BinaryTreeMaxPathSum.py

'''
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
'''

# 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: Optional[TreeNode]) -> int:
        
        res = [root.val]
        def dfs(root):
            if not root:
                return 0

            lMax, rMax = dfs(root.left), dfs(root.right)
            lMax, rMax = max(lMax, 0), max(rMax, 0)

            res[0] = max(res[0], root.val + lMax + rMax)

            return root.val + max(lMax, rMax)

        dfs(root)
        return res[0]

'''
Runtime 73 ms Beats 86.21%
Memory 23.8 MB Beats 40.32%
'''