day_29.py

'''
Problem Statement:
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
'''

# 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:
        def dfs(node):
            if not node:
                return 0
            left = dfs(node.left)
            right = dfs(node.right)
            curr = max(node.val, left+node.val, right+node.val)
            self.globalMax = max(curr, node.val+left+right, self.globalMax)
            return curr
        self.globalMax = float("-inf")
        dfs(root)
        return self.globalMax