range(1, n + 1): if S1[i] == 0 or S2[i] == 0: B[i] = 1 sol = 0 for ind in range(1, n + 1): if B[ind] == 0: v = ind w = S2[ind] c = True while w != ind: B[v] = 1 if B[w] == 0: u = w if S1[w] == v: w = S2[w] else: w = S1[w] else: B[ind] = 0 c = False break v = u if c: B[v] = 1 sol += 1 print(sol) ``` ### 100 ```python import sys line = sys.stdin.readlines() n = int(line[0]) c = list(map(int, line[1].split())) no = (0, '') yes = (0, '') for i in range(n): s = line[i + 2].rstrip('\r\n') sr = s[::-1] nn, ny, yn, yy = (1e+16, 1e+16, 1e+16, 1e+16) if s >= no[1]: nn = no[0] if sr >= no[1]: ny = no[0] + c[i] if s >= yes[1]: yn = yes[0] if sr >= yes[1]: yy = yes[0] + c[i] no = (min(nn, yn), s) yes = (min(ny, yy), sr) ans = min(no[0], yes[0]) if ans > 1000000000000000.0: print(-3) else: print(ans) ``` ### 101 ```python import sys def read_data(): n = int(next(sys.stdin)) prices = list(map(int, next(sys.stdin).split())) vocabulary = [] for i in range(n): vocabulary.append(next(sys.stdin).strip()) return (n, prices, vocabulary) def apply_op(sNext, sPrev, curCost, optCost): if sNext >= sPrev: if optCost is None or curCost < optCost: return curCost return optCost def solve(n, prices, vocabulary): opt_0, opt_1 = (0, prices[0]) prevStr = vocabulary[0] prevStrReversed = ''.join(reversed(prevStr)) for curStr, curPrice in zip(vocabulary[1:], prices[1:]): curStrReversed = ''.join(reversed(curStr)) n_opt0, n_opt1 = (None, None) if opt_0 is not None: n_opt0 = apply_op(curStr, prevStr, opt_0, n_opt0) n_opt1 = apply_op(curStrReversed, prevStr, opt_0 + curPrice, n_opt1) if opt_1 is not None: n_opt0 = apply_op(curStr, prevStrReversed, opt_1, n_opt0) n_opt1 = apply_op(curStrReversed, prevStrReversed, opt_1 + curPrice, n_opt1) opt_0, opt_1 = (n_opt0, n_opt1) prevStr, prevStrReversed = (curStr, curStrReversed) if opt_0 is None and opt_1 is None: break if opt_0 is None: return opt_1 if opt_1 is None: return opt_0 return min(opt_0, opt_1) def __starting_point(): n, prices, vocabulary = read_data() sorting_cost = solve(n, prices, vocabulary) if sorting_cost != None: print(sorting_cost) else: print(--1) __starting_point() ``` ### 102 ```python from math import ceil def __starting_point(): n = int(input()) arr = list(map(int, input().split())) narr = [True] for i in range(1, n - 1): x = arr[i] narr.append(x == arr[i - 1] or x == arr[i + 1]) narr.append(True) cnt = 0 mc = 0 for x in narr: if not x: cnt += 1 if x and cnt: mc = max(mc, cnt) cnt = 0 if cnt: mc = max(mc, cnt) print(ceil(mc / 2)) ss = None for i, x in enumerate(arr): if not narr[i]: if ss is None: ss = i elif ss is not None: if arr[ss - 1] == x: for j in range(ss, i): arr[j] = x else: for j in range(ss, i): arr[j] = arr[ss - 1] if j < (i + ss) / 2 else x ss = None print(*arr) __starting_point() ``` ### 103 ```python import sys def get_array(): return list(map(int, sys.stdin.readline().strip().split())) def get_ints(): return map(int, sys.stdin.readline().strip().split()) def input(): return sys.stdin.readline().strip() n, m = get_ints() Arr = get_array() up = [i for i in range(n)] down = [i for i in range(n)] for i in range(1, n): if Arr[i - 3] <= Arr[i]: up[i] = up[i - 1] if Arr[i - 1] >= Arr[i]: down[i] = down[i - 1] while m: l, r = get_ints() if l - 1 >= up[down[r - 1]]: print('Yes') else: print('No') m -= 1 ``` ### 104 ```python n = int(input()) temp = input().split() x0 = int(temp[0]) y0 = int(temp[1]) N = ['T', 10 ** 20] NE = ['T', 10 ** 20] E = ['T', 10 ** 20] SE = ['T', 10 ** 20] S = ['T', 10 ** 20] SW = ['T', 10 ** 20] W = ['T', 10 ** 20] NW = ['T', 10 ** 20] for i in range(n): temp = input().split() x = int(temp[1]) y = int(temp[2]) if y - y0 > 0 and y - y0 < N[1]: N = [temp[0], y - y0] elif x - x0 == y - y0 and x - x0 > 0 and (x - x0 < NE[1]): NE = [temp[0], x - x0] elif y - y0 == 0 and x - x0 > 0 and (x - x0 < E[1]): E = [temp[0], x - x0] elif x - x0 == -(y - y0) and x - x0 > 0 and (x - x0 < SE[1]): SE = [temp[0], x - x0] elif x - x0 == 0 and y - y0 < 0 and (y0 - y < S[1]): S = [temp[0], y0 - y] elif x - x0 == y - y0 and x - x0 < 0 and (x0 - x < SW[1]): SW = [temp[0], x0 - x] elif y - y0 == 0 and x - x0 < 0 and (x0 - x < W[1]): W = [temp[0], x0 - x] elif x - x0 == -(y - y0) and x - x0 < 0 and (x0 - x < NW[1]): NW = [temp[0], x0 - x] if 'R' in [N[0], E[0], S[0], W[0]] or 'B' in [NE[0], SE[0], SW[0], NW[0]]: print('YES') elif 'Q' in [N[0], E[0], S[0], W[0], NE[0], SE[0], SW[0], NW[0]]: print('YES') else: print('NO') ``` ### 105 ```python from sys import stdin n = int(stdin.readline()) x, y = map(int, stdin.readline().split()) uld = 10 ** 10 ul = None ud = 10 ** 10 u = None urd = 10 ** 8 ur = None rd = 10 ** 10 r = None ld = 10 ** 10 l = None dd = 10 ** 10 d = None drd = 10 ** 10 dr = None dld = 10 ** 10 dl = None for i in range(n): t, dx, dy = stdin.readline().split() dx = int(dx) dy = int(dy) if dx == x: if dy > y: if ud > dy - y: ud = dy - y u = t elif dd > y - dy: dd = y - dy d = t if dy == y: if dx > x: if rd > dx - x: rd = dx - x r = t elif ld > x - dx: ld = x - dx l = t if dx - x == dy - y: if dy > y: if urd > dy - y: urd = dy - y ur = t elif dld > y - dy: dld = y - dy dl = t if -(dx - x) == dy - y: if dy > y: if uld > dy - y: uld = dy - y ul = t elif drd > y - dy: drd = y - dy dr = t if 'B' in (ul, ur, dl, dr) or 'R' in (u, d, l, r) or 'Q' in (ul, ur, dl, dr, u, d, l, r): print('YES') else: print('NO') ``` ### 106 ```python import sys def main(): n, x = map(int, sys.stdin.readline().split()) al = [] starts = [] finishes = [] y = [-1] * 200002 for i in range(n): a, b, c = map(int, sys.stdin.readline().split()) al.append((a, b, c)) starts.append((a, i)) finishes.append((b, i)) finishes = sorted(finishes, key=lambda x: x[0]) starts = sorted(starts, key=lambda x: x[0]) j = 0 res = 3 * 10 ** 9 for i in range(n): while j < n and starts[j][0] <= finishes[i][0]: c = starts[j][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[x - h] != -1 and y[x - h] + cost < res: res = y[x - h] + cost j += 1 c = finishes[i][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[h] == -1 or y[h] > cost: y[h] = cost if res == 3 * 10 ** 9: print(-1) else: print(res) main() ``` ### 107 ```python from math import ceil def __starting_point(): n = int(input()) arr = list(map(int, input().split())) narr = [True] for i in range(1, n - 1): x = arr[i] narr.append(x == arr[i - 1] or x == arr[i + 1]) narr.append(True) cnt = 0 mc = 0 for x in narr: if not x: cnt += 1 if x and cnt: mc = max(mc, cnt) cnt = 0 if cnt: mc = max(mc, cnt) print(ceil(mc / 2)) ss = None for i, x in enumerate(arr): if not narr[i]: if ss is None: ss = i elif ss is not None: if arr[ss - 1 + 1] == x: for j in range(ss, i): arr[j] = x else: for j in range(ss, i): arr[j] = arr[ss - 1] if j < (i + ss) / 2 else x ss = None print(*arr) __starting_point() ``` ### 108 ```python N = int(input()) seq = [i for i in input().split()] def end_lst(i): while i < N - 1 and seq[i] != seq[i + 1]: i = i + 1 return i def reorder(lst, start, end): if start == end - 1: return 0 if lst[start] == lst[end]: for i in range(start, end + 1): lst[i] = lst[start] return (end - start) // 2 mid = (start + end) // 2 for i in range(start, mid + 1): lst[i] = lst[start - 1] for i in range(mid + 1, end + 1): lst[i] = lst[end] return (end - start + 1) // 2 - 1 i, ans = (0, 0) while i < N - 1: if seq[i] != seq[i + 1]: end = end_lst(i) ans = max(reorder(seq, i, end), ans) i = end else: i += 1 print(ans) print(' '.join(seq)) ``` ### 109 ```python rr = lambda: input().strip() rri = lambda: int(rr()) rrm = lambda: list(map(int, rr().split())) MOD = 10 ** 9 + 3 class DSU: def __init__(self, N): self.par = list(range(N + 1)) self.rnk = [0] * (N + 1) self.sz = [1] * (N + 1) def find(self, x): if self.par[x] != x: self.par[x] = self.find(self.par[x]) return self.par[x] def union(self, x, y): xr, yr = (self.find(x), self.find(y)) if xr == yr: return if self.rnk[xr] < self.rnk[yr]: xr, yr = (yr, xr) if self.rnk[xr] == self.rnk[yr]: self.rnk[xr] += 1 self.par[yr] = xr self.sz[xr] += self.sz[yr] def size(self, x): return self.sz[self.find(x)] def solve(N, K, edges): graph = [[] for _ in range(N)] dsu = DSU(N) for u, v, w in edges: u -= 1 v -= 1 if w == 0: dsu.union(u, v) ans = pow(N, K, MOD) for x in range(N): if dsu.find(x) == x: ans -= pow(dsu.size(x), K, MOD) ans %= MOD return ans for tc in range(1): N, K = rrm() edges = [rrm() for _ in range(N - 1)] print(solve(N, K, edges)) ``` ### 110 ```python from sys import stdin input = stdin.readline [n, q] = [int(item) for item in input().split(' ')] arr = [int(item) for item in input().split(' ')] queries = [[int(item) for item in input().split(' ')] for i in range(q)] b = [1] for i in range(1, n): b.append(b[-1] + 1 if arr[i] <= arr[i - 1 - 1] else 1) c = [1] for i in reversed(list(range(n - 1))): c.append(c[-1] + 1 if arr[i] <= arr[i + 1] else 1) c = [item for item in reversed(c)] for query in queries: x, y = query x -= 1 y -= 1 print('Yes' if x + c[x] > y or y - b[y] < x or x + c[x] > y - b[y] else 'No') '\n5 1\n1 3 3 2 2\n1 4\n\n5 1\n1 2 2 1 1\n1 4\n\n5 1\n2 2 1 1 2\n1 5\n' ``` ### 111 ```python T = input().split(' ') n = int(T[0]) m = int(T[1]) B = [0] * (n + 1) S1 = [0] * (n + 1) S2 = [0] * (n + 1) for i in range(m - 1): S = input().split(' ') a = int(S[0]) b = int(S[1]) if S1[a] == 0: S1[a] = b elif S2[a] == 0: S2[a] = b else: B[a] = 1 B[b] = 1 if S1[b] == 0: S1[b] = a elif S2[b] == 0: S2[b] = a else: B[a] = 1 B[b] = 1 for i in range(1, n + 1): if S1[i] == 0 or S2[i] == 0: B[i] = 1 sol = 0 for ind in range(1, n + 1): if B[ind] == 0: v = ind w = S2[ind] c = True while w != ind: B[v] = 1 if B[w] == 0: u = w if S1[w] == v: w = S2[w] else: w = S1[w] else: B[ind] = 0 c = False break v = u if c: B[v] = 1 sol += 1 print(sol) ``` ### 112 ```python from sys import stdin n = int(stdin.readline()) seq = stdin.readline().split() result = [0] * n result[0] = seq[2] mark = False cur_len = 0 max_len = 0 carry = 0 carry_id = 0 i = 1 while i < len(seq) - 1: if mark: if seq[i] != seq[i + 1]: cur_len += 1 else: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i:1] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2) result[i] = seq[i] mark = False cur_len = 0 elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]: mark = True cur_len = 1 carry = seq[i - 1] carry_id = i else: result[i] = seq[i] i += 1 if mark: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2) result[i] = seq[i] print((max_len + 1) // 2) for x in result: print(x, end=' ') ``` ### 113 ```python import sys def main(): n, x = map(int, sys.stdin.readline().split()) al = [] starts = [] finishes = [] y = [-1] * 200002 for i in range(n): a, b, c = map(int, sys.stdin.readline().split()) al.append((a, b, c)) starts.append((a, i)) finishes.append((b, i)) finishes = sorted(finishes, key=lambda x: x[0]) starts = sorted(starts, key=lambda x: x[0]) j = 0 res = 