AVL tree rotate

AVL tree

single rotate

/**
 * Rotate binary tree node with left child.
 * For AVL trees, this is a single rotation for case 1.
 * Update heights, then set new root.
 */
void rotateWithLeftChild( AvlNode * & k2 )
{
    AvlNode *k1 = k2->left;
    k2->left = k1->right;
    k1->right = k2;
    k2->height = max( height( k2->left ), height( k2->right ) ) + 1;
    k1->height = max( height( k1->left ), k2->height ) + 1;
    k2 = k1;
}

    k2
   / \
  k1  z
 / \
x   y
|

  k1
 / \
x   k2
|  / \
  y   z

---

/**
 * Rotate binary tree node with right child.
 * For AVL trees, this is a single rotation for case 4.
 * Update heights, then set new root.
 */
void rotateWithRightChild( AvlNode * & k1 )
{
    AvlNode *k2 = k1->right;
    k1->right = k2->left;
    k2->left = k1;
    k1->height = max( height( k1->left ), height( k1->right ) ) + 1;
    k2->height = max( height( k2->right ), k1->height ) + 1;
    k1 = k2;
}

   k1
  / \
 X   k2
     / \
     y  z
        |

-->

   k2
  /  \
  k1  z
 / \  |
x   y

---

doublerotate

/**
 * Double rotate binary tree node: first left child.
 * with its right child; then node k3 with new left child.
 * For AVL trees, this is a double rotation for case 2.
 * Update heights, then set new root.
 */
void doubleWithLeftChild( AvlNode * & k3 )
{
    rotateWithRightChild( k3->left );
    rotateWithLeftChild( k3 );
}

    k3
   / \
  k1  d
 / \
a   k2
   / \
  b   c

-->
    k2
   /  \
  k1   k3
 / \   / \
a  b   c  d

---

/**
 * Double rotate binary tree node: first right child.
 * with its left child; then node k1 with new right child.
 * For AVL trees, this is a double rotation for case 3.
 * Update heights, then set new root.
 */
void doubleWithRightChild( AvlNode * & k1 )
{
    rotateWithLeftChild( k1->right );
    rotateWithRightChild( k1 );
}

  k1
 / \
a   k3
   / \
  k2  d
 / \
b   c

-->
    k2
   /  \
  k1   k3
 / \   / \
a  b   c  d