124. 二叉树中的最大路径和

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/

# 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_