algorithms/AVL.cpp

// An AVL tree node
struct node {
    int key;
    struct node *left;
    struct node *right;
    int height;
};
 
// A utility function to get height of the tree
int height(struct node *N) {
    if (N == NULL)
        return 0;
    return N->height;
}
 
/* Helper function that allocates a new node with the given key and
    NULL left and right pointers. */
struct node* newNode(int key) {
    struct node* node = (struct node*)malloc(sizeof(struct node));
    node->key = key;
    node->left = node->right = NULL;
    node->height = 1;  // new node is initially added at leaf
    return node;
}
 
/*
T1, T2, T3 and T4 are subtrees.
         z                                      y
        / \                                   /   \
       y   T4      Right Rotate (z)          x      z
      / \          - - - - - - - - ->      /  \    /  \
     x   T3                               T1  T2  T3  T4
    / \
  T1   T2
*/
struct node *rightRotate(struct node *z) {
    struct node *y = z->left;
    struct node *T3 = y->right;
 
    // Perform rotation
    y->right = z;
    z->left = T3;
 
    // Update heights
    z->height = max(height(z->left), height(z->right)) + 1;
    y->height = max(height(y->left), height(y->right)) + 1;
 
    // Return new root
    return y;
}
 
/*
  z                                y
 /  \                            /   \
T1   y     Left Rotate(z)       z      x
    /  \   - - - - - - - ->    / \    / \
   T2   x                     T1  T2 T3  T4
       / \
     T3  T4
*/
struct node *leftRotate(struct node *z) {
    struct node *y = z->right;
    struct node *T2 = y->left;
 
    // Perform rotation
    y->left = z;
    z->right = T2;
 
    //  Update heights
    z->height = max(height(z->left), height(z->right)) + 1;
    y->height = max(height(y->left), height(y->right)) + 1;
 
    // Return new root
    return y;
}
 
// Get Balance factor of node N
int getBalance(struct node *N) {
    if (N == NULL)
        return 0;
    return height(N->left) - height(N->right);
}
 
// Time: O(logn)
struct node* insert(struct node* node, int key) {
    /* 1.  Perform the normal BST rotation */
    if (node == NULL)
        return(newNode(key));
 
    if (key < node->key)
        node->left  = insert(node->left, key);
    else
        node->right = insert(node->right, key);
 
    /* 2. Update height of this ancestor node */
    node->height = max(height(node->left), height(node->right)) + 1;
 
    /* 3. Get the balance factor of this ancestor node to check whether
       this node became unbalanced */
    int balance = getBalance(node);
 
    // If this node becomes unbalanced, then there are 4 cases
 
    // Left Left Case
    if (balance > 1 and key < node->left->key)
        return rightRotate(node);
 
    // Right Right Case
    if (balance < -1 and key > node->right->key)
        return leftRotate(node);
 
    // Left Right Case
    if (balance > 1 and key > node->left->key) {
        node->left =  leftRotate(node->left);
        return rightRotate(node);
    }
 
    // Right Left Case
    if (balance < -1 and key < node -> right->key) {
        node->right = rightRotate(node->right);
        return leftRotate(node);
    }
 
    /* return the (unchanged) node pointer */
    return node;
}
 
/* Given a non-empty binary search tree, return the node with minimum
   key value found in that tree. Note that the entire tree does not
   need to be searched. */
struct node * minValueNode(struct node* node) {
    struct node* current = node;
 
    /* loop down to find the leftmost leaf */
    while (current->left != NULL)
        current = current->left;
 
    return current;
}
 
struct node* deleteNode(struct node* root, int key) {
    // STEP 1: PERFORM STANDARD BST DELETE
 
    if (root == NULL)
        return root;
 
    // If the key to be deleted is smaller than the root's key,
    // then it lies in left subtree
    if ( key < root->key )
        root->left = deleteNode(root->left, key);
 
    // If the key to be deleted is greater than the root's key,
    // then it lies in right subtree
    else if( key > root->key )
        root->right = deleteNode(root->right, key);
 
    // if key is same as root's key, then This is the node
    // to be deleted
    else {
        // node with only one child or no child
        if( (root->left == NULL) or (root->right == NULL) ) {
            struct node *temp = root->left ? root->left : root->right;
 
            // No child case
            if(temp == NULL) {
                temp = root;
                root = NULL;
            } else // One child case
                *root = *temp; // Copy the contents of the non-empty child
 
            free(temp);
        } else {
            // node with two children: Get the inorder successor (smallest
            // in the right subtree)
            struct node* temp = minValueNode(root->right);
 
            // Copy the inorder successor's data to this node
            root->key = temp->key;
 
            // Delete the inorder successor
            root->right = deleteNode(root->right, temp->key);
        }
    }
 
    // If the tree had only one node then return
    if (root == NULL)
        return root;
 
    // STEP 2: UPDATE HEIGHT OF THE CURRENT NODE
    root->height = max(height(root->left), height(root->right)) + 1;
 
    // STEP 3: GET THE BALANCE FACTOR OF THIS NODE (to check whether
    //  this node became unbalanced)
    int balance = getBalance(root);
 
    // If this node becomes unbalanced, then there are 4 cases
 
    // Left Left Case
    if (balance > 1 and getBalance(root->left) >= 0)
        return rightRotate(root);
 
    // Left Right Case
    if (balance > 1 and getBalance(root->left) < 0) {
        root->left = leftRotate(root->left);
        return rightRotate(root);
    }
 
    // Right Right Case
    if (balance < -1 and getBalance(root->right) <= 0)
        return leftRotate(root);
 
    // Right Left Case
    if (balance < -1 and getBalance(root->right) > 0) {
        root->right = rightRotate(root->right);
        return leftRotate(root);
    }
 
    return root;
}
 
// A utility function to print preorder traversal of the tree.
// The function also prints height of every node
void preOrder(struct node *root) {
    if(root != NULL) {
        printf("%d ", root->key);
        preOrder(root->left);
        preOrder(root->right);
    }
}
 
/* Drier program to test above function*/
int main(void) {
    struct node *root = NULL;
 
    /* Constructing tree given in the above figure */
    root = insert(root, 9);
    root = insert(root, 5);
    root = insert(root, 10);
    root = insert(root, 0);
    root = insert(root, 6);
    root = insert(root, 11);
    root = insert(root, -1);
    root = insert(root, 1);
    root = insert(root, 2);
 
    /* The constructed AVL Tree would be
            9
           /  \
          1    10
        /  \     \
       0    5     11
      /    /  \
     -1   2    6
    */
 
    preOrder(root);
 
    root = deleteNode(root, 10);
 
    /* The AVL Tree after deletion of 10
            1
           /  \
          0    9
        /     /  \
       -1    5     11
           /  \
          2    6
    */
 
    printf("\nPre order traversal after deletion of 10 \n");
    preOrder(root);
 
    return 0;
}