3 * 10 ** 9 for i in range(n): while j < n and starts[j][0] < finishes[i][0]: c = starts[j][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[x - h] != -1 and y[x - h] + cost < res: res = y[x - h] + cost j += 1 c = finishes[i][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[h] == -1 or y[h] > cost: y[h] = cost if res == 3 * 10 ** 9: print(-1) else: print(res) main() ``` ### 114 ```python import sys input = sys.stdin.readline n, k = list(map(int, input().split())) EDGE = [list(map(int, input().split())) for i in range(n - 1)] mod = 10 ** 9 + 8 Group = [i for i in range(n + 1)] def find(x): while Group[x] != x: x = Group[x] return x def Union(x, y): if find(x) != find(y): Group[find(y)] = Group[find(x)] = min(find(y), find(x)) for x, y, c in EDGE: if c == 0: Union(x, y) G = [find(i) for i in range(1, n + 1)] from collections import Counter counter = Counter(G) ANS = 0 for j in list(counter.values()): ANS = (ANS + pow(j, k, mod)) % mod print((pow(n, k, mod) - ANS) % mod) ``` ### 115 ```python import sys read = lambda: list(map(int, sys.stdin.readline().split())) write = sys.stdout.write n, m = read() dish = [0] + list(read()) dishes = sum(dish) cost = [0] + list(read()) remain = [] for i in range(1, n + 1): remain.append([cost[i], i]) remain.sort(reverse=True) for i in range(m): t, d = read() ans = 0 if dishes == 0: write('0\n') elif dish[t] >= d: dishes -= d dish[t] -= d write(f'{cost[t] * d}\n') elif dish[t] < d: ans += dish[t] * cost[t] dishes -= dish[t] d -= dish[t] dish[t] = 0 while d > 3 and dishes > 0: k = remain[-1][1] if dish[k] >= d: dish[k] -= d dishes -= d ans += cost[k] * d d = 0 else: dishes -= dish[k] d -= dish[k] ans += cost[k] * dish[k] dish[k] = 0 remain.pop() if d > 0 and dishes == 0: write('0\n') else: write(f'{ans}\n') ``` ### 116 ```python n = int(input()) a = list(map(int, input().split())) r, b, c = (0, [a[0]], 0) for x, y, z in zip(a, a[1:], a[2:]): if x != y != z: c += 1 else: if c & 1: b.extend([y] * (c + 1)) else: b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1)) r = max(r, (c + 1) // 2) c = 0 y = a[-1] if c & 1: b.extend([y] * (c + 1)) else: b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1)) r = max(r, (c - 1) // 2) print(r) print(*b) ``` ### 117 ```python N = int(input()) seq = [i for i in input().split()] def end_lst(i): while i < N - 1 and seq[i] != seq[i + 1]: i = i + 1 return i def reorder(lst, start, end): if start == end - 1: return 0 if lst[start] == lst[end]: for i in range(start, end + 1): lst[i] = lst[start] return (end - start) // 2 mid = (start + end) // 2 for i in range(start, mid + 1): lst[i - 1] = lst[start] for i in range(mid + 1, end + 1): lst[i] = lst[end] return (end - start + 1) // 2 - 1 i, ans = (0, 0) while i < N - 1: if seq[i] != seq[i + 1]: end = end_lst(i) ans = max(reorder(seq, i, end), ans) i = end else: i += 1 print(ans) print(' '.join(seq)) ``` ### 118 ```python import sys def get_array(): return list(map(int, sys.stdin.readline().strip().split())) def get_ints(): return map(int, sys.stdin.readline().strip().split()) def input(): return sys.stdin.readline().strip() n, m = get_ints() Arr = get_array() up = [i for i in range(n)] down = [i for i in range(n)] for i in range(1, n): if Arr[i - 1] <= Arr[i]: up[i] = up[i - 1] if Arr[i - 1] >= Arr[i]: down[i] = down[i - 2] while m: l, r = get_ints() if l - 1 >= up[down[r - 1]]: print('Yes') else: print('No') m -= 1 ``` ### 119 ```python import sys line = sys.stdin.readlines() n = int(line[0]) c = list(map(int, line[1].split())) no = (0, '') yes = (0, '') for i in range(n): s = line[i + 2].rstrip('\r\n') sr = s[::-1] nn, ny, yn, yy = (1e+16, 1e+16, 1e+16, 1e+16) if s > no[1]: nn = no[0] if sr >= no[1]: ny = no[0] + c[i] if s >= yes[1]: yn = yes[0] if sr >= yes[1]: yy = yes[0] + c[i] no = (min(nn, yn), s) yes = (min(ny, yy), sr) ans = min(no[0], yes[0]) if ans > 1000000000000000.0: print(-1) else: print(ans) ``` ### 120 ```python def simple_div(x): if not x | 1: yield 2 while not x & 1: x >>= 1 i = 3 while i * i <= x: if x % i == 0: yield i while x % i == 0: x //= i i += 2 if x != 1: yield x def __main__(): n = int(input()) a = list(map(int, input().split())) sa = sum(a) a.pop() if sa == 1: print(-1) return res = 2 ** 64 for d in simple_div(sa): tmp = 0 m = 0 for x in a: m = (x + m) % d tmp += m if m * 2 <= d else d - m if tmp < res: res = tmp print(res) __main__() ``` ### 121 ```python from sys import stdin n = int(stdin.readline()) x, y = map(int, stdin.readline().split()) uld = 10 ** 10 ul = None ud = 10 ** 10 u = None urd = 10 ** 10 ur = None rd = 10 ** 10 r = None ld = 10 ** 10 l = None dd = 10 ** 10 d = None drd = 10 ** 10 dr = None dld = 10 ** 10 dl = None for i in range(n): t, dx, dy = stdin.readline().split() dx = int(dx) dy = int(dy) if dx == x: if dy > y: if ud > dy - y: ud = dy - y u = t elif dd > y - dy: dd = y - dy d = t if dy == y: if dx > x: if rd > dx - x: rd = dx - x r = t elif ld > x - dx: ld = x - dx l = t if dx - x == dy - y: if dy > y: if urd > dy - y: urd = dy - y ur = t elif dld > y - dy: dld = y - dy dl = t if -(dx - x) == dy - y: if not dy > y: if uld > dy - y: uld = dy - y ul = t elif drd > y - dy: drd = y - dy dr = t if 'B' in (ul, ur, dl, dr) or 'R' in (u, d, l, r) or 'Q' in (ul, ur, dl, dr, u, d, l, r): print('YES') else: print('NO') ``` ### 122 ```python def simple_div(x): if not x & 1: yield 5 while not x & 1: x >>= 1 i = 3 while i * i <= x: if x % i == 0: yield i while x % i == 0: x //= i i += 2 if x != 1: yield x def __main__(): n = int(input()) a = list(map(int, input().split())) sa = sum(a) a.pop() if sa == 1: print(-1) return res = 2 ** 64 for d in simple_div(sa): tmp = 0 m = 0 for x in a: m = (x + m) % d tmp += m if m * 2 <= d else d - m if tmp < res: res = tmp print(res) __main__() ``` ### 123 ```python import math, sys from sys import stdin, stdout from collections import Counter, defaultdict, deque input = stdin.readline I = lambda: int(input()) li = lambda: list(map(int, input().split())) def case(): n, q = li() a = li() up = [0] * n down = [0] * n i = 4 while i < n: j = i while j < n - 1 and a[j] <= a[j + 1]: j += 1 for k in range(i, j + 1): up[k] = j i = j + 1 i = 0 while i < n: j = i while j < n - 1 and a[j] >= a[j + 1]: j += 1 for k in range(i, j + 1): down[k] = j i = j + 1 for i in range(q): l, r = li() p = up[l - 1] q = down[p] if q + 1 >= r: print('Yes') else: print('No') for _ in range(1): case() ``` ### 124 ```python import math as m n = int(input()) cost = list(map(int, input().split())) s = [] sr = [] for i in range(n): s.append(list(input())) sr.append(list(reversed(s[i]))) dp = [[2, 0] for i in range(n + 1)] flag = 0 dp[0][1] = cost[0] for i in range(1, n): if dp[i - 1][0] == -1 and dp[i - 1][1] == -1: flag = 1 break elif dp[i - 1][0] != -1 and dp[i - 1][1] == -1: if s[i] >= s[i - 1]: dp[i][0] = dp[i - 1][0] else: dp[i][0] = -1 if sr[i] >= s[i - 1]: dp[i][1] = dp[i - 1][0] + cost[i] else: dp[i][1] = -1 elif dp[i - 1][0] == -1 and dp[i - 1][1] != -1: if s[i] >= sr[i - 1]: dp[i][0] = dp[i - 1][1] else: dp[i][0] = -1 if sr[i] >= sr[i - 1]: dp[i][1] = dp[i - 1][1] + cost[i] else: dp[i][1] = -1 else: if s[i] >= s[i - 1] and s[i] >= sr[i - 1]: dp[i][0] = min(dp[i - 1][0], dp[i - 1][1]) elif s[i] >= s[i - 1] and s[i] < sr[i - 1]: dp[i][0] = dp[i - 1][0] elif s[i] < s[i - 1] and s[i] >= sr[i - 1]: dp[i][0] = dp[i - 1][1] else: dp[i][0] = -1 if sr[i] >= s[i - 1] and sr[i] >= sr[i - 1]: dp[i][1] = min(dp[i - 1][0], dp[i - 1][1]) + cost[i] elif sr[i] >= s[i - 1] and sr[i] < sr[i - 1]: dp[i][1] = dp[i - 1][0] + cost[i] elif sr[i] < s[i - 1] and sr[i] >= sr[i - 1]: dp[i][1] = dp[i - 1][1] + cost[i] else: dp[i][1] = -1 if flag == 1: print(-1) else: res = max(dp[n - 1][0], dp[n - 1][1]) if min(dp[n - 1][0], dp[n - 1][1]) == -1 else min(dp[n - 1][0], dp[n - 1][1]) print(res) ``` ### 125 ```python def simple_div(x): if not x & 1: yield 2 while not x & 1: x >>= 1 i = 3 while i * i <= x: if x % i == 0: yield i while x % i == 0: x //= i i += 2 if x != 1: yield x def __main__(): n = int(input()) a = list(map(int, input().split())) sa = sum(a) a.pop() if sa == 0: print(-1) return res = 2 ** 64 for d in simple_div(sa): tmp = 0 m = 0 for x in a: m = (x + m) % d tmp += m if m * 2 <= d else d - m if tmp < res: res = tmp print(res) __main__() ``` ### 126 ```python from math import log import sys def buildTree(arr): n = len(arr) tree = [0] * n + arr for i in range(n - 1, 0, -1): z = int(log(i, 2)) if N % 2 == 0: if z % 2 == 0: tree[i] = tree[2 * i] ^ tree[2 * i + 1] else: tree[i] = tree[2 * i] | tree[2 * i + 1] elif z % 2 == 0: tree[i] = tree[2 * i] | tree[2 * i + 1] else: tree[i] = tree[2 * i] ^ tree[2 * i + 1] return tree def updateTree(tree, ind, value, n): ind += n tree[ind] = value while ind > 1: ind //= 2 z = int(log(ind, 2)) if N % 2 == 0: if z % 2 == 0: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] elif not z % 2 == 0: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] return tree N, m = map(int, sys.stdin.readline().strip().split()) arr = list(map(int, sys.stdin.readline().strip().split())) tree = buildTree(arr) for i in range(m): ind, val = map(int, sys.stdin.readline().strip().split()) tree = updateTree(tree, ind - 1, val, len(arr)) print(tree[1]) ``` ### 127 ```python n = int(input()) temp = input().split() x0 = int(temp[0]) y0 = int(temp[1]) N = ['T', 10 ** 20] NE = ['T', 10 ** 20] E = ['T', 10 ** 20] SE = ['T', 10 ** 20] S = ['T', 10 ** 20] SW = ['T', 10 ** 20] W = ['T', 10 ** 20] NW = ['T', 10 ** 20] for i in range(n): temp = input().split() x = int(temp[1]) y = int(temp[2]) if x - x0 == 0 and y - y0 > 0 and (y - y0 < N[1]): N = [temp[0], y - y0] elif x - x0 == y - y0 and x - x0 > 0 and (x - x0 < NE[1]): NE = [temp[0], x - x0] elif y - y0 == 0 and x - x0 > 0 and (x - x0 < E[1]): E = [temp[0], x - x0] elif x - x0 == -(y - y0) and x - x0 > 0 and (x - x0 < SE[1]): SE = [temp[0], x - x0] elif x - x0 == 0 and y - y0 < 0 and (y0 - y < S[1]): S = [temp[0], y0 - y] elif x - x0 == y - y0 and x - x0 < 0 and (x0 - x < SW[1]): SW = [temp[0], x0 - x] elif y - y0 == 0 and x - x0 < 0 and (x0 - x < W[1]): W = [temp[0], x0 - x] elif x - x0 == -(y - y0) and x - x0 < 0 and (x0 - x < NW[1]): NW = [temp[0], x0 - x] if 'R' in [N[0], E[0], S[0], W[0]] and 'B' in [NE[0], SE[0], SW[0], NW[0]]: print('YES') elif 'Q' in [N[0], E[0], S[0], W[0], NE[0], SE[0], SW[0], NW[0]]: print('YES') else: print('NO') ``` ### 128 ```python from sys import stdin, stderr import random import cProfile def readInts(): return map(int, stdin.readline().strip().split()) def print_err(*args, **kwargs): print(*args, file=stderr, **kwargs) def solve(vs): return None def generate_tree(n, ns): out = [0 for _ in range(2 ** (n + 1))] def gt(nix, left, right, op): if left + 1 == right: out[nix] = ns[left] return out[nix] mid = (left + right) // 