Python algorithm

from typing import Optional

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

def maxPathSum(self, root: Optional[TreeNode]) -> int:
    ans = float('-inf')

    def dfs(root: Optional[TreeNode], ) -> None:
        nonlocal ans
        if root == None:
            return 0

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

        ans = max(ans, root.val + left + right)
        return root.val + max(left, right)

    dfs(root)
    return ans

from typing import Optional

class TreeNode:
    """
    Represents a node in a binary tree.

    Attributes:
        val: The value of the node.
        left: The left child node.
        right: The right child node.
    """
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def maxPathSum(root: Optional[TreeNode]) -> int:
    """
    Finds the maximum path sum in a binary tree.

    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.  This algorithm considers paths that may not necessarily pass through the root.

    Args:
        root: The root node of the binary tree.

    Returns:
        The maximum sum of a path in the tree.  Returns negative infinity if the tree is empty.

    """
    ans = float('-inf') # Initialize the maximum path sum to negative infinity.  This handles cases with all negative values.

    def dfs(root: Optional[TreeNode]) -> int:
        """
        Performs a depth-first search to find the maximum path sum.

        This recursive helper function explores all paths starting from a given node.

        Args:
            root: The current node being visited.

        Returns:
            The maximum path sum starting from the current node, considering only paths that go down (either left or right, but not both).  This is crucial for preventing double-counting.
        """
        nonlocal ans # Access the 'ans' variable from the outer scope.

        if root is None: # Base case: empty subtree
            return 0

        # Recursively calculate the maximum path sum from the left and right subtrees.
        # We use max(dfs(root.left), 0) to handle negative path sums.  If a subtree's max path sum is negative, we ignore it.
        left = max(dfs(root.left), 0) 
        right = max(dfs(root.right), 0)

        # Update the maximum path sum found so far. This line considers paths that pass through the current node.
        ans = max(ans, root.val + left + right) 

        # Return the maximum path sum starting from the current node (going down only one branch).
        return root.val + max(left, right)

    dfs(root)
    return ans