The problem can be found at the following link: Question Link
This is a pretty common Data Structures and Algorithms problem. I strongly recommend checking out this article for a clearer understanding of AVL trees, left and right rotations, and the balancing factor.
Writing an editorial for such a lengthy code isn't feasible here. Please take a look at the article mentioned above for more insights.
- Time Complexity:
O(log N)
, whereN
is the number of nodes in the AVL tree. - Auxiliary Space Complexity:
O(log N)
, for the recursive call stack.
class Solution {
public:
int height(Node * N) {
if (!N)
return 0;
return N->height;
}
Node * rightRotate(Node * y) {
Node * x = y->left;
Node * T2 = x->right;
x->right = y;
y->left = T2;
y->height = max(height(y->left), height(y->right)) + 1;
x->height = max(height(x->left), height(x->right)) + 1;
return x;
}
Node * leftRotate(Node * x) {
Node * y = x->right;
Node * T2 = y->left;
y->left = x;
x->right = T2;
x->height = max(height(x->left), height(x->right)) + 1;
y->height = max(height(y->left), height(y->right)) + 1;
return y;
}
int getBalance(Node * N) {
if (!N)
return 0;
return height(N->left) - height(N->right);
}
Node * insertToAVL(Node * node, int key) {
if (node == NULL)
return (new Node(key));
if (key < node->data)
node->left = insertToAVL(node->left, key);
else if (key > node->data)
node->right = insertToAVL(node->right, key);
else
return node;
node->height = 1 + max(height(node->left), height(node->right));
int balance = getBalance(node);
if (balance > 1 && key < node->left->data)
return rightRotate(node);
if (balance < -1 && key > node->right->data)
return leftRotate(node);
if (balance > 1 && key > node->left->data) {
node->left = leftRotate(node->left);
return rightRotate(node);
}
if (balance < -1 && key < node->right->data) {
node->right = rightRotate(node->right);
return leftRotate(node);
}
return node;
}
};
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