{ "data": { "question": { "questionId": "2652", "questionFrontendId": "2581", "categoryTitle": "Algorithms", "boundTopicId": 2144482, "title": "Count Number of Possible Root Nodes", "titleSlug": "count-number-of-possible-root-nodes", "content": "

Alice has an undirected tree with n nodes labeled from 0 to n - 1. The tree is represented as a 2D integer array edges of length n - 1 where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree.

\n\n

Alice wants Bob to find the root of the tree. She allows Bob to make several guesses about her tree. In one guess, he does the following:

\n\n\n\n

Bob's guesses are represented by a 2D integer array guesses where guesses[j] = [uj, vj] indicates Bob guessed uj to be the parent of vj.

\n\n

Alice being lazy, does not reply to each of Bob's guesses, but just says that at least k of his guesses are true.

\n\n

Given the 2D integer arrays edges, guesses and the integer k, return the number of possible nodes that can be the root of Alice's tree. If there is no such tree, return 0.

\n\n

 

\n

Example 1:

\n\n

\"\"

\n\n
\nInput: edges = [[0,1],[1,2],[1,3],[4,2]], guesses = [[1,3],[0,1],[1,0],[2,4]], k = 3\nOutput: 3\nExplanation: \nRoot = 0, correct guesses = [1,3], [0,1], [2,4]\nRoot = 1, correct guesses = [1,3], [1,0], [2,4]\nRoot = 2, correct guesses = [1,3], [1,0], [2,4]\nRoot = 3, correct guesses = [1,0], [2,4]\nRoot = 4, correct guesses = [1,3], [1,0]\nConsidering 0, 1, or 2 as root node leads to 3 correct guesses.\n\n
\n\n

Example 2:

\n\n

\"\"

\n\n
\nInput: edges = [[0,1],[1,2],[2,3],[3,4]], guesses = [[1,0],[3,4],[2,1],[3,2]], k = 1\nOutput: 5\nExplanation: \nRoot = 0, correct guesses = [3,4]\nRoot = 1, correct guesses = [1,0], [3,4]\nRoot = 2, correct guesses = [1,0], [2,1], [3,4]\nRoot = 3, correct guesses = [1,0], [2,1], [3,2], [3,4]\nRoot = 4, correct guesses = [1,0], [2,1], [3,2]\nConsidering any node as root will give at least 1 correct guess. \n\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "统计可能的树根数目", "translatedContent": "

Alice 有一棵 n 个节点的树，节点编号为 0 到 n - 1 。树用一个长度为 n - 1 的二维整数数组 edges 表示，其中 edges[i] = [ai, bi] ，表示树中节点 ai 和 bi 之间有一条边。

\n\n

Alice 想要 Bob 找到这棵树的根。她允许 Bob 对这棵树进行若干次 猜测 。每一次猜测，Bob 做如下事情：

\n\n\n\n

Bob 的猜测用二维整数数组 guesses 表示，其中 guesses[j] = [uj, vj] 表示 Bob 猜 uj 是 vj 的父节点。

\n\n

Alice 非常懒，她不想逐个回答 Bob 的猜测，只告诉 Bob 这些猜测里面 至少 有 k 个猜测的结果为 true 。

\n\n

给你二维整数数组 edges ，Bob 的所有猜测和整数 k ，请你返回可能成为树根的 节点数目 。如果没有这样的树，则返回 0。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：edges = [[0,1],[1,2],[1,3],[4,2]], guesses = [[1,3],[0,1],[1,0],[2,4]], k = 3\n输出：3\n解释：\n根为节点 0 ，正确的猜测为 [1,3], [0,1], [2,4]\n根为节点 1 ，正确的猜测为 [1,3], [1,0], [2,4]\n根为节点 2 ，正确的猜测为 [1,3], [1,0], [2,4]\n根为节点 3 ，正确的猜测为 [1,0], [2,4]\n根为节点 4 ，正确的猜测为 [1,3], [1,0]\n节点 0 ，1 或 2 为根时，可以得到 3 个正确的猜测。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：edges = [[0,1],[1,2],[2,3],[3,4]], guesses = [[1,0],[3,4],[2,1],[3,2]], k = 1\n输出：5\n解释：\n根为节点 0 ，正确的猜测为 [3,4]\n根为节点 1 ，正确的猜测为 [1,0], [3,4]\n根为节点 2 ，正确的猜测为 [1,0], [2,1], [3,4]\n根为节点 3 ，正确的猜测为 [1,0], [2,1], [3,2], [3,4]\n根为节点 4 ，正确的猜测为 [1,0], [2,1], [3,2]\n任何节点为根，都至少有 1 个正确的猜测。\n
\n\n

 

\n\n

提示：

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\\u5df2\\u9884\\u5148 (require data\\/gvector data\\/queue data\\/order data\\/heap). \\u82e5\\u9700\\u4f7f\\u7528\\u5176\\u5b83\\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u53ef\\u81ea\\u884c require\\u3002<\\/p>\"],\"erlang\":[\"Erlang\",\"Erlang\\/OTP 24.2\"],\"elixir\":[\"Elixir\",\"Elixir 1.13.0 with Erlang\\/OTP 24.2\"],\"dart\":[\"Dart\",\"
Dart 2.17.3<\\/p>\\r\\n\\r\\n
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