Given a binary tree, find the maximum path sum. The path may start and end at any node in the tree. Solution: For root node, first check two subtrees and figure out the path with maximum sum in each subtree (and the path must contains the root node). More precisely, we can compare root->val, root->val + leftsubtree, root->val + rightsubtree. But this is not enough since the maximum path might contains two subtrees. We have to compute the value of root->val + leftsubtree + rightsubtree as well. The problem is, we cannot directly return this value since this path cannot go to upper nodes anymore. So we also use another global variable to store the maximum sum in each recursion, and update this variable once we find any path with larger sum. The following code passes the LeetCode Online Large Judge. Thanks for the useful comments.
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