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Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x and y (x > y) have an undirected edge between the...
instruction
0
18,671
13
37,342
Tags: combinatorics, graphs, greedy, math, number theory Correct Solution: ``` from collections import Counter def gcd(x, y): """greatest common divisor of x and y""" while y: x, y = y, x % y return x def memodict(f): """memoization decorator for a function taking a single argument""" cl...
output
1
18,671
13
37,343
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x and y (x > y) have an undirected edge between the...
instruction
0
18,672
13
37,344
Tags: combinatorics, graphs, greedy, math, number theory Correct Solution: ``` # region fastio # from https://codeforces.com/contest/1333/submission/75948789 import sys, io, os BUFSIZE = 8192 class FastIO(io.IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffe...
output
1
18,672
13
37,345
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x and y (x > y) have an undirected edge between the...
instruction
0
18,673
13
37,346
Tags: combinatorics, graphs, greedy, math, number theory Correct Solution: ``` import io, os import sys input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline D=int(input()) q=int(input()) mod=998244353 Q=[tuple(map(int,input().split())) for i in range(q)] from math import gcd from math import sqrt L=[] Q2=[] f...
output
1
18,673
13
37,347
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x and y (x > y) have an undirected edge between the...
instruction
0
18,674
13
37,348
Tags: combinatorics, graphs, greedy, math, number theory Correct Solution: ``` def gcd(a, b): while b: a, b = b, a % b return a def isPrimeMR(n): d = n - 1 d = d // (d & -d) L = [2, 3, 5, 7, 11, 13, 17] for a in L: t = d y = pow(a, t, n) if y == 1: continue while ...
output
1
18,674
13
37,349
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x an...
instruction
0
18,675
13
37,350
Yes
output
1
18,675
13
37,351
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x an...
instruction
0
18,676
13
37,352
Yes
output
1
18,676
13
37,353
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x an...
instruction
0
18,677
13
37,354
Yes
output
1
18,677
13
37,355
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x an...
instruction
0
18,678
13
37,356
Yes
output
1
18,678
13
37,357
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x an...
instruction
0
18,679
13
37,358
No
output
1
18,679
13
37,359
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x an...
instruction
0
18,680
13
37,360
No
output
1
18,680
13
37,361
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x an...
instruction
0
18,681
13
37,362
No
output
1
18,681
13
37,363
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer D. Let's build the following graph from it: * each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included); * two vertices x an...
instruction
0
18,682
13
37,364
No
output
1
18,682
13
37,365
Provide tags and a correct Python 3 solution for this coding contest problem. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and j (i<j) are added in the following manner: *...
instruction
0
18,772
13
37,544
Tags: constructive algorithms, dsu, graphs, greedy, number theory, sortings Correct Solution: ``` '''Author- Akshit Monga''' from sys import stdin, stdout input = stdin.readline class SortedList: def __init__(self, iterable=[], _load=200): """Initialize sorted list instance.""" values = sorted(iter...
output
1
18,772
13
37,545
Provide tags and a correct Python 3 solution for this coding contest problem. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and j (i<j) are added in the following manner: *...
instruction
0
18,773
13
37,546
Tags: constructive algorithms, dsu, graphs, greedy, number theory, sortings Correct Solution: ``` import sys input = sys.stdin.buffer.readline for _ in range(int(input())): n,p = map(int,input().split()) a = list(map(int,input().split())) locs = [] for i in range(n): locs.append([a[i],i]) ...
output
1
18,773
13
37,547
Provide tags and a correct Python 3 solution for this coding contest problem. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and j (i<j) are added in the following manner: *...
instruction
0
18,774
13
37,548
Tags: constructive algorithms, dsu, graphs, greedy, number theory, sortings Correct Solution: ``` def find(x): while(par[x]!=x): x=par[x] return x def union(x,y): if (rank[x]>rank[y]): par[y]=x elif (rank[y]>rank[x]): par[x]=y else: par[x]=y rank[y]+=1 ...
output
1
18,774
13
37,549
Provide tags and a correct Python 3 solution for this coding contest problem. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and j (i<j) are added in the following manner: *...
instruction
0
18,775
13
37,550
Tags: constructive algorithms, dsu, graphs, greedy, number theory, sortings Correct Solution: ``` import sys,os,io input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline for _ in range (int(input())): n,p = [int(i) for i in input().split()] a = [int(i) for i in input().split()] cost = [0]*n mini...
output
1
18,775
13
37,551
Provide tags and a correct Python 3 solution for this coding contest problem. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and j (i<j) are added in the following manner: *...
