{ "data": { "question": { "questionId": "2400", "questionFrontendId": "2322", "categoryTitle": "Algorithms", "boundTopicId": 1621121, "title": "Minimum Score After Removals on a Tree", "titleSlug": "minimum-score-after-removals-on-a-tree", "content": "

There is an undirected connected tree with n nodes labeled from 0 to n - 1 and n - 1 edges.

\n\n

You are given a 0-indexed integer array nums of length n where nums[i] represents the value of the ith node. You are also 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

Remove two distinct edges of the tree to form three connected components. For a pair of removed edges, the following steps are defined:

\n\n
    \n\t
  1. Get the XOR of all the values of the nodes for each of the three components respectively.
    2. \n\t
  2. The difference between the largest XOR value and the smallest XOR value is the score of the pair.
    3. \n
\n\n\n\n

Return the minimum score of any possible pair of edge removals on the given tree.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: nums = [1,5,5,4,11], edges = [[0,1],[1,2],[1,3],[3,4]]\nOutput: 9\nExplanation: The diagram above shows a way to make a pair of removals.\n- The 1st component has nodes [1,3,4] with values [5,4,11]. Its XOR value is 5 ^ 4 ^ 11 = 10.\n- The 2nd component has node [0] with value [1]. Its XOR value is 1 = 1.\n- The 3rd component has node [2] with value [5]. Its XOR value is 5 = 5.\nThe score is the difference between the largest and smallest XOR value which is 10 - 1 = 9.\nIt can be shown that no other pair of removals will obtain a smaller score than 9.\n
\n\n

Example 2:

\n\"\"\n
\nInput: nums = [5,5,2,4,4,2], edges = [[0,1],[1,2],[5,2],[4,3],[1,3]]\nOutput: 0\nExplanation: The diagram above shows a way to make a pair of removals.\n- The 1st component has nodes [3,4] with values [4,4]. Its XOR value is 4 ^ 4 = 0.\n- The 2nd component has nodes [1,0] with values [5,5]. Its XOR value is 5 ^ 5 = 0.\n- The 3rd component has nodes [2,5] with values [2,2]. Its XOR value is 2 ^ 2 = 0.\nThe score is the difference between the largest and smallest XOR value which is 0 - 0 = 0.\nWe cannot obtain a smaller score than 0.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "从树中删除边的最小分数", "translatedContent": "

存在一棵无向连通树，树中有编号从 0 到 n - 1 的 n 个节点， 以及 n - 1 条边。

\n\n

给你一个下标从 0 开始的整数数组 nums ，长度为 n ，其中 nums[i] 表示第 i 个节点的值。另给你一个二维整数数组 edges ，长度为 n - 1 ，其中 edges[i] = [ai, bi] 表示树中存在一条位于节点 ai 和 bi 之间的边。

\n\n

删除树中两条 不同 的边以形成三个连通组件。对于一种删除边方案，定义如下步骤以计算其分数：

\n\n
    \n\t
  1. 分别获取三个组件 每个 组件中所有节点值的异或值。
    2. \n\t
  2. 最大 异或值和 最小 异或值的 差值 就是这一种删除边方案的分数。
    3. \n
\n\n\n\n

返回在给定树上执行任意删除边方案可能的 最小 分数。

\n\n

 

\n\n

示例 1：

\n\"\"\n
输入：nums = [1,5,5,4,11], edges = [[0,1],[1,2],[1,3],[3,4]]\n输出：9\n解释：上图展示了一种删除边方案。\n- 第 1 个组件的节点是 [1,3,4] ，值是 [5,4,11] 。异或值是 5 ^ 4 ^ 11 = 10 。\n- 第 2 个组件的节点是 [0] ，值是 [1] 。异或值是 1 = 1 。\n- 第 3 个组件的节点是 [2] ，值是 [5] 。异或值是 5 = 5 。\n分数是最大异或值和最小异或值的差值，10 - 1 = 9 。\n可以证明不存在分数比 9 小的删除边方案。\n
\n\n

示例 2：

\n\"\"\n
输入：nums = [5,5,2,4,4,2], edges = [[0,1],[1,2],[5,2],[4,3],[1,3]]\n输出：0\n解释：上图展示了一种删除边方案。\n- 第 1 个组件的节点是 [3,4] ，值是 [4,4] 。异或值是 4 ^ 4 = 0 。\n- 第 2 个组件的节点是 [1,0] ，值是 [5,5] 。异或值是 5 ^ 5 = 0 。\n- 第 3 个组件的节点是 [2,5] ，值是 [2,2] 。异或值是 2 ^ 2 = 0 。\n分数是最大异或值和最小异或值的差值，0 - 0 = 0 。\n无法获得比 0 更小的分数 0 。\n
\n\n

 

\n\n

提示：

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            "exampleTestcases": "[1,5,5,4,11]\n[[0,1],[1,2],[1,3],[3,4]]\n[5,5,2,4,4,2]\n[[0,1],[1,2],[5,2],[4,3],[1,3]]",
            "__typename": "QuestionNode"
        }
    }
}