Binary tree path sum (#7748)

* feat: Implement binary tree path sum (#7135)

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* Update data_structures/binary_tree/binary_tree_path_sum.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* refactor: Rename `dfs` to `depth_first_search`

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

data_structures/binary_tree/binary_tree_path_sum.py

@@ -0,0 +1,88 @@
+"""
+Given the root of a binary tree and an integer target,
+find the number of paths where the sum of the values
+along the path equals target.
+
+
+Leetcode reference: https://leetcode.com/problems/path-sum-iii/
+"""
+
+from __future__ import annotations
+
+
+class Node:
+    """
+    A Node has value variable and pointers to Nodes to its left and right.
+    """
+
+    def __init__(self, value: int) -> None:
+        self.value = value
+        self.left: Node | None = None
+        self.right: Node | None = None
+
+
+class BinaryTreePathSum:
+    r"""
+    The below tree looks like this
+          10
+         /  \
+        5   -3
+       / \    \
+      3   2    11
+     / \   \
+    3  -2   1
+
+
+    >>> tree = Node(10)
+    >>> tree.left = Node(5)
+    >>> tree.right = Node(-3)
+    >>> tree.left.left = Node(3)
+    >>> tree.left.right = Node(2)
+    >>> tree.right.right = Node(11)
+    >>> tree.left.left.left = Node(3)
+    >>> tree.left.left.right = Node(-2)
+    >>> tree.left.right.right = Node(1)
+
+    >>> BinaryTreePathSum().path_sum(tree, 8)
+    3
+    >>> BinaryTreePathSum().path_sum(tree, 7)
+    2
+    >>> tree.right.right = Node(10)
+    >>> BinaryTreePathSum().path_sum(tree, 8)
+    2
+    """
+
+    target: int
+
+    def __init__(self) -> None:
+        self.paths = 0
+
+    def depth_first_search(self, node: Node | None, path_sum: int) -> None:
+        if node is None:
+            return
+
+        if path_sum == self.target:
+            self.paths += 1
+
+        if node.left:
+            self.depth_first_search(node.left, path_sum + node.left.value)
+        if node.right:
+            self.depth_first_search(node.right, path_sum + node.right.value)
+
+    def path_sum(self, node: Node | None, target: int | None = None) -> int:
+        if node is None:
+            return 0
+        if target is not None:
+            self.target = target
+
+        self.depth_first_search(node, node.value)
+        self.path_sum(node.left)
+        self.path_sum(node.right)
+
+        return self.paths
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()