GCD Counting【Educational Codeforces Round 58 (Rated for Div. 2) 1101D】【树的直径 + 质数筛】
题目链接
D. GCD Counting
time limit per test
4.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
You are given a tree consisting of ?n vertices. A number is written on each vertex; the number on vertex ?i is equal to ??ai.
Let's denote the function ?(?,?)g(x,y) as the greatest common divisor of the numbers written on the vertices belonging to the simple path from vertex ?x to vertex ?y (including these two vertices). Also let's denote ????(?,?)dist(x,y) as the number of vertices on the simple path between vertices ?x and ?y, including the endpoints. ????(?,?)=1dist(x,x)=1 for every vertex ?x.
Your task is calculate the maximum value of ????(?,?)dist(x,y) among such pairs of vertices that ?(?,?)>1g(x,y)>1.
Input
The first line contains one integer ?n — the number of vertices (1≤?≤2⋅105)(1≤n≤2⋅105).
The second line contains ?n integers ?1a1, ?2a2, ..., ??an (1≤??≤2⋅105)(1≤ai≤2⋅105) — the numbers written on vertices.
Then ?−1n−1 lines follow, each containing two integers ?x and ?y (1≤?,?≤?,?≠?)(1≤x,y≤n,x≠y) denoting an edge connecting vertex ?x with vertex ?y. It is guaranteed that these edges form a tree.
Output
If there is no pair of vertices ?,?x,y such that ?(?,?)>1g(x,y)>1, print 00. Otherwise print the maximum value of ????(?,?)dist(x,y) among such pairs.
Examples
input
Copy
3 2 3 4 1 2 2 3
output
Copy
1
input
Copy
3 2 3 4 1 3 2 3
output
Copy
2
input
Copy
3 1 1 1 1 2 2 3
output
Copy
0
题意：求一条gcd不为1的最长的链的长度。
思路：处理这样的一条链，说明这条链上的每个点都有一个相同的质因子，那不如就用这质因子去跑通过这个节点来跑这棵树，我们假设这条链都是以这个质因子为基础跑出来的，然后，就是质因子内存所有的节点，若是跑过的话，就说明已经是跑过该子树的树的直径了，就不需要进去跑了，否则，就是把这点放进去跑树的直径即可，然后每次ans更新最大的树的直径即可。
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