feat: Binary tree node sum (#7020) (#7162)

* feat: Binary tree node sum (#7020)

* feat: Sum of all nodes in binary tree explanation (#7020)

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update data_structures/binary_tree/binary_tree_node_sum.py

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

* refactor: Change replace method with `__iter__` overriding (#7020)

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

DIRECTORY.md

@@ -154,6 +154,7 @@
     * [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 Mirror](data_structures/binary_tree/binary_tree_mirror.py)
+    * [Binary Tree Node Sum](data_structures/binary_tree/binary_tree_node_sum.py)
     * [Binary Tree Traversals](data_structures/binary_tree/binary_tree_traversals.py)
     * [Fenwick Tree](data_structures/binary_tree/fenwick_tree.py)
     * [Inorder Tree Traversal 2022](data_structures/binary_tree/inorder_tree_traversal_2022.py)

data_structures/binary_tree/binary_tree_node_sum.py

@@ -0,0 +1,76 @@
+"""
+Sum of all nodes in a binary tree.
+
+Python implementation:
+    O(n) time complexity - Recurses through :meth:`depth_first_search`
+                            with each element.
+    O(n) space complexity - At any point in time maximum number of stack
+                            frames that could be in memory is `n`
+"""
+
+
+from __future__ import annotations
+
+from collections.abc import Iterator
+
+
+class Node:
+    """
+    A Node has a 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 BinaryTreeNodeSum:
+    r"""
+    The below tree looks like this
+        10
+       /  \
+      5   -3
+     /    / \
+    12   8  0
+
+    >>> tree = Node(10)
+    >>> sum(BinaryTreeNodeSum(tree))
+    10
+
+    >>> tree.left = Node(5)
+    >>> sum(BinaryTreeNodeSum(tree))
+    15
+
+    >>> tree.right = Node(-3)
+    >>> sum(BinaryTreeNodeSum(tree))
+    12
+
+    >>> tree.left.left = Node(12)
+    >>> sum(BinaryTreeNodeSum(tree))
+    24
+
+    >>> tree.right.left = Node(8)
+    >>> tree.right.right = Node(0)
+    >>> sum(BinaryTreeNodeSum(tree))
+    32
+    """
+
+    def __init__(self, tree: Node) -> None:
+        self.tree = tree
+
+    def depth_first_search(self, node: Node | None) -> int:
+        if node is None:
+            return 0
+        return node.value + (
+            self.depth_first_search(node.left) + self.depth_first_search(node.right)
+        )
+
+    def __iter__(self) -> Iterator[int]:
+        yield self.depth_first_search(self.tree)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()