{ "data": { "question": { "questionId": "2564", "questionFrontendId": "2467", "categoryTitle": "Algorithms", "boundTopicId": 1962308, "title": "Most Profitable Path in a Tree", "titleSlug": "most-profitable-path-in-a-tree", "content": "

There is an undirected tree with n nodes labeled from 0 to n - 1, rooted at node 0. You are given 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

At every node i, there is a gate. You are also given an array of even integers amount, where amount[i] represents:

\n\n\n\n

The game goes on as follows:

\n\n\n\n

Return the maximum net income Alice can have if she travels towards the optimal leaf node.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: edges = [[0,1],[1,2],[1,3],[3,4]], bob = 3, amount = [-2,4,2,-4,6]\nOutput: 6\nExplanation: \nThe above diagram represents the given tree. The game goes as follows:\n- Alice is initially on node 0, Bob on node 3. They open the gates of their respective nodes.\n  Alice's net income is now -2.\n- Both Alice and Bob move to node 1. \n  Since they reach here simultaneously, they open the gate together and share the reward.\n  Alice's net income becomes -2 + (4 / 2) = 0.\n- Alice moves on to node 3. Since Bob already opened its gate, Alice's income remains unchanged.\n  Bob moves on to node 0, and stops moving.\n- Alice moves on to node 4 and opens the gate there. Her net income becomes 0 + 6 = 6.\nNow, neither Alice nor Bob can make any further moves, and the game ends.\nIt is not possible for Alice to get a higher net income.\n
\n\n

Example 2:

\n\"\"\n
\nInput: edges = [[0,1]], bob = 1, amount = [-7280,2350]\nOutput: -7280\nExplanation: \nAlice follows the path 0->1 whereas Bob follows the path 1->0.\nThus, Alice opens the gate at node 0 only. Hence, her net income is -7280. \n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "树上最大得分和路径", "translatedContent": "

一个 n 个节点的无向树，节点编号为 0 到 n - 1 ，树的根结点是 0 号节点。给你一个长度为 n - 1 的二维整数数组 edges ，其中 edges[i] = [ai, bi] ，表示节点 ai 和 bi 在树中有一条边。

\n\n

在每一个节点 i 处有一扇门。同时给你一个都是偶数的数组 amount ，其中 amount[i] 表示：

\n\n\n\n

游戏按照如下规则进行：

\n\n\n\n

请你返回 Alice 朝最优叶子结点移动的 最大 净得分。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
输入：edges = [[0,1],[1,2],[1,3],[3,4]], bob = 3, amount = [-2,4,2,-4,6]\n输出：6\n解释：\n上图展示了输入给出的一棵树。游戏进行如下：\n- Alice 一开始在节点 0 处，Bob 在节点 3 处。他们分别打开所在节点的门。\n  Alice 得分为 -2 。\n- Alice 和 Bob 都移动到节点 1 。\n  因为他们同时到达这个节点，他们一起打开门并平分得分。\n  Alice 的得分变为 -2 + (4 / 2) = 0 。\n- Alice 移动到节点 3 。因为 Bob 已经打开了这扇门，Alice 得分不变。\n  Bob 移动到节点 0 ，并停止移动。\n- Alice 移动到节点 4 并打开这个节点的门，她得分变为 0 + 6 = 6 。\n现在，Alice 和 Bob 都不能进行任何移动了，所以游戏结束。\nAlice 无法得到更高分数。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
输入：edges = [[0,1]], bob = 1, amount = [-7280,2350]\n输出：-7280\n解释：\nAlice 按照路径 0->1 移动，同时 Bob 按照路径 1->0 移动。\n所以 Alice 只打开节点 0 处的门，她的得分为 -7280 。\n
\n\n

 

\n\n

提示：

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