instruction
0
18,776
13
37,552
Tags: constructive algorithms, dsu, graphs, greedy, number theory, sortings Correct Solution: ``` def I(): return map(int, input().split()) t, = I() r = range for _ in r(t): n, p = I() a = *I(), b = [p]*(n-1) c = a[0] for i in r(1, n): if a[i] % c: c = a[i] else: ...
output
1
18,776
13
37,553
Provide tags and a correct Python 3 solution for this coding contest problem. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and j (i<j) are added in the following manner: *...
instruction
0
18,777
13
37,554
Tags: constructive algorithms, dsu, graphs, greedy, number theory, sortings Correct Solution: ``` I=lambda:map(int,input().split()) t,=I();r=range for _ in r(t): n,p=I();a=*I(),;b=[p]*(n-1);c=a[0] for i in r(1,n): if a[i]%c<1:b[i-1]=min(c,b[i-1]) else:c=a[i] c=a[n-1] for i in r(n-2,-1,-1): if a[i]%c<1:b[i]=mi...
output
1
18,777
13
37,555
Provide tags and a correct Python 3 solution for this coding contest problem. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and j (i<j) are added in the following manner: *...
instruction
0
18,778
13
37,556
Tags: constructive algorithms, dsu, graphs, greedy, number theory, sortings Correct Solution: ``` import sys sys.setrecursionlimit(10**5) int1 = lambda x: int(x)-1 p2D = lambda x: print(*x, sep="\n") def II(): return int(sys.stdin.buffer.readline()) def LI(): return list(map(int, sys.stdin.buffer.readline().split())) ...
output
1
18,778
13
37,557
Provide tags and a correct Python 3 solution for this coding contest problem. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and j (i<j) are added in the following manner: *...
instruction
0
18,779
13
37,558
Tags: constructive algorithms, dsu, graphs, greedy, number theory, sortings Correct Solution: ``` from sys import stdin,stdout from math import gcd,sqrt,factorial,pi,inf from collections import deque,defaultdict from bisect import bisect,bisect_left from time import time from itertools import permutations as per input=...
output
1
18,779
13
37,559
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and ...
instruction
0
18,780
13
37,560
Yes
output
1
18,780
13
37,561
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and ...
instruction
0
18,781
13
37,562
Yes
output
1
18,781
13
37,563
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and ...
instruction
0
18,782
13
37,564
Yes
output
1
18,782
13
37,565
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and ...
instruction
0
18,783
13
37,566
Yes
output
1
18,783
13
37,567
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and ...
instruction
0
18,784
13
37,568
No
output
1
18,784
13
37,569
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and ...
instruction
0
18,785
13
37,570
No
output
1
18,785
13
37,571
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and ...
instruction
0
18,786
13
37,572
No
output
1
18,786
13
37,573
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and ...
instruction
0
18,787
13
37,574
No
output
1
18,787
13
37,575
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains two integers n and m (2 ≤ n ≤ 105, 0 ≤ m ≤ 105)...
instruction
0
18,800
13
37,600
Tags: graphs, shortest paths Correct Solution: ``` #!/usr/bin/env python from heapq import heappop, heappush def dijkstra(graph, start=0): n = len(graph) dist, parents = [float('inf')] * n, [-1] * n dist[start] = 0 queue = [(0, start)] while queue: path_len, v = heappop(queue) if ...
output
1
18,800
13
37,601
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains two integers n and m (2 ≤ n ≤ 105, 0 ≤ m ≤ 105)...
instruction
0
18,801
13
37,602
Tags: graphs, shortest paths Correct Solution: ``` import heapq n,m=map(int,input().split()) g={i:[] for i in range(1,n+1)} dis=[float('inf') for i in range(n+1)] visited=[False for i in range(n+1)] for i in range(m): a,b,w=map(int,input().split()) g[a].append((b,w)) g[b].append((a,w)) q=[] p=[-1 for i in r...
output
1
18,801
13
37,603
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains two integers n and m (2 ≤ n ≤ 105, 0 ≤ m ≤ 105)...
instruction
0
18,802
13
37,604
Tags: graphs, shortest paths Correct Solution: ``` from heapq import heappush, heappop n, m = map(int, input().split()) g = [[] for _ in range(n + 1)] for _ in range(m): a, b, w = map(int, input().split()) g[a].append((b, w)) g[b].append((a, w)) h, tt, parent = [(0, 1)], [2 ** 40] * (n + 1), [0] * (n + 1) w...
output
1
18,802
13
37,605
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains two integers n and m (2 ≤ n ≤ 105, 0 ≤ m ≤ 105)...
instruction
0
18,803
13
37,606
Tags: graphs, shortest paths Correct Solution: ``` import sys from collections import defaultdict import heapq input = sys.stdin.readline def get_adj_mat(src, dst, weight): matrix = defaultdict(list) for src_i, dst_i, weight_i in zip(src, dst, weight): matrix[src_i].append((weight_i, dst_i)) ma...
