题:https://leetcode.com/problems/binary-tree-maximum-path-sum/description/
题目
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 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
思路
该类问题往往都需要往动态规划上面靠,写出状态转移方程。
在这个问题中,最重要的是 求解的量,不是状态转移方程所需要的结果。它只是结果的一部分。
code
python
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# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def getPathSum(self,root):
if root == None:
return 0
left = max(0,self.getPathSum(root.left))
right = max(0,self.getPathSum(root.right))
nodeSum = left+right+root.val
if nodeSum > self.maxSum:
self.maxSum = nodeSum
return max(left,right)+root.val
def maxPathSum(self, root):
"""
:type root: TreeNode
:rtype: int
"""
if root == None:
return 0
self.maxSum = root.val
self.getPathSum(root)
return self.maxSum