Add splay tree implementation with explanation

data_structures/binary_tree/splay_tree.py

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+#class node
+class Node:
+ """A node in the Splay Tree."""
+ def __init__(self, key, parent=None, left=None, right=None):
+ self.key = key # The value stored in the node
+ self.parent = parent # Pointer to the parent node
+ self.left = left # Pointer to the left child
+ self.right = right # Pointer to the right child
+
+
+#Spary tree class
+class SplayTree:
+ """A self-adjusting Binary Search Tree."""
+ def __init__(self):
+ self.root = None # The root of the tree
+
+ # --- Basic Rotation Operations ---
+
+ def _rotate_left(self, x):
+ """Perform a left rotation around node x (moving x down and right)."""
+ y = x.right
+ # 1. Update x's right child to be y's left child
+ x.right = y.left
+ if y.left:
+ y.left.parent = x
+
+ # 2. Update y's parent to be x's parent
+ y.parent = x.parent
+ if not x.parent:
+ self.root = y # y becomes the new root
+ elif x == x.parent.left:
+ x.parent.left = y
+ else:
+ x.parent.right = y
+
+ # 3. Update y's left child to be x
+ y.left = x
+ x.parent = y
+
+ def _rotate_right(self, x):
+ """Perform a right rotation around node x (moving x down and left)."""
+ y = x.left
+ # 1. Update x's left child to be y's right child
+ x.left = y.right
+ if y.right:
+ y.right.parent = x
+
+ # 2. Update y's parent to be x's parent
+ y.parent = x.parent
+ if not x.parent:
+ self.root = y # y becomes the new new root
+ elif x == x.parent.right:
+ x.parent.right = y
+ else:
+ x.parent.left = y
+
+ # 3. Update y's right child to be x
+ y.right = x
+ x.parent = y
+
+ # --- Core Splay Operation ---
+
+ def _splay(self, x):
+ """Moves node x to the root of the tree using a sequence of rotations."""
+ while x.parent:
+ parent = x.parent
+ grandparent = parent.parent
+
+ if not grandparent:
+ # Zig Case (x is a child of the root)
+ # One single rotation (Right if x is left child, Left if x is right child)
+ if x == parent.left:
+ self._rotate_right(parent)
+ else:
+ self._rotate_left(parent)
+
+ else:
+ # Two rotations are performed: Zig-Zig or Zig-Zag
+
+ # Case 1: Zig-Zig (x, parent, and grandparent are all on one side)
+ if (x == parent.left and parent == grandparent.left):
+ # x and parent are both left children (Left-Left)
+ self._rotate_right(grandparent) # Rotate grandparent down
+ self._rotate_right(parent) # Rotate parent down
+ elif (x == parent.right and parent == grandparent.right):
+ # x and parent are both right children (Right-Right)
+ self._rotate_left(grandparent) # Rotate grandparent down
+ self._rotate_left(parent) # Rotate parent down
+
+ # Case 2: Zig-Zag (x is on one side, parent is on the other)
+ elif (x == parent.left and parent == grandparent.right):
+ # x is left child, parent is right child
+ self._rotate_right(parent) # Rotate parent first
+ self._rotate_left(grandparent) # Rotate grandparent next
+ else: # x == parent.right and parent == grandparent.left
+ # x is right child, parent is left child
+ self._rotate_left(parent) # Rotate parent first
+ self._rotate_right(grandparent) # Rotate grandparent next
+
+ # --- Example Search Method (Uses splay) ---
+
+ def search(self, key):
+ """Searches for a key. If found, splays it to the root."""
+ current = self.root
+ found_node = None
+ while current:
+ if key == current.key:
+ found_node = current
+ break
+ elif key < current.key:
+ current = current.left
+ else:
+ current = current.right
+
+ if found_node:
+ self._splay(found_node) # Node is brought to the root
+ return True
+ return False
+