avl-tree.cpp

// C++ program to insert a node in AVL tree
#include <bits/stdc++.h>
using namespace std;

class Node {
    public:
    int key;
    Node *left;
    Node *right;
    int height;
};

int max(int a, int b);

int height(Node *N) {
    if(N == NULL)
        return 0;
    return N->height;
}

int max(int a, int b) {
    return ((a>b)? a : b);

}

Node *newNode(int key) {
    Node* node = new Node();
    node->key = key;
    node->left = NULL;
    node->right = NULL;
    node->height = 1; //new node is initially added at leaf

    return (node);
}

Node *rightRotate(Node *y) {
    Node *x = y->left;
    Node *T2 = x->right;

    //Perform rotation
    x->right = y;
    y->left = T2;

    //Update heights
    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;

    //Perform rotation
    y->left = x;
    x->right = T2;

    //Update heights
    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 == NULL)
        return 0;
    return height(N->left) - height(N->right);
}

// Recursive function to insert a key in the subtree rooted with node and returns the new root of the subtree.
Node* insert(Node* node, int key) {
    // 1. Perform the BST insertion
    if(node == NULL)
        return (newNode(key));

    if(key < node->key)
        node->left = insert(node->left, key);
    else if(key > node->key)
        node->right = insert(node->right, key);
    else //Equal keys are not allowed in BST
        return node;

    //2. Update height of this ancestor node
    node->height = 1+ max(height(node->left), height(node->right));

    //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 && key < node->left->key)
        return rightRotate(node);
    
    //Right Right Case
    if(balance < -1 && key > node->right->key)
        return leftRotate(node);
    
    //Left Right Case
    if(balance > 1 && key > node->right->key) {
        node->left = leftRotate(node->left);
        return rightRotate(node);
    }

    //Right Left Case
    if (balance < -1 && key < node->right->key){
        node->right = rightRotate(node->right);
        return leftRotate(node);
    }

    return node;
}

void preOrder(Node *root) {
    if(root != NULL) {
        cout << root->key <<" ";
        preOrder(root->left);
        preOrder(root->right);
    }
}

int main(void) {
    Node *root = NULL;

    root = insert(root, 10);
    root = insert(root, 20);
    root = insert(root, 30);
    root = insert(root, 40);
    root = insert(root, 50);
    root = insert(root, 25);

    /* The constructed AVL Tree would be
             30
            / \
            20 40
            / \ \
           10 25 50
    */
    cout << "Preorder traversal of the "
            "constructed AVL tree is \n";
    preOrder(root);

    return 0;
}