Description
https://leetcode.com/problems/binary-tree-maximum-path-sum/
A path in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence at most once. Note that the path does not need to pass through the root.
The path sum of a path is the sum of the node’s values in the path.
Given the root of a binary tree, return the maximum path sum of any path.
Example 1:
Input: root = [1,2,3] Output: 6 Explanation: The optimal path is 2 -> 1 -> 3 with a path sum of 2 + 1 + 3 = 6.
Example 2:
Input: root = [-10,9,20,null,null,15,7] Output: 42 Explanation: The optimal path is 15 -> 20 -> 7 with a path sum of 15 + 20 + 7 = 42.
Constraints:
- The number of nodes in the tree is in the range
[1, 3 * 104]. -1000 <= Node.val <= 1000
Explanation
Use a helper function to find the max path value from a node. Traverse each node to globally find the maximum path sum of the whole tree.
Python Solution
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
class Solution:
def maxPathSum(self, root: TreeNode) -> int:
self.max_sum = -sys.maxsize
self.helper(root)
return self.max_sum
def helper(self, root):
if root == None:
return 0
left = max(self.helper(root.left), 0)
right = max(self.helper(root.right), 0)
self.max_sum = max(self.max_sum, left + right + root.val)
return max(left, right) + root.val
- Time Complexity: O(N).
- Space Complexity: O(N).