feat(data_structures/binary_tree): add Splay Tree implementation

Author: krrish175-byte

data_structures/binary_tree/splay_tree.py

@@ -0,0 +1,146 @@
+"""
+Splay Tree implementation in Python.
+
+A Splay Tree is a self-adjusting binary search tree that brings the most
+recently accessed element to the root via tree rotations. It provides
+amortized O(log n) time complexity for search, insert, and delete operations.
+
+Reference:
+https://en.wikipedia.org/wiki/Splay_tree
+"""
+
+from __future__ import annotations
+from typing import Optional, List
+
+
+class Node:
+    """Node class for the Splay Tree."""
+
+    def __init__(self, key: int) -> None:
+        self.key = key
+        self.left: Optional[Node] = None
+        self.right: Optional[Node] = None
+
+
+class SplayTree:
+    """Splay Tree Data Structure."""
+
+    def __init__(self) -> None:
+        self.root: Optional[Node] = None
+
+    # ------------------------- ROTATIONS -------------------------
+    def _right_rotate(self, x: Node) -> Node:
+        y = x.left
+        x.left = y.right
+        y.right = x
+        return y
+
+    def _left_rotate(self, x: Node) -> Node:
+        y = x.right
+        x.right = y.left
+        y.left = x
+        return y
+
+    # ------------------------- SPLAY OPERATION -------------------------
+    def _splay(self, root: Optional[Node], key: int) -> Optional[Node]:
+        if root is None or root.key == key:
+            return root
+
+        # Key in left subtree
+        if key < root.key:
+            if root.left is None:
+                return root
+
+            # Zig-Zig (Left Left)
+            if key < root.left.key:
+                root.left.left = self._splay(root.left.left, key)
+                root = self._right_rotate(root)
+            # Zig-Zag (Left Right)
+            elif key > root.left.key:
+                root.left.right = self._splay(root.left.right, key)
+                if root.left.right:
+                    root.left = self._left_rotate(root.left)
+            return root if root.left is None else self._right_rotate(root)
+
+        # Key in right subtree
+        else:
+            if root.right is None:
+                return root
+
+            # Zig-Zig (Right Right)
+            if key > root.right.key:
+                root.right.right = self._splay(root.right.right, key)
+                root = self._left_rotate(root)
+            # Zig-Zag (Right Left)
+            elif key < root.right.key:
+                root.right.left = self._splay(root.right.left, key)
+                if root.right.left:
+                    root.right = self._right_rotate(root.right)
+            return root if root.right is None else self._left_rotate(root)
+
+    # ------------------------- INSERTION -------------------------
+    def insert(self, key: int) -> None:
+        """Inserts a key into the Splay Tree."""
+        if self.root is None:
+            self.root = Node(key)
+            return
+
+        self.root = self._splay(self.root, key)
+        if self.root.key == key:
+            return  # No duplicates
+
+        new_node = Node(key)
+        if key < self.root.key:
+            new_node.right = self.root
+            new_node.left = self.root.left
+            self.root.left = None
+        else:
+            new_node.left = self.root
+            new_node.right = self.root.right
+            self.root.right = None
+        self.root = new_node
+
+    # ------------------------- SEARCH -------------------------
+    def search(self, key: int) -> bool:
+        """Searches for a key and splays it to the root."""
+        self.root = self._splay(self.root, key)
+        return self.root is not None and self.root.key == key
+
+    # ------------------------- DELETION -------------------------
+    def delete(self, key: int) -> None:
+        """Deletes a key from the Splay Tree."""
+        if not self.root:
+            return
+
+        self.root = self._splay(self.root, key)
+        if self.root.key != key:
+            return  # Key not found
+
+        if self.root.left is None:
+            self.root = self.root.right
+        else:
+            temp = self.root.right
+            self.root = self._splay(self.root.left, key)
+            self.root.right = temp
+
+    # ------------------------- TRAVERSALS -------------------------
+    def inorder(self, root: Optional[Node]) -> List[int]:
+        """Returns an inorder traversal of the tree."""
+        return [] if not root else self.inorder(root.left) + [root.key] + self.inorder(root.right)
+
+    def preorder(self, root: Optional[Node]) -> List[int]:
+        """Returns a preorder traversal of the tree."""
+        return [] if not root else [root.key] + self.preorder(root.left) + self.preorder(root.right)
+
+
+if __name__ == "__main__":
+    # Example usage and demonstration
+    tree = SplayTree()
+    for value in [10, 20, 30, 40, 50, 25]:
+        tree.insert(value)
+
+    print("Inorder traversal:", tree.inorder(tree.root))
+    print("Search for 25:", tree.search(25))
+    print("After searching 25, root =", tree.root.key)
+    tree.delete(20)
+    print("After deleting 20:", tree.inorder(tree.root))