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Try to build the answer bit by bit from the most significant bit to the least significant.
Use the Trie Data Structure to decide for each bit if it exists in the final answer.
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Problems involving subtree aggregation, XOR optimization, and Trie usage are common in FAANG-style interviews. While the exact question may vary, the techniques used in this problem are frequently tested.
A bitwise Trie (prefix tree) is typically the best data structure for this problem. It allows efficient maximum XOR queries in O(B) time, where B is the number of bits in the integer representation.
DFS helps compute subtree sums and track the traversal order of nodes. With entry and exit times from DFS, you can determine whether two subtrees overlap, which is critical for selecting valid pairs.
The optimal approach combines DFS and a bitwise Trie. DFS is used to compute the sum of every subtree, while the Trie helps quickly find another subtree sum that maximizes the XOR value. Additional bookkeeping ensures the chosen subtrees do not overlap.