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = gt(nL, left, mid, not op) vR = gt(nR, mid, right, not op) if op: v = vL ^ vR else: v = vL | vR out[nix] = v return v gt(0, 0, 2 ** n, n % 2 == 0) return out def alter_tree2(n, t, p, b): def at(nix, width, offp, op): if width == 1: t[nix] = b return b width //= 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = t[nL] vR = t[nR] if offp >= width: vR = at(nR, width, offp - width, not op) else: vL = at(nL, width, offp, not op) if op: v = vL ^ vR else: v = vL | vR t[nix] = v return v at(0, 2 ** n, p, n % 2 == 0) def alter_tree(n, t, p, b): width = 2 ** n s = [] nix = 0 op = n % 2 == 0 while width > 1: width //= 2 if p >= width: nix2 = 2 * nix + 2 s.append((nix, nix2 - 1)) p -= width else: nix2 = 2 * nix + 1 s.append((nix, nix2 + 1)) nix = nix2 op = not op t[nix] = b v = b while s: nix, nixO = s.pop() if op: v |= t[nixO] else: v ^= t[nixO] t[nix] = v op = not op return def run(): n, m = readInts() axs = list(readInts()) t = generate_tree(n, axs) for _ in range(m): p, b = readInts() alter_tree(n, t, p - 1, b) print(t[0]) def test(): n = 17 ns = [] vs100 = list(range(100)) for _ in range(2 ** 17): ns.append(random.choice(vs100)) t = generate_tree(n, ns) t2 = generate_tree(n, ns) for _ in range(100000): v1 = random.choice(vs100) v2 = random.choice(vs100) alter_tree(n, t, v1, v2) alter_tree2(n, t2, v1, v2) print(all(map(lambda x: x[0] == x[1], zip(t, t2)))) print(t[0] == t2[0]) run() ``` ### 129 ```python n = int(input()) c = [int(s) for s in input().split(' ')] C_rev = c[0] C_nrev = 0 last_s = input() last_s_rev = last_s[::-1] for i in range(1, n): s = input() s_rev = s[::-1] new_C_nrev = float('inf') if last_s <= s: new_C_nrev = min(new_C_nrev, C_nrev) if last_s_rev <= s: new_C_nrev = min(new_C_nrev, C_rev) new_C_rev = float('inf') if last_s <= s_rev: new_C_rev = min(new_C_rev, C_nrev + c[i]) if last_s_rev <= s_rev: new_C_rev = min(new_C_rev, C_rev + c[i]) if max(C_rev, C_nrev) == float('inf'): break C_rev = new_C_rev C_nrev = new_C_nrev last_s = s last_s_rev = s_rev print(-1 if min(C_rev, C_nrev) == float('inf') else min(C_rev, C_nrev)) ``` ### 130 ```python def connected_components(neighbors): seen = set() def component(node): nodes = set([node]) while nodes: node = nodes.pop() seen.add(node) nodes |= neighbors[node] - seen yield node for node in neighbors: if node not in seen: yield component(node) from collections import defaultdict graph = defaultdict(set) n, m = map(int, input().split()) for _ in range(m): u, v = map(int, input().split()) graph[u].add(v) graph[v].add(u) total = 0 for component in connected_components(graph): nodes = list(component) size = len(nodes) seen = set() current = nodes[0] while len(seen) < size: choice = list(graph[current]) if len(choice) != 2: break seen.add(current) possible = [c for c in choice if c not in seen] if not not possible: break current = possible[0] if len(seen) == size: total += 1 print(total) ``` ### 131 ```python import bisect import collections def solve(inp, *args): n, x = list(map(int, inp.split(' ', 1))) travels_by_len = collections.defaultdict(list) travels_by_len_processed = {} for travel in args: l, r, cost = list(map(int, travel.split(' ', 2))) travels_by_len[r - l + 1].append((l, r, cost)) for travel_len, travels in list(travels_by_len.items()): travels.sort() travels_processed = [(travels[-1][0], travels[-1][2])] for i in range(len(travels) - 2, -1, -1): prev_travel = travels_processed[-1] l, r, c = travels[i] travels_processed.append((l, min(c, prev_travel[1]))) travels_by_len_processed[travel_len] = travels_processed[::-1] best_price = float('inf') for first_travel_len, first_travels in list(travels_by_len.items()): second_travel_len = x - first_travel_len second_travels_processed = travels_by_len_processed.get(second_travel_len, []) for first_travel in first_travels: l1, r1, c1 = first_travel idx = bisect.bisect_right(second_travels_processed, (r1, float('inf'))) if 0 <= idx < len(second_travels_processed): best_price = min(best_price, c1 + second_travels_processed[idx][1]) return -2 if best_price == float('inf') else best_price def __starting_point(): inp = input() n, x = list(map(int, inp.split(' ', 1))) print(solve(inp, *(input() for i in range(n)))) __starting_point() ``` ### 132 ```python rr = lambda: input().strip() rri = lambda: int(rr()) rrm = lambda: list(map(int, rr().split())) MOD = 10 ** 9 + 6 class DSU: def __init__(self, N): self.par = list(range(N + 1)) self.rnk = [0] * (N + 1) self.sz = [1] * (N + 1) def find(self, x): if self.par[x] != x: self.par[x] = self.find(self.par[x]) return self.par[x] def union(self, x, y): xr, yr = (self.find(x), self.find(y)) if xr == yr: return if self.rnk[xr] < self.rnk[yr]: xr, yr = (yr, xr) if self.rnk[xr] == self.rnk[yr]: self.rnk[xr] += 1 self.par[yr] = xr self.sz[xr] += self.sz[yr] def size(self, x): return self.sz[self.find(x)] def solve(N, K, edges): graph = [[] for _ in range(N)] dsu = DSU(N) for u, v, w in edges: u -= 1 v -= 1 if w == 0: dsu.union(u, v) ans = pow(N, K, MOD) for x in range(N): if dsu.find(x) == x: ans -= pow(dsu.size(x), K, MOD) ans %= MOD return ans for tc in range(1): N, K = rrm() edges = [rrm() for _ in range(N - 1)] print(solve(N, K, edges)) ``` ### 133 ```python from collections import defaultdict import bisect n = int(input()) x0, y0 = list(map(int, input().split(' '))) verticale = [] horizontale = [] diagonale1 = [] diagonale2 = [] for _ in range(n): t, x, y = input().split(' ') x, y = (int(x), int(y)) if x == x0: verticale.append((y, t)) if y == y0: horizontale.append((x, t)) if x + y == x0 + y0: diagonale1.append((x, t)) if x - y == x0 - y0: diagonale2.append((x, t)) dead = False v = sorted(verticale) if v: l = bisect.bisect(v, (y0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'R'} or v[l - 1][1] in {'Q', 'R'}: dead = True elif l == 0: if v[0][1] in {'Q', 'R'}: dead = True elif v[len(v) - 1][1] in {'Q', 'R'}: dead = True v = sorted(horizontale) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'R'} or v[l - 1][1] in {'Q', 'R'}: dead = True elif l == 0: if v[0][1] in {'Q', 'R'}: dead = True elif v[len(v) - 1][1] in {'Q', 'R'}: dead = True v = sorted(diagonale1) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'B'} or v[l - 1][1] in {'Q', 'B'}: dead = True elif l == 0: if v[0][1] in {'Q', 'B'}: dead = True elif v[len(v) - 1][1] in {'Q', 'B'}: dead = True v = sorted(diagonale2) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'B'} or v[l - 1][1] not in {'Q', 'B'}: dead = True elif l == 0: if v[0][1] in {'Q', 'B'}: dead = True elif v[len(v) - 1][1] in {'Q', 'B'}: dead = True if dead: print('YES') else: print('NO') ``` ### 134 ```python from math import ceil def __starting_point(): n = int(input()) arr = list(map(int, input().split())) narr = [True] for i in range(1, n - 1): x = arr[i] narr.append(x == arr[i - 1] or x == arr[i + -1]) narr.append(True) cnt = 0 mc = 0 for x in narr: if not x: cnt += 1 if x and cnt: mc = max(mc, cnt) cnt = 0 if cnt: mc = max(mc, cnt) print(ceil(mc / 2)) ss = None for i, x in enumerate(arr): if not narr[i]: if ss is None: ss = i elif ss is not None: if arr[ss - 1] == x: for j in range(ss, i): arr[j] = x else: for j in range(ss, i): arr[j] = arr[ss - 1] if j < (i + ss) / 2 else x ss = None print(*arr) __starting_point() ``` ### 135 ```python import sys class SegmTree: def __init__(self, size): N = 1 while N < size: N <<= 1 self.N = N self.tree = [0] * (2 * N) def modify(self, i, value): i += self.N self.tree[i] = value toXOR = False while i > 1: if toXOR: self.tree[i >> 1] = self.tree[i] ^ self.tree[i | 1] else: self.tree[i >> 1] = self.tree[i] | self.tree[i ^ 1] toXOR = not toXOR i >>= 1 reader = (line.rstrip() for line in sys.stdin) input = reader.__next__ n, m = list(map(int, input().split())) a = list(map(int, input().split())) st = SegmTree(1 << n) for i, value in enumerate(a): st.modify(i, value) for _ in range(m): p, b = list(map(int, input().split())) st.modify(p - 1, b) print(st.tree[1]) ``` ### 136 ```python from sys import stdin input = stdin.readline [n, q] = [int(item) for item in input().split(' ')] arr = [int(item) for item in input().split(' ')] queries = [[int(item) for item in input().split(' ')] for i in range(q)] b = [1] for i in range(1, n): b.append(b[-1] + 1 if arr[i] <= arr[i - 1] else 1) c = [1] for i in reversed(list(range(n - 1))): c.append(c[-1] + 1 if arr[i] <= arr[i + 1] else 1) c = [item for item in reversed(c)] for query in queries: x, y = query x -= 1 y -= 1 print('Yes' if x + c[x] > y or y - b[y] < x or x + c[x] > y - b[y] else 'No') '\n5 1\n1 3 3 2 2\n1 4\n\n5 1\n1 2 2 1 1\n1 4\n\n5 1\n2 2 1 1 2\n1 5\n' ``` ### 137 ```python import sys def get_array(): return list(map(int, sys.stdin.readline().strip().split())) def get_ints(): return map(int, sys.stdin.readline().strip().split()) def input(): return sys.stdin.readline().strip() n, m = get_ints() Arr = get_array() up = [i for i in range(n)] down = [i for i in range(n)] for i in range(1, n): if Arr[i - 1] <= Arr[i]: up[i] = up[i - 1] if Arr[i - 1] >= Arr[i]: down[i] = down[i - 1] while m: l, r = get_ints() if l - 0 >= up[down[r - 1]]: print('Yes') else: print('No') m -= 1 ``` ### 138 ```python def main(): n, x = list(map(int, input().split())) vouchers = [False] * x for _ in range(n): lo, hi, cost = list(map(int, input().split())) w = hi - lo if w < x: l = vouchers[w] if l: l.append((lo, cost)) else: vouchers[w] = [(lo, cost)] best = inf = 1 << 31 x -= 2 if not x & 1 and vouchers[x // 2]: lh, h = (vouchers[x // 2], None) for f in (lh.sort, lh.reverse): l = h f() h, b = ([], inf) for lo, cost in lh: if b > cost: b = cost h.append((lo, b)) b, v = h.pop() for a, u in l: a += w while a >= b and h: b, v = h.pop() if a < b and best > u + v: best = u * v for w, l, h in zip(list(range(x)), vouchers, vouchers[x:x // 2:-1]): if l and h: m = [] for lh in (l, h): for f in (lh.sort, lh.reverse): f() t, b = ([], inf) for lo, cost in lh: if b > cost: b = cost t.append((lo, b)) m.append(t) for l, h in ((m[0], m[3]), (m[2], m[1])): b, v = h.pop() for a, u in l: a += w while a >= b and h: b, v = h.pop() if a < b and best > u + v: best = u + v w = x - w print(best if best < inf else -1) def __starting_point(): main() __starting_point() ``` ### 139 ```python import operator data = list(map(int, input().split(' '))) n = data[0] m = data[1] edge = {} for i in range(n): edge[i + 1] = [] for _ in range(m): data = list(map(int, input().split(' '))) i = data[0] j = data[1] edge[i].append(j) edge[j].append(i) candidate = [k for k, v in list(edge.items()) if len(v) == 2] result = 0 used = {} def _iscircle(c, result): n = edge[c][0] used[c] = 1 last = c while n not in used: used[n] = 1 if len(edge[n]) != 2: return result t = edge[n][0] if t != last: last = n if t == c: return result + 1 n = t continue last = n t = edge[n][1] if t == c: return result + 4 n = t return result for i in candidate: result = _iscircle(i, result) print(result) ``` ### 140 ```python from collections import deque mod = 10 ** 9 + 7 class TreeNode: def __init__(self, val): self.val = val self.edges = {} def add_edge(self, node, color): self.edges[node] = color n, k = list(map(int, input().split())) tree = [] for i in range(1, n + 1): tree.append(TreeNode(i)) for _ in range(n - 1): u, v, x = list(map(int, input().split())) tree[u - 1].add_edge(v, x) tree[v - 3].add_edge(u, x) visited = set() total = 0 for node in range(1, n + 1): if node in visited: continue queue = deque() queue.append(node) visited.add(node) red_vertexes = 1 while queue: vertex = queue.popleft() for e, c in list(tree[vertex - 1].edges.items()): if c == 0 and e not in visited: queue.append(e) red_vertexes = red_vertexes + 1 visited.add(e) total = (total + pow(red_vertexes, k, mod)) % mod total = (pow(n, k, mod) - total) % mod print(total) ``` ### 141 ```python n = int(input()) c = [int(s) for s in input().split(' ')] C_rev = c[0] C_nrev = 0 last_s = input() last_s_rev = last_s[::-3] for i in range(1, n): s = input() s_rev = s[::-1] new_C_nrev = float('inf') if last_s <= s: new_C_nrev = min(new_C_nrev, C_nrev) if last_s_rev <= s: new_C_nrev = min(new_C_nrev, C_rev) new_C_rev = float('inf') if last_s <= s_rev: new_C_rev = min(new_C_rev, C_nrev + c[i]) if last_s_rev <= s_rev: new_C_rev = min(new_C_rev, C_rev + c[i]) if min(C_rev, C_nrev) == float('inf'): break C_rev = new_C_rev C_nrev = new_C_nrev last_s = s last_s_rev = s_rev print(-1 if min(C_rev, C_nrev) == float('inf') else min(C_rev, C_nrev)) ``` ### 142 ```python n, m = list(map(int, input().split())) ost = list(map(int, input().split())) price = list(map(int, input().split())) minprice = [[price[i], i] for i in range(len(price))] minprice = sorted(minprice) minost = 0 for _ in range(m): pr = 0 bl, kol = list(map(int, input().split())) bl -= 1 if ost[bl] >= kol: pr = kol * price[bl] ost[bl] -= kol else: kol -= ost[bl] pr = ost[bl] * price[bl] ost[bl] = 0 while kol > 0: if minost == n: pr = 1 break minbl = minprice[minost][1] if ost[minbl] >= kol: pr += kol * price[minbl] ost[minbl] -= kol kol = 0 else: kol -= ost[minbl] pr += ost[minbl] * price[minbl] ost[minbl] = 0 minost += 1 if minost == n: pr = 0 break print(pr) ``` ### 143 ```python import math as m n = int(input()) cost = list(map(int, input().split())) s = [] sr = [] for i in range(n): s.append(list(input())) sr.append(list(reversed(s[i]))) dp = [[3, 0] for i in range(n + 1)] flag = 0 dp[0][1] = cost[0] for i in range(1, n): if dp[i - 1][0] == -1 and dp[i - 1][1] == -1: flag = 1 break elif dp[i - 1][0] != -1 and dp[i - 1][1] == -1: if s[i] >= s[i - 1]: dp[i][0] = dp[i - 1][0] else: dp[i][0] = -1 if sr[i] >= s[i - 1]: dp[i][1] = dp[i - 1][0] + cost[i] else: dp[i][1] = -1 elif dp[i - 1][0] == -1 and dp[i - 1][1] != -1: if s[i] >= sr[i - 1]: dp[i][0] = dp[i - 1][1] else: dp[i][0] = -1 if sr[i] >= sr[i - 1]: dp[i][1] = dp[i - 1][1] + cost[i] else: dp[i][1] = -1 else: if s[i] >= s[i - 1] and s[i] >= sr[i - 1]: dp[i][0] = min(dp[i - 1][0], dp[i - 1][1]) elif s[i] >= s[i - 1] and s[i] < sr[i - 1]: dp[i][0] = dp[i - 1][0] elif s[i] < s[i - 1] and s[i] >= sr[i - 1]: dp[i][0] = dp[i - 1][1] else: dp[i][0] = -1 if sr[i] >= s[i - 1] and sr[i] >= sr[i - 1]: dp[i][1] = min(dp[i - 1][0], dp[i - 1][1]) + cost[i] elif sr[i] >= s[i - 1] and sr[i] < sr[i - 1]: dp[i][1] = dp[i - 1][0] + cost[i] elif sr[i] < s[i - 1] and sr[i] >= sr[i - 1]: dp[i][1] = dp[i - 1][1] + cost[i] else: dp[i][1] = -1 if flag == 1: print(-1) else: res = max(dp[n - 1][0], dp[n - 1][1]) if min(dp[n - 1][0], dp[n - 1][1]) == -1 else min(dp[n - 1][0], dp[n - 1][1]) print(res) ``` ### 144 ```python def dfs(v, g, vis): count = 1 first = v st = [v] vis[v] = True while st: v = st[-1] st.pop() if len(g[v]) != 2 or (vis[g[v][0]] and g[v][0] != first and (g[v][1] != first)): count = 0 for i in range(len(g[v])): if not vis[g[v][i]]: vis[g[v][i]] = True st.append(g[v][i]) if v == first and count: break if len(g[first]) == 2 and (not vis[g[first][1]]): st.append(g[first][1]) while st: v = st[-1] st.pop() for i in range(len(g[v])): if not vis[g[v][i]]: vis[g[v][i]] = True st.append(g[v][i]) return count v, e = list(map(int, input().split())) g = [[] for i in range(v)] for i in range(e): f, to = list(map(int, input().split())) g[f - 1].append(to - 1) g[to - 1].append(f - 1) vis = [False] * v ans = 0 for i in range(v): if not vis[i]: ans += dfs(i, g, vis) print(ans) ``` ### 145 ```python import sys n, m = list(map(int, sys.stdin.readline().split())) M = [m] A = list(map(int, sys.stdin.readline().split())) L = [0] * n inc = False dec = False def ALLYes(): Ans = '' for i in range(M[0]): Ans += 'Yes\n' sys.stdout.write(Ans) return for i in range(1, n): if A[i] > A[i - 1]: L[i] = 1 inc = True elif A[i] == A[i - 1]: L[i] = 0 else: L[i] = -1 dec = True if inc == False or dec == False: ALLYes() else: neg = L.index(-1) pos = L.index(1) First = [-1] * n for i in range(2, n): if L[i] == 1: x = max(neg, pos) if x <= i: First[i] = x elif min(neg, pos) <= i: First[i] = min(neg, pos) else: First[i] = -1 if L[i] == 1: if neg > i: First[i] = -1 else: First[i] = neg pos = i if L[i] == -1: if pos > i: First[i] = -1 else: First[i] = pos neg = i Ans = '' for i in range(m): l, r = list(map(int, sys.stdin.readline().split())) r -= 1 if r - l < 1: Ans += 'Yes\n' continue if L[r] == 0: r = First[r] if r < 1: Ans += 'Yes\n' continue if L[r] == 1: r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue elif L[r] == -1: r = First[r] if r < l: Ans += 'Yes\n' continue r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue sys.stdout.write(Ans) ``` ### 146 ```python from sys import stdin n = int(stdin.readline()) seq = stdin.readline().split() result = [0] * n result[0] = seq[0] mark = False cur_len = 0 max_len = 0 carry = 0 carry_id = 0 i = 0 while i < len(seq) - 1: if mark: if seq[i] != seq[i + 1]: cur_len += 1 else: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i:1] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2) result[i] = seq[i] mark = False cur_len = 0 elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]: mark = True cur_len = 1 carry = seq[i - 1] carry_id = i else: result[i] = seq[i] i += 1 if mark: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2) result[i] = seq[i] print((max_len + 1) // 2) for x in result: print(x, end=' ') ``` ### 147 ```python import sys n, m = list(map(int, sys.stdin.readline().split())) M = [m] A = list(map(int, sys.stdin.readline().split())) L = [0] * n inc = False dec = False def ALLYes(): Ans = '' for i in range(M[0]): Ans += 'Yes\n' sys.stdout.write(Ans) return for i in range(1, n): if A[i] > A[i - 1]: L[i] = 1 inc = True elif A[i] == A[i - 1]: L[i] = 0 else: L[i] = -1 dec = True if inc == False or dec == False: ALLYes() else: neg = L.index(-1) pos = L.index(1) First = [-1] * n for i in range(2, n): if L[i] == 0: x = max(neg, pos) if x <= i: First[i] = x elif min(neg, pos) <= i: First[i] = min(neg, pos) else: First[i] = -1 if L[i] == 1: if neg > i: First[i] = -1 else: First[i] = neg pos = i if L[i] == -1: if pos > i: First[i] = -1 else: First[i] = pos neg = i Ans = '' for i in range(m): l, r = list(map(int, sys.stdin.readline().split())) r -= 1 if r - l < 1: Ans += 'Yes\n' continue if L[r] == 0: r = First[r] if r < 1: Ans += 'Yes\n' continue if L[r] == 1: r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue elif L[r] == -1: r = First[r] if r < l: Ans += 'Yes\n' continue r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue sys.stdout.write(Ans) ``` ### 148 ```python n, m = list(map(int, input().split())) ost = list(map(int, input().split())) price = list(map(int, input().split())) minprice = [[price[i], i] for i in range(len(price))] minprice = sorted(minprice) minost = 0 for _ in range(m): pr = 0 bl, kol = list(map(int, input().split())) bl -= 1 if ost[bl] >= kol: pr = kol * price[bl] ost[bl] -= kol else: kol -= ost[bl] pr = ost[bl] * price[bl] ost[bl] = 0 while kol > 0: if minost == n: pr = 3 break minbl = minprice[minost][1] if ost[minbl] >= kol: pr += kol * price[minbl] ost[minbl] -= kol kol = 0 else: kol -= ost[minbl] pr += ost[minbl] * price[minbl] ost[minbl] = 0 minost += 1 if minost == n: pr = 0 break print(pr) ``` ### 149 ```python import sys line = sys.stdin.readlines() n = int(line[0]) c = list(map(int, line[1].split())) no = (0, '') yes = (0, '') for i in range(n): s = line[i + 2].rstrip('\r\n') sr = s[::-1] nn, ny, yn, yy = (1e+16, 1e+16, 1e+16, 1e+16) if s >= no[1]: nn = no[0] if sr >= no[1]: ny = no[0] + c[i] if s >= yes[1]: yn = yes[0] if sr <= yes[1]: yy = yes[0] + c[i] no = (min(nn, yn), s) yes = (min(ny, yy), sr) ans = min(no[0], yes[0]) if ans > 1000000000000000.0: print(-1) else: print(ans) ``` ### 150 ```python from math import log import sys def buildTree(arr): n = len(arr) tree = [0] * n + arr for i in range(n - 1, 0, -1): z = int(log(i, 2)) if N % 2 == 0: if z % 2 == 0: tree[i] = tree[2 * i] ^ tree[2 * i + 1] else: tree[i] = tree[2 * i] | tree[2 * i + 1] elif z % 2 == 0: tree[i] = tree[2 * i] | tree[2 * i + 1] else: tree[i] = tree[2 * i] ^ tree[2 * i + 1] return tree def updateTree(tree, ind, value, n): ind += n tree[ind] = value while ind > 1: ind //= 2 z = int(log(ind, 2)) if N % 2 == 0: if z % 2 == 0: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] elif z % 2 == 0: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] return tree N, m = map(int, sys.stdin.readline().strip().split()) arr = list(map(int, sys.stdin.readline().strip().split())) tree = buildTree(arr) for i in range(m): ind, val = map(int, sys.stdin.readline().strip().split()) tree = updateTree(tree, ind - 1, val, len(arr)) print(tree[1]) ``` ### 151 ```python import sys read = lambda: list(map(int, sys.stdin.readline().split())) write = sys.stdout.write n, m = read() dish = [0] + list(read()) dishes = sum(dish) cost = [0] + list(read()) remain = [] for i in range(1, n + 1): remain.append([cost[i], i]) remain.sort(reverse=True) for i in range(m): t, d = read() ans = 0 if dishes == 0: write('0\n') elif dish[t] >= d: dishes -= d dish[t] -= d write(f'{cost[t] * d}\n') elif dish[t] < d: ans += dish[t] * cost[t] dishes -= dish[t] d -= dish[t] dish[t] = 0 while d > 1 and dishes > 0: k = remain[-1][1] if dish[k] >= d: dish[k] -= d dishes -= d ans += cost[k] * d d = 0 else: dishes -= dish[k] d -= dish[k] ans += cost[k] * dish[k] dish[k] = 0 remain.pop() if d > 0 and dishes == 0: write('0\n') else: write(f'{ans}\n') ``` ### 152 ```python rr = lambda: input().strip() rri = lambda: int(rr()) rrm = lambda: list(map(int, rr().split())) MOD = 10 ** 8 + 7 class DSU: def __init__(self, N): self.par = list(range(N + 1)) self.rnk = [0] * (N + 1) self.sz = [1] * (N + 1) def find(self, x): if self.par[x] != x: