There is an undirected connected tree with n nodes labeled from 0 to n - 1 and n - 1 edges.
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.
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[4,5,7], [1,9], and [3,3,3]. The three XOR values are 4 ^ 5 ^ 7 = 6, 1 ^ 9 = 8, and 3 ^ 3 ^ 3 = 3. The largest XOR value is 8 and the smallest XOR value is 3. The score is then 8 - 3 = 5.Return the minimum score of any possible pair of edge removals on the given tree.
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Example 1:
\n![\"\"](\"https://assets.leetcode.com/uploads/2022/05/03/ex1drawio.png\")
\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![\"\"](\"https://assets.leetcode.com/uploads/2022/05/03/ex2drawio.png\")
\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\nn == nums.length3 <= n <= 10001 <= nums[i] <= 108edges.length == n - 1edges[i].length == 20 <= ai, bi < nai != biedges represents a valid tree.Compiled with clang 11 using the latest C++ 20 standard.
Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
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