Added functionality to calculate the diameter of given binary tree (#10526)

* Added code to find diameter of given binary tree

* Modified diameter_of_binary_tree file

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* Update diameter_of_binary_tree.py

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

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

* Update diameter_of_binary_tree.py

---------

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/diameter_of_binary_tree.py

@@ -0,0 +1,72 @@
+"""
+The diameter/width of a tree is defined as the number of nodes on the longest path
+between two end nodes.
+"""
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+
+@dataclass
+class Node:
+    data: int
+    left: Node | None = None
+    right: Node | None = None
+
+    def depth(self) -> int:
+        """
+        >>> root = Node(1)
+        >>> root.depth()
+        1
+        >>> root.left = Node(2)
+        >>> root.depth()
+        2
+        >>> root.left.depth()
+        1
+        >>> root.right = Node(3)
+        >>> root.depth()
+        2
+        """
+        left_depth = self.left.depth() if self.left else 0
+        right_depth = self.right.depth() if self.right else 0
+        return max(left_depth, right_depth) + 1
+
+    def diameter(self) -> int:
+        """
+        >>> root = Node(1)
+        >>> root.diameter()
+        1
+        >>> root.left = Node(2)
+        >>> root.diameter()
+        2
+        >>> root.left.diameter()
+        1
+        >>> root.right = Node(3)
+        >>> root.diameter()
+        3
+        """
+        left_depth = self.left.depth() if self.left else 0
+        right_depth = self.right.depth() if self.right else 0
+        return left_depth + right_depth + 1
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+    root = Node(1)
+    root.left = Node(2)
+    root.right = Node(3)
+    root.left.left = Node(4)
+    root.left.right = Node(5)
+    r"""
+    Constructed binary tree is
+        1
+       / \
+      2	  3
+     / \
+    4	 5
+    """
+    print(f"{root.diameter() = }")  # 4
+    print(f"{root.left.diameter() = }")  # 3
+    print(f"{root.right.diameter() = }")  # 1