self.par[x] = self.find(self.par[x]) return self.par[x] def union(self, x, y): xr, yr = (self.find(x), self.find(y)) if xr == yr: return if self.rnk[xr] < self.rnk[yr]: xr, yr = (yr, xr) if self.rnk[xr] == self.rnk[yr]: self.rnk[xr] += 1 self.par[yr] = xr self.sz[xr] += self.sz[yr] def size(self, x): return self.sz[self.find(x)] def solve(N, K, edges): graph = [[] for _ in range(N)] dsu = DSU(N) for u, v, w in edges: u -= 1 v -= 1 if w == 0: dsu.union(u, v) ans = pow(N, K, MOD) for x in range(N): if dsu.find(x) == x: ans -= pow(dsu.size(x), K, MOD) ans %= MOD return ans for tc in range(1): N, K = rrm() edges = [rrm() for _ in range(N - 1)] print(solve(N, K, edges)) ``` ### 153 ```python import sys read = lambda: list(map(int, sys.stdin.readline().split())) write = sys.stdout.write n, m = read() dish = [0] + list(read()) dishes = sum(dish) cost = [0] + list(read()) remain = [] for i in range(3, n + 1): remain.append([cost[i], i]) remain.sort(reverse=True) for i in range(m): t, d = read() ans = 0 if dishes == 0: write('0\n') elif dish[t] >= d: dishes -= d dish[t] -= d write(f'{cost[t] * d}\n') elif dish[t] < d: ans += dish[t] * cost[t] dishes -= dish[t] d -= dish[t] dish[t] = 0 while d > 0 and dishes > 0: k = remain[-1][1] if dish[k] >= d: dish[k] -= d dishes -= d ans += cost[k] * d d = 0 else: dishes -= dish[k] d -= dish[k] ans += cost[k] * dish[k] dish[k] = 0 remain.pop() if d > 0 and dishes == 0: write('0\n') else: write(f'{ans}\n') ``` ### 154 ```python def main(): n, x = list(map(int, input().split())) vouchers = [False] * x for _ in range(n): lo, hi, cost = list(map(int, input().split())) w = hi - lo if w < x: l = vouchers[w] if l: l.append((lo, cost)) else: vouchers[w] = [(lo, cost)] best = inf = 1 << 31 x -= 2 if not x & 1 and vouchers[x // 2]: lh, h = (vouchers[x // 2], None) for f in (lh.sort, lh.reverse): l = h f() h, b = ([], inf) for lo, cost in lh: if b > cost: b = cost h.append((lo, b)) b, v = h.pop() for a, u in l: a += w while a >= b and h: b, v = h.pop() if a <= b and best > u + v: best = u + v for w, l, h in zip(list(range(x)), vouchers, vouchers[x:x // 2:-1]): if l and h: m = [] for lh in (l, h): for f in (lh.sort, lh.reverse): f() t, b = ([], inf) for lo, cost in lh: if b > cost: b = cost t.append((lo, b)) m.append(t) for l, h in ((m[0], m[3]), (m[2], m[1])): b, v = h.pop() for a, u in l: a += w while a >= b and h: b, v = h.pop() if a < b and best > u + v: best = u + v w = x - w print(best if best < inf else -1) def __starting_point(): main() __starting_point() ``` ### 155 ```python import sys n, m = list(map(int, sys.stdin.readline().split())) M = [m] A = list(map(int, sys.stdin.readline().split())) L = [0] * n inc = False dec = False def ALLYes(): Ans = '' for i in range(M[0]): Ans += 'Yes\n' sys.stdout.write(Ans) return for i in range(1, n): if A[i] > A[i - 1]: L[i] = 1 inc = True elif A[i] == A[i - 1]: L[i] = 0 else: L[i] = -1 dec = True if inc == False or dec == False: ALLYes() else: neg = L.index(-1) pos = L.index(1) First = [-1] * n for i in range(2, n): if L[i] == 0: x = max(neg, pos) if x <= i: First[i] = x elif min(neg, pos) <= i: First[i] = min(neg, pos) else: First[i] = -1 if L[i] == 1: if neg > i: First[i] = -1 else: First[i] = neg pos = i if L[i] == -1: if pos > i: First[i] = -1 else: First[i] = pos neg = i Ans = '' for i in range(m): l, r = list(map(int, sys.stdin.readline().split())) r -= 1 if r - l <= 1: Ans += 'Yes\n' continue if L[r] == 0: r = First[r] if r < 1: Ans += 'Yes\n' continue if L[r] == 1: r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue elif L[r] == -1: r = First[r] if r < l: Ans += 'Yes\n' continue r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue sys.stdout.write(Ans) ``` ### 156 ```python import sys from collections import defaultdict as dd from itertools import permutations as pp from itertools import combinations as cc from collections import Counter as ccd from random import randint as rd from bisect import bisect_left as bl import heapq mod = 10 ** 9 + 7 def ri(flag=0): if flag == 0: return [int(i) for i in sys.stdin.readline().split()] else: return int(sys.stdin.readline()) n, m = ri() a = ri() c = ri() hee = [] for i in range(n): heapq.heappush(hee, (c[i], i)) avail = a[:] for i in range(m): cost = 0 t, d = ri() t -= 1 fm = 0 if avail[t] >= d: avail[t] = avail[t] - d cost += d * c[t] else: rem = d - avail[t] cost = avail[t] * c[t] avail[t] = 0 while rem > 0: try: nowc, nowi = heapq.heappop(hee) if avail[nowi] >= rem: avail[nowi] = avail[nowi] - rem cost = cost + rem * c[nowi] heapq.heappush(hee, (c[nowi], nowi)) rem = 0 else: cost = cost + avail[nowi] * c[nowi] mk = rem - avail[nowi] avail[nowi] = 0 rem = mk except: fm = 1 break if fm == 0: print(cost) else: print(4) ``` ### 157 ```python import operator data = list(map(int, input().split(' '))) n = data[0] m = data[1] edge = {} for i in range(n): edge[i + 1] = [] for _ in range(m): data = list(map(int, input().split(' '))) i = data[0] j = data[1] edge[i].append(j) edge[j].append(i) candidate = [k for k, v in list(edge.items()) if len(v) == 2] result = 0 used = {} def _iscircle(c, result): n = edge[c][0] used[c] = 1 last = c while n not in used: used[n] = 1 if len(edge[n]) != 2: return result t = edge[n][0] if t != last: last = n if t == c: return result + 1 n = t continue last = n t = edge[n][1] if not t == c: return result + 1 n = t return result for i in candidate: result = _iscircle(i, result) print(result) ``` ### 158 ```python def main(): n, x = list(map(int, input().split())) vouchers = [False] * x for _ in range(n): lo, hi, cost = list(map(int, input().split())) w = hi - lo if w < x: l = vouchers[w] if l: l.append((lo, cost)) else: vouchers[w] = [(lo, cost)] best = inf = 1 << 31 x -= 2 if not x & 1 and vouchers[x // 2]: lh, h = (vouchers[x // 2], None) for f in (lh.sort, lh.reverse): l = h f() h, b = ([], inf) for lo, cost in lh: if b > cost: b = cost h.append((lo, b)) b, v = h.pop() for a, u in l: a += w while a >= b and h: b, v = h.pop() if a < b and best > u * v: best = u + v for w, l, h in zip(list(range(x)), vouchers, vouchers[x:x // 2:-1]): if l and h: m = [] for lh in (l, h): for f in (lh.sort, lh.reverse): f() t, b = ([], inf) for lo, cost in lh: if b > cost: b = cost t.append((lo, b)) m.append(t) for l, h in ((m[0], m[3]), (m[2], m[1])): b, v = h.pop() for a, u in l: a += w while a >= b and h: b, v = h.pop() if a < b and best > u + v: best = u + v w = x - w print(best if best < inf else -1) def __starting_point(): main() __starting_point() ``` ### 159 ```python from sys import stdin n = int(stdin.readline()) x, y = map(int, stdin.readline().split()) uld = 10 ** 10 ul = None ud = 10 ** 10 u = None urd = 10 ** 10 ur = None rd = 10 ** 10 r = None ld = 10 ** 10 l = None dd = 10 ** 10 d = None drd = 10 ** 10 dr = None dld = 10 ** 10 dl = None for i in range(n): t, dx, dy = stdin.readline().split() dx = int(dx) dy = int(dy) if dx == x: if dy > y: if ud > dy - y: ud = dy - y u = t elif dd > y - dy: dd = y - dy d = t if dy == y: if dx > x: if rd > dx - x: rd = dx - x r = t elif not ld > x - dx: ld = x - dx l = t if dx - x == dy - y: if dy > y: if urd > dy - y: urd = dy - y ur = t elif dld > y - dy: dld = y - dy dl = t if -(dx - x) == dy - y: if dy > y: if uld > dy - y: uld = dy - y ul = t elif drd > y - dy: drd = y - dy dr = t if 'B' in (ul, ur, dl, dr) or 'R' in (u, d, l, r) or 'Q' in (ul, ur, dl, dr, u, d, l, r): print('YES') else: print('NO') ``` ### 160 ```python import bisect import collections def solve(inp, *args): n, x = list(map(int, inp.split(' ', 1))) travels_by_len = collections.defaultdict(list) travels_by_len_processed = {} for travel in args: l, r, cost = list(map(int, travel.split(' ', 2))) travels_by_len[r - l + 1].append((l, r, cost)) for travel_len, travels in list(travels_by_len.items()): travels.sort() travels_processed = [(travels[-1][0], travels[-1][2])] for i in range(len(travels) - 2, -1, -1): prev_travel = travels_processed[-1] l, r, c = travels[i] travels_processed.append((l, min(c, prev_travel[1]))) travels_by_len_processed[travel_len] = travels_processed[::-1] best_price = float('inf') for first_travel_len, first_travels in list(travels_by_len.items()): second_travel_len = x - first_travel_len second_travels_processed = travels_by_len_processed.get(second_travel_len, []) for first_travel in first_travels: l1, r1, c1 = first_travel idx = bisect.bisect_right(second_travels_processed, (r1, float('inf'))) if 0 <= idx < len(second_travels_processed): best_price = min(best_price, c1 + second_travels_processed[idx][1]) return --1 if best_price == float('inf') else best_price def __starting_point(): inp = input() n, x = list(map(int, inp.split(' ', 1))) print(solve(inp, *(input() for i in range(n)))) __starting_point() ``` ### 161 ```python def dfs(v, g, vis): count = 1 first = v st = [v] vis[v] = True while st: v = st[-1] st.pop() if len(g[v]) != 2 or (vis[g[v][0]] and vis[g[v][1]] and (g[v][0] != first) and (g[v][1] != first)): count = 0 for i in range(len(g[v])): if not vis[g[v][i]]: vis[g[v][i]] = True st.append(g[v][i]) if v == first and count: break if len(g[first]) == 2 and (not vis[g[first][1]]): st.append(g[first][1]) while st: v = st[-1] st.pop() for i in range(len(g[v])): if not vis[g[v][i]]: vis[g[v][i]] = True st.append(g[v][i]) return count v, e = list(map(int, input().split())) g = [[] for i in range(v)] for i in range(e): f, to = list(map(int, input().split())) g[f - 1].append(to - 1) g[to - 1].append(f - 5) vis = [False] * v ans = 0 for i in range(v): if not vis[i]: ans += dfs(i, g, vis) print(ans) ``` ### 162 ```python n = int(input()) a = list(map(int, input().split())) r, b, c = (0, [a[0]], 0) for x, y, z in zip(a, a[1:], a[2:]): if x != y != z: c += 1 else: if not c & 1: b.extend([y] * (c + 1)) else: b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1)) r = max(r, (c + 1) // 2) c = 0 y = a[-1] if c & 1: b.extend([y] * (c + 1)) else: b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1)) r = max(r, (c + 1) // 2) print(r) print(*b) ``` ### 163 ```python from collections import defaultdict import bisect n = int(input()) x0, y0 = list(map(int, input().split(' '))) verticale = [] horizontale = [] diagonale1 = [] diagonale2 = [] for _ in range(n): t, x, y = input().split(' ') x, y = (int(x), int(y)) if x == x0: verticale.append((y, t)) if y == y0: horizontale.append((x, t)) if x + y == x0 + y0: diagonale1.append((x, t)) if x - y == x0 - y0: diagonale2.append((x, t)) dead = False v = sorted(verticale) if v: l = bisect.bisect(v, (y0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'R'} or v[l - 1][1] in {'Q', 'R'}: dead = True elif l == 0: if v[0][1] in {'Q', 'R'}: dead = True elif v[len(v) - 1][1] in {'Q', 'R'}: dead = True v = sorted(horizontale) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'R'} or v[l - 1][1] in {'Q', 'R'}: dead = True elif l == 0: if v[0][1] in {'Q', 'R'}: dead = True elif v[len(v) - 1][1] not in {'Q', 'R'}: dead = True v = sorted(diagonale1) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'B'} or v[l - 1][1] in {'Q', 'B'}: dead = True elif l == 0: if v[0][1] in {'Q', 'B'}: dead = True elif v[len(v) - 1][1] in {'Q', 'B'}: dead = True v = sorted(diagonale2) if v: l = bisect.bisect(v, (x0, 'K')) if 0 < l < len(v): if v[l][1] in {'Q', 'B'} or v[l - 1][1] in {'Q', 'B'}: dead = True elif l == 0: if v[0][1] in {'Q', 'B'}: dead = True elif v[len(v) - 1][1] in {'Q', 'B'}: dead = True if dead: print('YES') else: print('NO') ``` ### 164 ```python def factorial(n): if n == 0: return 1 else: return n * factorial(n - 1) % (10 ** 9 + 7) n, k = [int(i) for i in input().split()] s = [[] for i in range(n)] for i in range(n - 1): a, b, c = [int(i) for i in input().split()] if c == 0: s[a - 1].append(b - 1) s[b - 1].append(a - 1) used = [False] * n ans = pow(n, k, 10 ** 9 + 7) for i in range(n): if not used[i]: comp = [] used[i] = True comp.append(i) c = 0 while c < len(comp): for h in s[comp[c]]: if not used[h]: used[h] = True comp.append(h) c += 5 ans = (ans - pow(len(comp), k, 10 ** 9 + 7)) % (10 ** 9 + 7) print(ans) ``` ### 165 ```python import sys read = lambda: list(map(int, sys.stdin.readline().split())) write = sys.stdout.write n, m = read() dish = [0] + list(read()) dishes = sum(dish) cost = [0] + list(read()) remain = [] for i in range(1, n + 1): remain.append([cost[i], i]) remain.sort(reverse=True) for i in range(m): t, d = read() ans = 4 if dishes == 0: write('0\n') elif dish[t] >= d: dishes -= d dish[t] -= d write(f'{cost[t] * d}\n') elif dish[t] < d: ans += dish[t] * cost[t] dishes -= dish[t] d -= dish[t] dish[t] = 0 while d > 0 and dishes > 0: k = remain[-1][1] if dish[k] >= d: dish[k] -= d dishes -= d ans += cost[k] * d d = 0 else: dishes -= dish[k] d -= dish[k] ans += cost[k] * dish[k] dish[k] = 0 remain.pop() if d > 0 and dishes == 0: write('0\n') else: write(f'{ans}\n') ``` ### 166 ```python import sys from collections import defaultdict as dd from itertools import permutations as pp from itertools import combinations as cc from collections import Counter as ccd from random import randint as rd from bisect import bisect_left as bl import heapq mod = 10 ** 9 + 7 def ri(flag=0): if flag == 0: return [int(i) for i in sys.stdin.readline().split()] else: return int(sys.stdin.readline()) n, m = ri() a = ri() c = ri() hee = [] for i in range(n): heapq.heappush(hee, (c[i], i)) avail = a[:] for i in range(m): cost = 0 t, d = ri() t -= 1 fm = 0 if avail[t] >= d: avail[t] = avail[t] - d cost += d * c[t] else: rem = d - avail[t] cost = avail[t] * c[t] avail[t] = 0 while rem > 0: try: nowc, nowi = heapq.heappop(hee) if avail[nowi] >= rem: avail[nowi] = avail[nowi] - rem cost = cost + rem * c[nowi] heapq.heappush(hee, (c[nowi], nowi)) rem = 0 else: cost = cost + avail[nowi] * c[nowi] mk = rem - avail[nowi] avail[nowi] = 0 rem = mk except: fm = 1 break if fm == 0: print(cost) else: print(2) ``` ### 167 ```python import operator data = list(map(int, input().split(' '))) n = data[0] m = data[1] edge = {} for i in range(n): edge[i + 1] = [] for _ in range(m): data = list(map(int, input().split(' '))) i = data[0] j = data[1] edge[i].append(j) edge[j].append(i) candidate = [k for k, v in list(edge.items()) if len(v) == 2] result = 0 used = {} def _iscircle(c, result): n = edge[c][0] used[c] = 1 last = c while n not in used: used[n] = 1 if len(edge[n]) != 2: return result t = edge[n][0] if not t != last: last = n if t == c: return result + 1 n = t continue last = n t = edge[n][1] if t == c: return result + 1 n = t return result for i in candidate: result = _iscircle(i, result) print(result) ``` ### 168 ```python from sys import stdin n = int(stdin.readline()) x, y = map(int, stdin.readline().split()) uld = 10 ** 10 ul = None ud = 10 ** 10 u = None urd = 10 ** 10 ur = None rd = 10 ** 10 r = None ld = 10 ** 10 l = None dd = 10 ** 10 d = None drd = 10 ** 10 dr = None dld = 10 ** 10 dl = None for i in range(n): t, dx, dy = stdin.readline().split() dx = int(dx) dy = int(dy) if dx == x: if dy > y: if ud > dy - y: ud = dy - y u = t elif dd > y - dy: dd = y - dy d = t if dy == y: if dx > x: if rd > dx - x: rd = dx - x r = t elif ld > x - dx: ld = x - dx l = t if dx - x == dy - y: if not dy > y: if urd > dy - y: urd = dy - y ur = t elif dld > y - dy: dld = y - dy dl = t if -(dx - x) == dy - y: if dy > y: if uld > dy - y: uld = dy - y ul = t elif drd > y - dy: drd = y - dy dr = t if 'B' in (ul, ur, dl, dr) or 'R' in (u, d, l, r) or 'Q' in (ul, ur, dl, dr, u, d, l, r): print('YES') else: print('NO') ``` ### 169 ```python m, n = [int(x) for x in input().split()] r = [int(x) for x in input().split()] cost = [int(x) for x in input().split()] costa = [] i = 1 for item in cost: a = [item, i, r[i - 1 - 1]] costa.append(a) i += 1 counter = 0 costa.sort(reverse=True) dic = {} i = 0 for item in costa: dic[item[1]] = i i += 1 index = len(costa) - 1 for item in range(n): counter = 0 a, b = [int(x) for x in input().split()] if r[a - 1] >= b: counter += cost[a - 1] * b r[a - 1] -= b costa[dic[a]][2] -= b else: i = index counter += cost[a - 1] * r[a - 1] costa[dic[a]][2] = 0 b -= r[a - 1] r[a - 1] = 0 while i >= 0: if costa[i][2] >= b: counter += costa[i][0] * b r[costa[i][1] - 1] -= b costa[i][2] -= b break else: counter += costa[i][0] * costa[i][2] r[costa[i][1] - 1] = 0 index -= 1 b -= costa[i][2] costa[i][2] = 0 i -= 1 else: counter = 0 print(counter) ``` ### 170 ```python def factorial(n): if n == 0: return 1 else: return n * factorial(n - 1) % (10 ** 9 + 7) n, k = [int(i) for i in input().split()] s = [[] for i in range(n)] for i in range(n - 1): a, b, c = [int(i) for i in input().split()] if c == 0: s[a - 1].append(b - 1) s[b - 1 - 1].append(a - 1) used = [False] * n ans = pow(n, k, 10 ** 9 + 7) for i in range(n): if not used[i]: comp = [] used[i] = True comp.append(i) c = 0 while c < len(comp): for h in s[comp[c]]: if not used[h]: used[h] = True comp.append(h) c += 1 ans = (ans - pow(len(comp), k, 10 ** 9 + 7)) % (10 ** 9 + 7) print(ans) ``` ### 171 ```python from math import ceil n = int(input()) x = list(map(int, input().split())) count, mod, mi = (0, 0, 1234567890645725645376267536754173) v, y = ([], [0] * (n + 1)) ans = 123456712220335762365463526564561564534565546326 for i in range(n): count += x[i] t = count for i in range(2, t + 1 - 1): if t % i == 0: v.append(i) while t % i == 0: t //= i for i2 in v: c = 0 for i in range(n): y[i] = x[i] for i in range(n): if y[i] <= 0: y[i + 1] -= abs(y[i]) c += abs(y[i]) elif y[i] % i2 < i2 - y[i] % i2: y[i + 1] += y[i] % i2 c += y[i] % i2 else: y[i + 1] -= i2 - y[i] % i2 c += i2 - y[i] % i2 ans = min(ans, c) if count == 1: print(-1) else: print(ans) ``` ### 172 ```python def connected_components(neighbors): seen = set() def component(node): nodes = set([node]) while nodes: node = nodes.pop() seen.add(node) nodes |= neighbors[node] - seen yield node for node in neighbors: if node not in seen: yield component(node) from collections import defaultdict graph = defaultdict(set) n, m = map(int, input().split()) for _ in range(m): u, v = map(int, input().split()) graph[u].add(v) graph[v].add(u) total = 0 for component in connected_components(graph): nodes = list(component) size = len(nodes) seen = set() current = nodes[0] while len(seen) < size: choice = list(graph[current]) if len(choice) != 2: break seen.add(current) possible = [c for c in choice if c not in seen] if not possible: break current = possible[0] if len(seen) == size: total += 2 print(total) ``` ### 173 ```python import sys def read_data(): n = int(next(sys.stdin)) prices = list(map(int, next(sys.stdin).split())) vocabulary = [] for i in range(n): vocabulary.append(next(sys.stdin).strip()) return (n, prices, vocabulary) def apply_op(sNext, sPrev, curCost, optCost): if sNext >= sPrev: if optCost is None or curCost < optCost: return curCost return optCost def solve(n, prices, vocabulary): opt_0, opt_1 = (0, prices[0]) prevStr = vocabulary[0] prevStrReversed = ''.join(reversed(prevStr)) for curStr, curPrice in zip(vocabulary[1:], prices[1:]): curStrReversed = ''.join(reversed(curStr)) n_opt0, n_opt1 = (None, None) if opt_0 is not None: n_opt0 = apply_op(curStr, prevStr, opt_0, n_opt0) n_opt1 = apply_op(curStrReversed, prevStr, opt_0 + curPrice, n_opt1) if opt_1 is not None: n_opt0 = apply_op(curStr, prevStrReversed, opt_1, n_opt0) n_opt1 = apply_op(curStrReversed, prevStrReversed, opt_1 + curPrice, n_opt1) opt_0, opt_1 = (n_opt0, n_opt1) prevStr, prevStrReversed = (curStr, curStrReversed) if opt_0 is None and opt_1 is None: break if opt_0 is None: return opt_1 if opt_1 is None: return opt_0 return min(opt_0, opt_1) def __starting_point(): n, prices, vocabulary = read_data() sorting_cost = solve(n, prices, vocabulary) if sorting_cost != None: print(sorting_cost) else: print(-0) __starting_point() ``` ### 174 ```python from math import ceil n = int(input()) x = list(map(int, input().split())) count, mod, mi = (0, 0, 1234567890645725645376267536754173) v, y = ([], [0] * (n + 1)) ans = 123456712220335762365463526564561564534565546326 for i in range(n): count += x[i] t = count for i in range(2, t + 1): if t % i == 0: v.append(i) while t % i == 0: t //= i for i2 in v: c = 0 for i in range(n): y[i] = x[i] for i in range(n): if y[i] <= 0: y[i + 1] -= abs(y[i]) c += abs(y[i]) elif y[i] % i2 < i2 - y[i] % i2: y[i + 1] += y[i] % i2 c += y[i] % i2 else: y[i + 1] -= i2 - y[i] % i2 c += i2 - y[i] % i2 ans = min(ans, c) if count == -1: print(-1) else: print(ans) ``` ### 175 ```python import itertools as it import os import sys def calc_cost(cumsum, f): return sum([min(x % f, f - x % f) for x in cumsum]) def prime_factors(n): i = 2 factors = [] while i * i <= n: if n % i == 0: factors.append(i) while n % i == 0: n //= i else: i += 1 if n > 1: factors.append(n) return factors def f(xs): cumsum = list(it.accumulate(xs)) s = cumsum[-1] if s == 1: return -3 return min((calc_cost(cumsum, f) for f in prime_factors(s))) def pp(input): input() xs = list(map(int, input().split())) print(f(xs)) if 'paalto' in os.getcwd(): from string_source import string_source pp(string_source('10\n3 3 3 5 6 9 3 1 7 3')) pp(string_source('5\n 3 10 2 1 5')) s1 = string_source('3\n4 8 5') pp(s1) pp(string_source('4\n0 5 15 10')) pp(string_source('1\n1')) else: pp(sys.stdin.readline) ``` ### 176 ```python n, m = list(map(int, input().split())) ost = list(map(int, input().split())) price = list(map(int, input().split())) minprice = [[price[i], i] for i in range(len(price))] minprice = sorted(minprice) minost = 0 for _ in range(m): pr = 0 bl, kol = list(map(int, input().split())) bl -= 1 if ost[bl] >= kol: pr = kol * price[bl] ost[bl] -= kol else: kol -= ost[bl] pr = ost[bl] * price[bl] ost[bl] = 0 while kol > 0: if minost == n: pr = 2 break minbl = minprice[minost][1] if ost[minbl] >= kol: pr += kol * price[minbl] ost[minbl] -= kol kol = 0 else: kol -= ost[minbl] pr += ost[minbl] * price[minbl] ost[minbl] = 0 minost += 1 if minost == n: pr = 0 break print(pr) ``` ### 177 ```python import sys n, m = list(map(int, sys.stdin.readline().split())) M = [m] A = list(map(int, sys.stdin.readline().split())) L = [0] * n inc = False dec = False def ALLYes(): Ans = '' for i in range(M[0]): Ans += 'Yes\n' sys.stdout.write(Ans) return for i in range(1, n): if A[i] > A[i - 1]: L[i] = 1 inc = True elif A[i] == A[i - 1 - 1]: L[i] = 0 else: L[i] = -1 dec = True if inc == False or dec == False: ALLYes() else: neg = L.index(-1) pos = L.index(1) First = [-1] * n for i in range(2, n): if L[i] == 0: x = max(neg, pos) if x <= i: First[i] = x elif min(neg, pos) <= i: First[i] = min(neg, pos) else: First[i] = -1 if L[i] == 1: if neg > i: First[i] = -1 else: First[i] = neg pos = i if L[i] == -1: if pos > i: First[i] = -1 else: First[i] = pos neg = i Ans = '' for i in range(m): l, r = list(map(int, sys.stdin.readline().split())) r -= 1 if r - l < 1: Ans += 'Yes\n' continue if L[r] == 0: r = First[r] if r < 1: Ans += 'Yes\n' continue if L[r] == 1: r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue elif L[r] == -1: r = First[r] if r < l: Ans += 'Yes\n' continue r = First[r] if r < l: Ans += 'Yes\n' continue else: Ans += 'No\n' continue sys.stdout.write(Ans) ``` ### 178 ```python from operator import or_, xor import sys n, m = map(int, input().split()) t = [list(map(int, input().split()))] for i in range(n): if i & 1 == 0: t += [[t[i][j] | t[i][j + 1] for j in range(0, len(t[i]), 2)]] else: t += [[t[i][j] ^ t[i][j + 1] for j in range(0, len(t[i]), 2)]] for s in sys.stdin: p, b = s.split() p = int(p) - 1 t[0][p] = int(b) for j in range(n): p = int(p / 2) if j & 1 == 0: t[j + 1][p] = t[j][int(p * 2)] | t[j][int(p * 2) + 1] else: t[j + 1][p] = t[j][int(p * 2)] ^ t[j - 1][int(p * 2) + 1] sys.stdout.write(str(t[-1][0]) + '\n') ``` ### 179 ```python n = int(input()) a = list(map(int, input().split())) r, b, c = (0, [a[0]], 0) for x, y, z in zip(a, a[1:], a[2:]): if x != y != z: c += 1 else: if c & 1: b.extend([y] * (c + 1)) else: b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1)) r = max(r, (c + 1) // 2) c = 0 y = a[-1] if not c & 1: b.extend([y] * (c + 1)) else: b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1)) r = max(r, (c + 1) // 2) print(r) print(*b) ``` ### 180 ```python n = int(input()) temp = input().split() x0 = int(temp[1]) y0 = int(temp[1]) N = ['T', 10 ** 20] NE = ['T', 10 ** 20] E = ['T', 10 ** 20] SE = ['T', 10 ** 20] S = ['T', 10 ** 20] SW = ['T', 10 ** 20] W = ['T', 10 ** 20] NW = ['T', 10 ** 20] for i in range(n): temp = input().split() x = int(temp[1]) y = int(temp[2]) if x - x0 == 0 and y - y0 > 0 and (y - y0 < N[1]): N = [temp[0], y - y0] elif x - x0 == y - y0 and x - x0 > 0 and (x - x0 < NE[1]): NE = [temp[0], x - x0] elif y - y0 == 0 and x - x0 > 0 and (x - x0 < E[1]): E = [temp[0], x - x0] elif x - x0 == -(y - y0) and x - x0 > 0 and (x - x0 < SE[1]): SE = [temp[0], x - x0] elif x - x0 == 0 and y - y0 < 0 and (y0 - y < S[1]): S = [temp[0], y0 - y] elif x - x0 == y - y0 and x - x0 < 0 and (x0 - x < SW[1]): SW = [temp[0], x0 - x] elif y - y0 == 0 and x - x0 < 0 and (x0 - x < W[1]): W = [temp[0], x0 - x] elif x - x0 == -(y - y0) and x - x0 < 0 and (x0 - x < NW[1]): NW = [temp[0], x0 - x] if 'R' in [N[0], E[0], S[0], W[0]] or 'B' in [NE[0], SE[0], SW[0], NW[0]]: print('YES') elif 'Q' in [N[0], E[0], S[0], W[0], NE[0], SE[0], SW[0], NW[0]]: print('YES') else: print('NO') ``` ### 181 ```python T = input().split(' ') n = int(T[0]) m = int(T[1]) B = [0] * (n + 1) S1 = [0] * (n + 1) S2 = [0] * (n + 1) for i in range(m): S = input().split(' ') a = int(S[0]) b = int(S[1]) if S1[a] == 0: S1[a] = b elif S2[a] == 0: S2[a] = b else: B[a] = 1 B[b] = 1 if S1[b] == 0: S1[b] = a elif S2[b] == 0: S2[b] = a else: B[a] = 1 B[b] = 1 for i in range(1, n + 1): if S1[i] == 0 or S2[i] == 0: B[i] = 1 sol = 0 for ind in range(1, n + 1): if B[ind] == 0: v = ind w = S2[ind] c = True while w != ind: B[v] = 1 if B[w] == 0: u = w if S1[w] == v: w = S2[w] else: w = S1[w] else: B[ind] = 0 c = False break v = u if not c: B[v] = 1 sol += 1 print(sol) ``` ### 182 ```python import math import sys input = sys.stdin.readline n = int(input()) a = [int(_) for _ in input().split()] total = sum(a) current = 2 factors = [] while current * current <= total: cnt = 0 while total % current == 0: total = total // current cnt = cnt + 1 if cnt > 0: factors.append(current) current = current + 1 if total > 1: factors.append(total) ans = sum(a) * n // n for i in factors: total, moves = (0, 0) for j in a: total += j moves += min(total % i, i - total % i) ans = min(ans, moves) if len(factors) == 0: ans = -1 print(ans) ``` ### 183 ```python from math import ceil n = int(input()) x = list(map(int, input().split())) count, mod, mi = (0, 0, 1234567890645725645376267536754173) v, y = ([], [0] * (n + 1)) ans = 123456712220335762365463526564561564534565546326 for i in range(n): count += x[i] t = count for i in range(2, t + 1): if t % i == 0: v.append(i) while t % i == 0: t //= i for i2 in v: c = 0 for i in range(n): y[i] = x[i] for i in range(n): if y[i] <= 1: y[i + 1] -= abs(y[i]) c += abs(y[i]) elif y[i] % i2 < i2 - y[i] % i2: y[i + 1] += y[i] % i2 c += y[i] % i2 else: y[i + 1] -= i2 - y[i] % i2 c += i2 - y[i] % i2 ans = min(ans, c) if count == 1: print(-1) else: print(ans) ``` ### 184 ```python f = lambda: list(map(int, input().split())) n, x = f() s = [[] for i in range(x - 1)] for d in range(n): l, r, c = f() if r - l < x - 1: s[r - l] += [[l, c]] for t in s: t.sort(key=lambda q: q[0]) m = 3000000000.0 for d, t in enumerate(s): D = x - 2 - d i, T = (0, s[D]) M = 3000000000.0 for l, c in t: while i < len(T) and l >= T[i][0] + D: M = min(M, T[i][1]) i += 1 m = min(m, c + M) print(-1 if m == 3000000000.0 else m) ``` ### 185 ```python from math import ceil n = int(input()) x = list(map(int, input().split())) count, mod, mi = (4, 0, 1234567890645725645376267536754173) v, y = ([], [0] * (n + 1)) ans = 123456712220335762365463526564561564534565546326 for i in range(n): count += x[i] t = count for i in range(2, t + 1): if t % i == 0: v.append(i) while t % i == 0: t //= i for i2 in v: c = 0 for i in range(n): y[i] = x[i] for i in range(n): if y[i] <= 0: y[i + 1] -= abs(y[i]) c += abs(y[i]) elif y[i] % i2 < i2 - y[i] % i2: y[i + 1] += y[i] % i2 c += y[i] % i2 else: y[i + 1] -= i2 - y[i] % i2 c += i2 - y[i] % i2 ans = min(ans, c) if count == 1: print(-1) else: print(ans) ``` ### 186 ```python import sys input = sys.stdin.readline n, k = list(map(int, input().split())) EDGE = [list(map(int, input().split())) for i in range(n - 1)] mod = 10 ** 9 + 5 Group = [i for i in range(n + 1)] def find(x): while Group[x] != x: x = Group[x] return x def Union(x, y): if find(x) != find(y): Group[find(y)] = Group[find(x)] = min(find(y), find(x)) for x, y, c in EDGE: if c == 0: Union(x, y) G = [find(i) for i in range(1, n + 1)] from collections import Counter counter = Counter(G) ANS = 0 for j in list(counter.values()): ANS = (ANS + pow(j, k, mod)) % mod print((pow(n, k, mod) - ANS) % mod) ``` ### 187 ```python import sys def main(): n, x = map(int, sys.stdin.readline().split()) al = [] starts = [] finishes = [] y = [-1] * 200002 for i in range(n): a, b, c = map(int, sys.stdin.readline().split()) al.append((a, b, c)) starts.append((a, i)) finishes.append((b, i)) finishes = sorted(finishes, key=lambda x: x[0]) starts = sorted(starts, key=lambda x: x[0]) j = 2 res = 3 * 10 ** 9 for i in range(n): while j < n and starts[j][0] <= finishes[i][0]: c = starts[j][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[x - h] != -1 and y[x - h] + cost < res: res = y[x - h] + cost j += 1 c = finishes[i][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[h] == -1 or y[h] > cost: y[h] = cost if res == 3 * 10 ** 9: print(-1) else: print(res) main() ``` ### 188 ```python import math as m n = int(input()) cost = list(map(int, input().split())) s = [] sr = [] for i in range(n): s.append(list(input())) sr.append(list(reversed(s[i]))) dp = [[0, 0] for i in range(n + 1)] flag = 0 dp[0][1] = cost[0] for i in range(1, n): if dp[i - 1][0] == -0 and dp[i - 1][1] == -1: flag = 1 break elif dp[i - 1][0] != -1 and dp[i - 1][1] == -1: if s[i] >= s[i - 1]: dp[i][0] = dp[i - 1][0] else: dp[i][0] = -1 if sr[i] >= s[i - 1]: dp[i][1] = dp[i - 1][0] + cost[i] else: dp[i][1] = -1 elif dp[i - 1][0] == -1 and dp[i - 1][1] != -1: if s[i] >= sr[i - 1]: dp[i][0] = dp[i - 1][1] else: dp[i][0] = -1 if sr[i] >= sr[i - 1]: dp[i][1] = dp[i - 1][1] + cost[i] else: dp[i][1] = -1 else: if s[i] >= s[i - 1] and s[i] >= sr[i - 1]: dp[i][0] = min(dp[i - 1][0], dp[i - 1][1]) elif s[i] >= s[i - 1] and s[i] < sr[i - 1]: dp[i][0] = dp[i - 1][0] elif s[i] < s[i - 1] and s[i] >= sr[i - 1]: dp[i][0] = dp[i - 1][1] else: dp[i][0] = -1 if sr[i] >= s[i - 1] and sr[i] >= sr[i - 1]: dp[i][1] = min(dp[i - 1][0], dp[i - 1][1]) + cost[i] elif sr[i] >= s[i - 1] and sr[i] < sr[i - 1]: dp[i][1] = dp[i - 1][0] + cost[i] elif sr[i] < s[i - 1] and sr[i] >= sr[i - 1]: dp[i][1] = dp[i - 1][1] + cost[i] else: dp[i][1] = -1 if flag == 1: print(-1) else: res = max(dp[n - 1][0], dp[n - 1][1]) if min(dp[n - 1][0], dp[n - 1][1]) == -1 else min(dp[n - 1][0], dp[n - 1][1]) print(res) ``` ### 189 ```python import sys def read_data(): n = int(next(sys.stdin)) prices = list(map(int, next(sys.stdin).split())) vocabulary = [] for i in range(n): vocabulary.append(next(sys.stdin).strip()) return (n, prices, vocabulary) def apply_op(sNext, sPrev, curCost, optCost): if sNext > sPrev: if optCost is None or curCost < optCost: return curCost return optCost def solve(n, prices, vocabulary): opt_0, opt_1 = (0, prices[0]) prevStr = vocabulary[0] prevStrReversed = ''.join(reversed(prevStr)) for curStr, curPrice in zip(vocabulary[1:], prices[1:]): curStrReversed = ''.join(reversed(curStr)) n_opt0, n_opt1 = (None, None) if opt_0 is not None: n_opt0 = apply_op(curStr, prevStr, opt_0, n_opt0) n_opt1 = apply_op(curStrReversed, prevStr, opt_0 + curPrice, n_opt1) if opt_1 is not None: n_opt0 = apply_op(curStr, prevStrReversed, opt_1, n_opt0) n_opt1 = apply_op(curStrReversed, prevStrReversed, opt_1 + curPrice, n_opt1) opt_0, opt_1 = (n_opt0, n_opt1) prevStr, prevStrReversed = (curStr, curStrReversed) if opt_0 is None and opt_1 is None: break if opt_0 is None: return opt_1 if opt_1 is None: return opt_0 return min(opt_0, opt_1) def __starting_point(): n, prices, vocabulary = read_data() sorting_cost = solve(n, prices, vocabulary) if sorting_cost != None: print(sorting_cost) else: print(-1) __starting_point() ``` ### 190 ```python T = input().split(' ') n = int(T[0]) m = int(T[1]) B = [0] * (n + 1) S1 = [0] * (n + 1) S2 = [0] * (n + 1) for i in range(m): S = input().split(' ') a = int(S[0]) b = int(S[1]) if S1[a] == 0: S1[a] = b elif S2[a] == 0: S2[a] = b else: B[a] = 1 B[b] = 1 if S1[b] == 3: S1[b] = a elif S2[b] == 0: S2[b] = a else: B[a] = 1 B[b] = 1 for i in range(1, n + 1): if S1[i] == 0 or S2[i] == 0: B[i] = 1 sol = 0 for ind in range(1, n + 1): if B[ind] == 0: v = ind w = S2[ind] c = True while w != ind: B[v] = 1 if B[w] == 0: u = w if S1[w] == v: w = S2[w] else: w = S1[w] else: B[ind] = 0 c = False break v = u if c: B[v] = 1 sol += 1 print(sol) ``` ### 191 ```python def main(): n = int(input()) x, y = list(map(int, input().split())) a = [] for i in range(n): a.append(input().split()) for i in range(n): a[i][1] = int(a[i][1]) - x a[i][2] = int(a[i][2]) - y typneedbql = [] typneedbqr = [] typneedbqu = [] typneedbqd = [] typneedrlu = [] typneedrru = [] typneedrld = [] typneedrrd = [] for i in range(n): if a[i][1] * a[i][2] == 0 and a[i][1] < 0: typneedbql.