modify just the last two functions in order to implement double rotations directly instead of calling the two single rotations. thank you very much

class AvlNode{

public methods below.... private: struct AvlNode { Comparable element; AvlNode *left; AvlNode *right; int height;

AvlNode *root; int nodeCount(AvlNode *t){ if(t == NULL) return 0; return (nodeCount(t->left) + nodeCount(t->right)) + 1; } /** * Return the height of node t or -1 if nullptr. */ int height( AvlNode *t ) const { return t == nullptr ? -1 : t->height; }

int max( int lhs, int rhs ) const { return lhs > rhs ? lhs : rhs; }

/** * 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; }

/** * 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; }

/** * 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 ); }

/** * 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 ); }

};

Instread of doing two single rotations for the double rotations please implement so it directly.

thank you so much.