AVL Tree — Rotations Animated

Balance factor

int balanceFactor(Node n) {
  return height(n.left) - height(n.right);
}

Left rotation

Node rotateLeft(Node a) {
  Node b = a.right;
  a.right = b.left;
  b.left = a;
  updateHeight(a); updateHeight(b);
  return b;
}

Four cases

• LL: right rotation.
• RR: left rotation.
• LR: left then right (double).
• RL: right then left (double).

Complexity

Insert + delete + search: O(log N). Rotation cost: O(1) per rotation, O(log N) rotations per insert.

Balance factor

int balanceFactor(Node n) {
  return height(n.left) - height(n.right);
}

Left rotation

Node rotateLeft(Node a) {
  Node b = a.right;
  a.right = b.left;
  b.left = a;
  updateHeight(a); updateHeight(b);
  return b;
}

Four cases

• LL: right rotation.
• RR: left rotation.
• LR: left then right (double).
• RL: right then left (double).

Complexity

Insert + delete + search: O(log N). Rotation cost: O(1) per rotation, O(log N) rotations per insert.