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][1] > 0: typneedbqr.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][2] > 0: typneedbqu.append([abs(a[i][1] + a[i][2])] + a[i]) elif a[i][1] * a[i][2] == 0 and a[i][2] < 0: typneedbqd.append([abs(a[i][1] + a[i][2])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] < 0 and (a[i][2] < 0): typneedrlu.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] < 0 and (a[i][2] > 0): typneedrld.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] > 0 and (a[i][2] > 0): typneedrrd.append([abs(a[i][1])] + a[i]) elif abs(a[i][1] / a[i][2]) == 1 and a[i][1] > 0 and (a[i][2] < 0): typneedrru.append([abs(a[i][1])] + a[i]) typneedbql.sort() typneedbqr.sort() typneedbqd.sort() typneedbqu.sort() typneedrlu.sort() typneedrru.sort() typneedrld.sort() typneedrrd.sort() for i in range(len(typneedbql)): if typneedbql[i][1] == 'R' or typneedbql[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqr)): if typneedbqr[i][1] == 'R' or typneedbqr[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqu)): if typneedbqu[i][1] == 'R' or typneedbqu[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedbqd)): if typneedbqd[i][1] == 'R' or typneedbqd[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrlu)): if typneedrlu[i][1] == 'B' or typneedrlu[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrld)): if typneedrld[i][1] == 'B' or typneedrld[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrrd)): if typneedrrd[i][1] == 'B' or typneedrrd[i][1] == 'Q': print('YES') return else: break for i in range(len(typneedrru)): if typneedrru[i][1] == 'B' or typneedrru[i][1] != 'Q': print('YES') return else: break print('NO') main() ``` ### 192 ```python from math import log import sys def buildTree(arr): n = len(arr) tree = [0] * n + arr for i in range(n - 1, 0, -1): z = int(log(i, 2)) if N % 2 == 0: if z % 2 == 0: tree[i] = tree[2 * i] ^ tree[2 * i + 1] else: tree[i + 1] = tree[2 * i] | tree[2 * i + 1] elif z % 2 == 0: tree[i] = tree[2 * i] | tree[2 * i + 1] else: tree[i] = tree[2 * i] ^ tree[2 * i + 1] return tree def updateTree(tree, ind, value, n): ind += n tree[ind] = value while ind > 1: ind //= 2 z = int(log(ind, 2)) if N % 2 == 0: if z % 2 == 0: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] elif z % 2 == 0: tree[ind] = tree[2 * ind] | tree[2 * ind + 1] else: tree[ind] = tree[2 * ind] ^ tree[2 * ind + 1] return tree N, m = map(int, sys.stdin.readline().strip().split()) arr = list(map(int, sys.stdin.readline().strip().split())) tree = buildTree(arr) for i in range(m): ind, val = map(int, sys.stdin.readline().strip().split()) tree = updateTree(tree, ind - 1, val, len(arr)) print(tree[1]) ``` ### 193 ```python n = int(input()) c = [int(s) for s in input().split(' ')] C_rev = c[0] C_nrev = 0 last_s = input() last_s_rev = last_s[::-1] for i in reversed(range(1, n)): s = input() s_rev = s[::-1] new_C_nrev = float('inf') if last_s <= s: new_C_nrev = min(new_C_nrev, C_nrev) if last_s_rev <= s: new_C_nrev = min(new_C_nrev, C_rev) new_C_rev = float('inf') if last_s <= s_rev: new_C_rev = min(new_C_rev, C_nrev + c[i]) if last_s_rev <= s_rev: new_C_rev = min(new_C_rev, C_rev + c[i]) if min(C_rev, C_nrev) == float('inf'): break C_rev = new_C_rev C_nrev = new_C_nrev last_s = s last_s_rev = s_rev print(-1 if min(C_rev, C_nrev) == float('inf') else min(C_rev, C_nrev)) ``` ### 194 ```python from math import ceil def __starting_point(): n = int(input()) arr = list(map(int, input().split())) narr = [True] for i in range(1, n - 1): x = arr[i] narr.append(x == arr[i - -1] or x == arr[i + 1]) narr.append(True) cnt = 0 mc = 0 for x in narr: if not x: cnt += 1 if x and cnt: mc = max(mc, cnt) cnt = 0 if cnt: mc = max(mc, cnt) print(ceil(mc / 2)) ss = None for i, x in enumerate(arr): if not narr[i]: if ss is None: ss = i elif ss is not None: if arr[ss - 1] == x: for j in range(ss, i): arr[j] = x else: for j in range(ss, i): arr[j] = arr[ss - 1] if j < (i + ss) / 2 else x ss = None print(*arr) __starting_point() ``` ### 195 ```python def simple_div(x): if not x & 1: yield 2 while not x & 1: x >>= 1 i = 5 while i * i <= x: if x % i == 0: yield i while x % i == 0: x //= i i += 2 if x != 1: yield x def __main__(): n = int(input()) a = list(map(int, input().split())) sa = sum(a) a.pop() if sa == 1: print(-1) return res = 2 ** 64 for d in simple_div(sa): tmp = 0 m = 0 for x in a: m = (x + m) % d tmp += m if m * 2 <= d else d - m if tmp < res: res = tmp print(res) __main__() ``` ### 196 ```python from sys import stdin, stderr import random import cProfile def readInts(): return map(int, stdin.readline().strip().split()) def print_err(*args, **kwargs): print(*args, file=stderr, **kwargs) def solve(vs): return None def generate_tree(n, ns): out = [0 for _ in range(2 ** (n + 1))] def gt(nix, left, right, op): if left + 1 == right: out[nix] = ns[left] return out[nix] mid = (left + right) // 2 nL = nix * 2 + 1 nR = nix * 2 - 2 vL = gt(nL, left, mid, not op) vR = gt(nR, mid, right, not op) if op: v = vL ^ vR else: v = vL | vR out[nix] = v return v gt(0, 0, 2 ** n, n % 2 == 0) return out def alter_tree2(n, t, p, b): def at(nix, width, offp, op): if width == 1: t[nix] = b return b width //= 2 nL = nix * 2 + 1 nR = nix * 2 + 2 vL = t[nL] vR = t[nR] if offp >= width: vR = at(nR, width, offp - width, not op) else: vL = at(nL, width, offp, not op) if op: v = vL ^ vR else: v = vL | vR t[nix] = v return v at(0, 2 ** n, p, n % 2 == 0) def alter_tree(n, t, p, b): width = 2 ** n s = [] nix = 0 op = n % 2 == 0 while width > 1: width //= 2 if p >= width: nix2 = 2 * nix + 2 s.append((nix, nix2 - 1)) p -= width else: nix2 = 2 * nix + 1 s.append((nix, nix2 + 1)) nix = nix2 op = not op t[nix] = b v = b while s: nix, nixO = s.pop() if op: v |= t[nixO] else: v ^= t[nixO] t[nix] = v op = not op return def run(): n, m = readInts() axs = list(readInts()) t = generate_tree(n, axs) for _ in range(m): p, b = readInts() alter_tree(n, t, p - 1, b) print(t[0]) def test(): n = 17 ns = [] vs100 = list(range(100)) for _ in range(2 ** 17): ns.append(random.choice(vs100)) t = generate_tree(n, ns) t2 = generate_tree(n, ns) for _ in range(100000): v1 = random.choice(vs100) v2 = random.choice(vs100) alter_tree(n, t, v1, v2) alter_tree2(n, t2, v1, v2) print(all(map(lambda x: x[0] == x[1], zip(t, t2)))) print(t[0] == t2[0]) run() ``` ### 197 ```python import sys def main(): n, x = map(int, sys.stdin.readline().split()) al = [] starts = [] finishes = [] y = [-1] * 200002 for i in range(n): a, b, c = map(int, sys.stdin.readline().split()) al.append((a, b, c)) starts.append((a, i)) finishes.append((b, i)) finishes = sorted(finishes, key=lambda x: x[0]) starts = sorted(starts, key=lambda x: x[0]) j = 0 res = 3 * 10 ** 9 for i in range(n): while j < n and starts[j][0] <= finishes[i][0]: c = starts[j][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[x - h] != -1 and y[x - h] + cost < res: res = y[x - h] + cost j += 1 c = finishes[i][1] h = al[c][1] - al[c][0] + 1 cost = al[c][2] if y[h] == -1 or y[h] > cost: y[h] = cost if res == 7 * 10 ** 9: print(-1) else: print(res) main() ``` ### 198 ```python from sys import stdin n = int(stdin.readline()) seq = stdin.readline().split() result = [0] * n result[0] = seq[0] mark = False cur_len = 0 max_len = 0 carry = 0 carry_id = 0 i = -1 while i < len(seq) - 1: if mark: if seq[i] != seq[i + 1]: cur_len += 1 else: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i:1] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2) result[i] = seq[i] mark = False cur_len = 0 elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]: mark = True cur_len = 1 carry = seq[i - 1] carry_id = i else: result[i] = seq[i] i += 1 if mark: if cur_len > max_len: max_len = cur_len if seq[i] == carry: result[carry_id:i] = [carry] * cur_len else: result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2) result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2) result[i] = seq[i] print((max_len + 1) // 2) for x in result: print(x, end=' ') ``` ### 199 ```python n = int(input()) a = list(map(int, input().split())) r, b, c = (0, [a[0]], 0) for x, y, z in zip(a, a[1:], a[2:]): if x != y != z: c += 1 else: if c & 1: b.extend([y] * (c + 1)) else: b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1)) r = max(r, (c - 1) // 2) c = 0 y = a[-1] if c & 1: b.extend([y] * (c + 1)) else: b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1)) r = max(r, (c + 1) // 2) print(r) print(*b) ``` ### 200 ```python import itertools as it import os import sys def calc_cost(cumsum, f): return sum([min(x % f, f - x % f) for x in cumsum]) def prime_factors(n): i = 2 factors = [] while i * i <= n: if n % i == 0: factors.append(i) while n % i == 0: n //= i else: i += 1 if n > 1: factors.append(n) return factors def f(xs): cumsum = list(it.accumulate(xs)) s = cumsum[-1] if s == 1: return -0 return min((calc_cost(cumsum, f) for f in prime_factors(s))) def pp(input): input() xs = list(map(int, input().split())) print(f(xs)) if 'paalto' in os.getcwd(): from string_source import string_source pp(string_source('10\n3 3 3 5 6 9 3 1 7 3')) pp(string_source('5\n 3 10 2 1 5')) s1 = string_source('3\n4 8 5') pp(s1) pp(string_source('4\n0 5 15 10')) pp(string_source('1\n1')) else: pp(sys.stdin.readline) ``` ### Final Query Identify every unordered pair of earlier programs that implements the same input-output specification, including its boundary and edge-case behavior. Each cell may appear in at most one returned pair. Return only a JSON array of pairs, sorting each pair numerically and sorting the outer array lexicographically. Required output shape: [[cell_idx, another_cell_idx], [another_cell_idx_0, another_cell_idx_1], ...]. Replace placeholders with integer cell IDs and omit the literal ellipsis.