output
1
18,803
13
37,607
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains two integers n and m (2 ≤ n ≤ 105, 0 ≤ m ≤ 105)...
instruction
0
18,804
13
37,608
Tags: graphs, shortest paths Correct Solution: ``` from heapq import * import sys input=sys.stdin.readline n,m=map(int,input().split()) g=[[] for i in range(n+1)] for i in range(m): x,y,w=map(int,input().split()) if x!=y: g[x].append((y,w)) g[y].append((x,w)) path=[i for i in range(n+1)] dis=[float('inf')]*(n+1) ...
output
1
18,804
13
37,609
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains two integers n and m (2 ≤ n ≤ 105, 0 ≤ m ≤ 105)...
instruction
0
18,805
13
37,610
Tags: graphs, shortest paths Correct Solution: ``` from collections import defaultdict,deque,Counter,OrderedDict from heapq import heappop,heappush def main(): n,m = map(int,input().split()) adj = [[] for i in range(n+1)] for i in range(m): a,b,c = map(int,input().split()) adj[a].append((b,c...
output
1
18,805
13
37,611
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains two integers n and m (2 ≤ n ≤ 105, 0 ≤ m ≤ 105)...
instruction
0
18,806
13
37,612
Tags: graphs, shortest paths Correct Solution: ``` # from debug import debug import sys from heapq import * inf = int(1e12) n, m = map(int, input().split()) parent = [-1]*n dis = [inf]*n graph = [[] for i in range(n)] dis[0] = 0 for i in range(m): a,b,c = map(int, input().split()) graph[a-1].append((b-1,c)) graph[...
output
1
18,806
13
37,613
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains two integers n and m (2 ≤ n ≤ 105, 0 ≤ m ≤ 105)...
instruction
0
18,807
13
37,614
Tags: graphs, shortest paths Correct Solution: ``` import heapq INF = 10**13 def dijk(st, d, p, g): q = [(d[st], st)] while q: ln, v = heapq.heappop(q) if(ln > d[v]): continue for (to, w) in (g[v]): if d[to] > ln + w: d[to] = ln + w p[to] = v heapq.heappush(q, (d[to], to)) def main(): n, ...
output
1
18,807
13
37,615
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains ...
instruction
0
18,808
13
37,616
Yes
output
1
18,808
13
37,617
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains ...
instruction
0
18,809
13
37,618
Yes
output
1
18,809
13
37,619
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains ...
instruction
0
18,810
13
37,620
Yes
output
1
18,810
13
37,621
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains ...
instruction
0
18,811
13
37,622
Yes
output
1
18,811
13
37,623
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains ...
instruction
0
18,812
13
37,624
No
output
1
18,812
13
37,625
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains ...
instruction
0
18,813
13
37,626
No
output
1
18,813
13
37,627
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains ...
instruction
0
18,814
13
37,628
No
output
1
18,814
13
37,629
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n. Input The first line contains ...
instruction
0
18,815
13
37,630
No
output
1
18,815
13
37,631
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Bogdan has a birthday today and mom gave him a tree consisting of n vertecies. For every edge of the tree i, some number xi was written on it. In case you forget, a tree is a connected non-direc...
instruction
0
18,965
13
37,930
No
output
1
18,965
13
37,931
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Bogdan has a birthday today and mom gave him a tree consisting of n vertecies. For every edge of the tree i, some number xi was written on it. In case you forget, a tree is a connected non-direc...
instruction
0
18,966
13
37,932
No
output
1
18,966
13
37,933
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Bogdan has a birthday today and mom gave him a tree consisting of n vertecies. For every edge of the tree i, some number xi was written on it. In case you forget, a tree is a connected non-direc...
instruction
0
18,967
13
37,934
No
output
1
18,967
13
37,935
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a tree of n nodes. The tree is rooted at node 1, which is not considered as a leaf regardless of its degree. Each leaf of the tree has one of the two colors: red or blue. Leaf nod...
instruction
0
20,367
13
40,734
No
output
1
20,367
13
40,735
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a tree of n nodes. The tree is rooted at node 1, which is not considered as a leaf regardless of its degree. Each leaf of the tree has one of the two colors: red or blue. Leaf nod...
instruction
0
20,368
13
40,736
No
output
1
20,368
13
40,737
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a tree of n nodes. The tree is rooted at node 1, which is not considered as a leaf regardless of its degree. Each leaf of the tree has one of the two colors: red or blue. Leaf nod...
instruction
0
20,369
13
40,738
No
output
1
20,369
13
40,739