Binary Tree Maximum Path Sum

Problem:

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.

Input and output examples

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

Solution

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution(object):
    def maxPathSum(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        self.max_sum = float('-inf')
        self.max_gain(root)
        return self.max_sum
    
    def max_gain(self, node):
        if not node:
            return 0
        
        left_gain = max(self.max_gain(node.left), 0)
        right_gain = max(self.max_gain(node.right), 0)
        
        price_newpath = node.val + left_gain + right_gain
        
        self.max_sum = max(self.max_sum, price_newpath)
        
        return node.val + max(left_gain, right_gain)

Test the the solution:

class TreeNode(object):
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)

solution = Solution()
print( solution.maxPathSum(root) )

# output: 6

# test the solution      
class TreeNode(object):
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

root = TreeNode(-10)
root.left = TreeNode(9)
root.right = TreeNode(20)
root.right.left = TreeNode(15)
root.right.right = TreeNode(7)

solution = Solution()
print(solution.maxPathSum(root))

# output: 42

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Algorithm