Added an algorithm transfrom bst to greater sum tree (#9777)

* Added an algorithm transfrom bst to greater sum tree

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* Update and rename transform_bst_sum_tree.py to is_sum_tree.py

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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>

data_structures/binary_tree/is_sum_tree.py

@@ -0,0 +1,161 @@
+"""
+Is a binary tree a sum tree where the value of every non-leaf node is equal to the sum
+of the values of its left and right subtrees?
+https://www.geeksforgeeks.org/check-if-a-given-binary-tree-is-sumtree
+"""
+from __future__ import annotations
+
+from collections.abc import Iterator
+from dataclasses import dataclass
+
+
+@dataclass
+class Node:
+    data: int
+    left: Node | None = None
+    right: Node | None = None
+
+    def __iter__(self) -> Iterator[int]:
+        """
+        >>> root = Node(2)
+        >>> list(root)
+        [2]
+        >>> root.left = Node(1)
+        >>> tuple(root)
+        (1, 2)
+        """
+        if self.left:
+            yield from self.left
+        yield self.data
+        if self.right:
+            yield from self.right
+
+    def __len__(self) -> int:
+        """
+        >>> root = Node(2)
+        >>> len(root)
+        1
+        >>> root.left = Node(1)
+        >>> len(root)
+        2
+        """
+        return sum(1 for _ in self)
+
+    @property
+    def is_sum_node(self) -> bool:
+        """
+        >>> root = Node(3)
+        >>> root.is_sum_node
+        True
+        >>> root.left = Node(1)
+        >>> root.is_sum_node
+        False
+        >>> root.right = Node(2)
+        >>> root.is_sum_node
+        True
+        """
+        if not self.left and not self.right:
+            return True  # leaf nodes are considered sum nodes
+        left_sum = sum(self.left) if self.left else 0
+        right_sum = sum(self.right) if self.right else 0
+        return all(
+            (
+                self.data == left_sum + right_sum,
+                self.left.is_sum_node if self.left else True,
+                self.right.is_sum_node if self.right else True,
+            )
+        )
+
+
+@dataclass
+class BinaryTree:
+    root: Node
+
+    def __iter__(self) -> Iterator[int]:
+        """
+        >>> list(BinaryTree.build_a_tree())
+        [1, 2, 7, 11, 15, 29, 35, 40]
+        """
+        return iter(self.root)
+
+    def __len__(self) -> int:
+        """
+        >>> len(BinaryTree.build_a_tree())
+        8
+        """
+        return len(self.root)
+
+    def __str__(self) -> str:
+        """
+        Returns a string representation of the inorder traversal of the binary tree.
+
+        >>> str(list(BinaryTree.build_a_tree()))
+        '[1, 2, 7, 11, 15, 29, 35, 40]'
+        """
+        return str(list(self))
+
+    @property
+    def is_sum_tree(self) -> bool:
+        """
+        >>> BinaryTree.build_a_tree().is_sum_tree
+        False
+        >>> BinaryTree.build_a_sum_tree().is_sum_tree
+        True
+        """
+        return self.root.is_sum_node
+
+    @classmethod
+    def build_a_tree(cls) -> BinaryTree:
+        r"""
+        Create a binary tree with the specified structure:
+              11
+           /     \
+          2       29
+         / \     /  \
+        1   7  15    40
+                       \
+                        35
+        >>> list(BinaryTree.build_a_tree())
+        [1, 2, 7, 11, 15, 29, 35, 40]
+        """
+        tree = BinaryTree(Node(11))
+        root = tree.root
+        root.left = Node(2)
+        root.right = Node(29)
+        root.left.left = Node(1)
+        root.left.right = Node(7)
+        root.right.left = Node(15)
+        root.right.right = Node(40)
+        root.right.right.left = Node(35)
+        return tree
+
+    @classmethod
+    def build_a_sum_tree(cls) -> BinaryTree:
+        r"""
+        Create a binary tree with the specified structure:
+             26
+            /  \
+          10    3
+         /  \    \
+        4    6    3
+        >>> list(BinaryTree.build_a_sum_tree())
+        [4, 10, 6, 26, 3, 3]
+        """
+        tree = BinaryTree(Node(26))
+        root = tree.root
+        root.left = Node(10)
+        root.right = Node(3)
+        root.left.left = Node(4)
+        root.left.right = Node(6)
+        root.right.right = Node(3)
+        return tree
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+    tree = BinaryTree.build_a_tree()
+    print(f"{tree} has {len(tree)} nodes and {tree.is_sum_tree = }.")
+    tree = BinaryTree.build_a_sum_tree()
+    print(f"{tree} has {len(tree)} nodes and {tree.is_sum_tree = }.")