Binary Tree Maximum Path Sum.py

'''
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
'''

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

class Solution(object):
    res = float('-inf')
        
    def maxPathSum(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        if not root:
            return 0
        self.call(root)
        return self.res
    
    def call(self, node):
        if not node:
            return 0
        
        left = max(0, self.call(node.left))
        right = max(0, self.call(node.right))
        
        self.res = max(self.res, node.val + left + right)
        
        return max(left, right) + node.val