Algorithm to get maximum path sum of a binary tree. (#9414)

* Algorithm to get maximum path sum of a binary tree.

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* Added "TreeNode | None" as traverse method argument type hints to accept both

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* Added doctest for construct_tree and type hints for TreeNode

* Added type hint and doctest

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* Organized imports

* updating DIRECTORY.md

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---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: 3 people

DIRECTORY.md

@@ -251,6 +251,7 @@
     * [Basic Binary Tree](data_structures/binary_tree/basic_binary_tree.py)
     * [Binary Search Tree](data_structures/binary_tree/binary_search_tree.py)
     * [Binary Search Tree Recursive](data_structures/binary_tree/binary_search_tree_recursive.py)
+    * [Binary Tree Maximum Path Sum](data_structures/binary_tree/binary_tree_maximum_path_sum.py)
     * [Binary Tree Mirror](data_structures/binary_tree/binary_tree_mirror.py)
     * [Binary Tree Node Sum](data_structures/binary_tree/binary_tree_node_sum.py)
     * [Binary Tree Path Sum](data_structures/binary_tree/binary_tree_path_sum.py)
@@ -876,6 +877,7 @@
   * [Test Factorial](maths/test_factorial.py)
   * [Test Prime Check](maths/test_prime_check.py)
   * [Three Sum](maths/three_sum.py)
+  * [Tonelli Shanks](maths/tonelli_shanks.py)
   * [Trailing Zeroes](maths/trailing_zeroes.py)
   * [Trapezoidal Rule](maths/trapezoidal_rule.py)
   * [Triplet Sum](maths/triplet_sum.py)

data_structures/binary_tree/binary_tree_maximum_path_sum.py

@@ -0,0 +1,116 @@
+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() = }")