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124. 二叉树中的最大路径和
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https://leetcode-cn.com/problems/binary-tree-maximum-path-sum/

给定一个非空二叉树，返回其最大路径和。

本题中，路径被定义为一条从树中任意节点出发，达到任意节点的序列。该路径至少包含一个节点，且不一定经过根节点。

示例 1:
::

    输入: [1,2,3]

           1
          / \
         2   3

    输出: 6

示例 2:
::

    输入: [-10,9,20,null,null,15,7]

       -10
       / \
      9  20
        /  \
       15   7

    输出: 42


题解：https://leetcode-cn.com/problems/binary-tree-maximum-path-sum/solution/xiang-xi-tong-su-de-si-lu-fen-xi-duo-jie-fa-by-30/


.. code:: python

    # Definition for a binary tree node.
    # class TreeNode(object):
    #     def __init__(self, x):
    #         self.val = x
    #         self.left = None
    #         self.right = None

    class Solution(object):
        def maxPathSum(self, root):
            """
            :type root: TreeNode
            :rtype: int
            """
            def dfs(node):
                if not node:
                    return 0
                left = dfs(node.left)
                right = dfs(node.right)

                self.sum_ = max(self.sum_, left+right+node.val)
                return max(node.val + max(left, right), 0)

            self.sum_ = float('-inf')
            dfs(root)
            return self.sum_