from __future__ import annotations

from dataclasses import dataclass


# Leetcode Reference : https://leetcode.com/problems/binary-tree-maximum-path-sum/
@dataclass
class TreeNode:
    val: int
    left: TreeNode | None = None
    right: TreeNode | None = None


class GetMaxPathSum:
    r"""

    GetMaxPathSum takes root node of a tree as initial argument.
    Upon calling max_path_sum(), it returns maximum path
    sum from the tree.

    # Test

    The below tree looks like this
          10
         /  \
        5   -3
       / \    \
      3   2    11
     / \   \
    3  -2   1

    Result will be calculated like : 3 -> 3 -> 5 -> 10 -> -3 -> 11
    As it is the maximum path possible.


    >>> root = TreeNode(10)
    >>> root.left = TreeNode(5)
    >>> root.right = TreeNode(-3)
    >>> root.left.left = TreeNode(3)
    >>> root.left.right = TreeNode(2)
    >>> root.right.right = TreeNode(11)
    >>> root.left.left.left = TreeNode(3)
    >>> root.left.left.right = TreeNode(-2)
    >>> root.left.right.right = TreeNode(1)

    >>> GetMaxPathSum(root).max_path_sum()
    29
    """

    def __init__(self, root: TreeNode) -> None:
        self.sum = -9999999999
        self.root = root

    def traverse(self, root: TreeNode | None) -> int:
        """
        Returns maximum path sum by recursively taking max_path_sum from left
        and max_path_sum from right if current Node has a left or right Node.

        :param root -> tree root:
        :return int:
        """

        if root is None:
            return 0

        right_sum = max(self.traverse(root.right), 0)
        left_sum = max(self.traverse(root.left), 0)

        val = root.val + right_sum + left_sum
        self.sum = max(val, self.sum)

        return root.val + max(right_sum, left_sum)

    def max_path_sum(self) -> int:
        """
        Driver method to get max_path_sum by calling traverse method.
        :return max_path_sum:
        """
        self.traverse(self.root)
        return self.sum


def construct_tree() -> TreeNode:
    r"""
    The below tree
       -10
       / \
      9   20
         /  \
       15    7

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

    >>> GetMaxPathSum(construct_tree()).max_path_sum()
    42
    """

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    tree = GetMaxPathSum(construct_tree())
    print(f"{tree.max_path_sum() = }")