0124: Binary Tree Maximum Path Sum

Problem Statement

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 non-empty 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

Code Solution

class Solution:
    def maxPathSum(self, root):
	    
        cmax = float('-inf')
        def rec(node):
            nonlocal cmax
            if not node:
                return 0
            lsum = max(0, rec(node.left))
            rsum = max(0, rec(node.right))
            cmax = max(cmax, node.val + lsum + rsum)
            return node.val + max(lsum, rsum)
        
        rec(root)
        return cmax