【leetcode】(python)124. Binary Tree Maximum Path Sum二叉树最大路径和

124. Binary Tree Maximum Path Sum Hard

Description

Given a non-empty binary tree, find the maximum path sum.

For this problem, a path is defined as any sequence of nodes from some starting node to any node in the tree along the parent-child connections. The path must contain at least one node and does not need to go through the root.

Example

• Example 1:

Input: [1,2,3]

       1
      / \
     2   3

Output: 6

• Example 2:

Input: [-10,9,20,null,null,15,7]

   -10
   / \
  9  20
    /  \
   15   7

Output: 42

题意

求一非空二叉树的最大路径和

解体思路

树的问题大多可用递归思想，该题递归思路：左子树中的最大路径和，右子树中的最大路径和，以及左子树中以root.left为起点的最大路径（大于零）+ 右子树中以root.right为起点的最大路径（大于零）+ 根的值root.val），这三者中的最大值就是最大的路径和。

code

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

class Solution:
    def maxPathSum(self, root: TreeNode) -> int:
        if not root:
            return 0
        res = [-2**32]
        def fun(root):
            if not root:
                return 0
            rt,l,r = root.val,0,0
            if root.left:
                l = fun(root.left)
            if root.right:
                r = fun(root.right)
            res[0] = max(res[0],rt+max(0,l)+max(0,r))
            return rt + max(l,r,0)
        fun(root)
        return res[0]