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
来源:力扣(LeetCode)
链接:https://leetcode-cn.com/problems/binary-tree-maximum-path-sum
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解
# 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:
def max_gain(node):
nonlocal max_sum
if not node:
return 0
# max sum on the left and right sub-trees of node
left_gain = max(max_gain(node.left), 0)
right_gain = max(max_gain(node.right), 0)
# the price to start a new path where `node` is a highest node
price_newpath = node.val + left_gain + right_gain
# update max_sum if it's better to start a new path
max_sum = max(max_sum, price_newpath)
# for recursion :
# return the max gain if continue the same path
return node.val + max(left_gain, right_gain)
max_sum = float('-inf')
max_gain(root)
return max_sum