124. 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:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right

maxSum = -2**31
class Solution:
    def maxPathSum(self, root: TreeNode) -> int:
        global maxSum
        maxSum = -2**31
        DFS(root)
        return maxSum
        
        
def DFS(root):
    global maxSum
    if root==None:
        return -2**31
    
    l = DFS(root.left)
    r = DFS(root.right)
    v = root.val
    maxSum = max(v, v+l, v+r, l+r+v, maxSum)
    return max(v,v+l,v+r)