{ "data": { "question": { "questionId": "3112", "questionFrontendId": "2867", "categoryTitle": "Algorithms", "boundTopicId": 2453611, "title": "Count Valid Paths in a Tree", "titleSlug": "count-valid-paths-in-a-tree", "content": "

There is an undirected tree with n nodes labeled from 1 to n. You are given the integer n and a 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the tree.

\n\n

Return the number of valid paths in the tree.

\n\n

A path (a, b) is valid if there exists exactly one prime number among the node labels in the path from a to b.

\n\n

Note that:

\n\n\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: n = 5, edges = [[1,2],[1,3],[2,4],[2,5]]\nOutput: 4\nExplanation: The pairs with exactly one prime number on the path between them are: \n- (1, 2) since the path from 1 to 2 contains prime number 2. \n- (1, 3) since the path from 1 to 3 contains prime number 3.\n- (1, 4) since the path from 1 to 4 contains prime number 2.\n- (2, 4) since the path from 2 to 4 contains prime number 2.\nIt can be shown that there are only 4 valid paths.\n
\n\n

Example 2:

\n\"\"\n
\nInput: n = 6, edges = [[1,2],[1,3],[2,4],[3,5],[3,6]]\nOutput: 6\nExplanation: The pairs with exactly one prime number on the path between them are: \n- (1, 2) since the path from 1 to 2 contains prime number 2.\n- (1, 3) since the path from 1 to 3 contains prime number 3.\n- (1, 4) since the path from 1 to 4 contains prime number 2.\n- (1, 6) since the path from 1 to 6 contains prime number 3.\n- (2, 4) since the path from 2 to 4 contains prime number 2.\n- (3, 6) since the path from 3 to 6 contains prime number 3.\nIt can be shown that there are only 6 valid paths.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "统计树中的合法路径数目", "translatedContent": "

给你一棵 n 个节点的无向树，节点编号为 1 到 n 。给你一个整数 n 和一个长度为 n - 1 的二维整数数组 edges ，其中 edges[i] = [ui, vi] 表示节点 ui 和 vi 在树中有一条边。

\n\n

请你返回树中的 合法路径数目 。

\n\n

如果在节点 a 到节点 b 之间 恰好有一个 节点的编号是质数，那么我们称路径 (a, b) 是 合法的 。

\n\n

注意：

\n\n\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：n = 5, edges = [[1,2],[1,3],[2,4],[2,5]]\n输出：4\n解释：恰好有一个质数编号的节点路径有：\n- (1, 2) 因为路径 1 到 2 只包含一个质数 2 。\n- (1, 3) 因为路径 1 到 3 只包含一个质数 3 。\n- (1, 4) 因为路径 1 到 4 只包含一个质数 2 。\n- (2, 4) 因为路径 2 到 4 只包含一个质数 2 。\n只有 4 条合法路径。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：n = 6, edges = [[1,2],[1,3],[2,4],[3,5],[3,6]]\n输出：6\n解释：恰好有一个质数编号的节点路径有：\n- (1, 2) 因为路径 1 到 2 只包含一个质数 2 。\n- (1, 3) 因为路径 1 到 3 只包含一个质数 3 。\n- (1, 4) 因为路径 1 到 4 只包含一个质数 2 。\n- (1, 6) 因为路径 1 到 6 只包含一个质数 3 。\n- (2, 4) 因为路径 2 到 4 只包含一个质数 2 。\n- (3, 6) 因为路径 3 到 6 只包含一个质数 3 。\n只有 6 条合法路径。\n
\n\n

 

\n\n

提示：

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