AVL with duplicate keys
Please refer below post before reading about AVL tree handling of duplicates.
How to handle duplicates in Binary Search Tree?
The is to augment AVL tree node to store count together with regular fields like key, left and right pointers.
Insertion of keys 12, 10, 20, 9, 11, 10, 12, 12 in an empty Binary Search Tree would create following.
12(3)
/ \
10(2) 20(1)
/ \
9(1) 11(1)
Count of a key is shown in bracket
Below is implementation of normal AVL Tree with count with every key. This code basically is taken from code for insert and delete in AVL tree. The changes made for handling duplicates are highlighted, rest of the code is same.
The important thing to note is changes are very similar to simple Binary Search Tree changes.
C++
// AVL tree that handles duplicates #include<stdio.h> #include<stdlib.h> // An AVL tree node struct node { int key; struct node *left; struct node *right; int height; int count; }; // A utility function to get maximum of two integers int max(int a, int b); // A utility function to get height of the tree int height(struct node *N) { if (N == NULL) return 0; return N->height; } // A utility function to get maximum of two integers int max(int a, int b) { return (a > b)? a : b; } /* 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 = NULL; node->right = NULL; node->height = 1; // new node is initially added at leaf node->count = 1; return(node); } // A utility function to right rotate subtree rooted with y // See the diagram given above. struct node *rightRotate(struct node *y) { struct node *x = y->left; struct 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 new root return x; } // A utility function to left rotate subtree rooted with x // See the diagram given above. struct node *leftRotate(struct node *x) { struct node *y = x->right; struct 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 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); } struct node* insert(struct node* node, int key) { /* 1. Perform the normal BST rotation */ if (node == NULL) return (newNode(key)); // If key already exists in BST, icnrement count and return if (key == node->key) { (node->count)++; return node; } /* Otherwise, recur down the tree */ 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 && 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->left->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 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 { // If key is present more than once, simply decrement // count and return if (root->count > 1) { (root->count)--; return; } // ElSE, delete the node // node with only one child or no child if( (root->left == NULL) || (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 && getBalance(root->left) >= 0) return rightRotate(root); // Left Right Case if (balance > 1 && getBalance(root->left) < 0) { root->left = leftRotate(root->left); return rightRotate(root); } // Right Right Case if (balance < -1 && getBalance(root->right) <= 0) return leftRotate(root); // Right Left Case if (balance < -1 && 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(%d) ", root->key, root->count); preOrder(root->left); preOrder(root->right); } } /* Drier program to test above function*/int main() { 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, 5); root = insert(root, 9); root = insert(root, 7); root = insert(root, 17); printf("Pre order traversal of the constructed AVL tree is \n"); preOrder(root); root = deleteNode(root, 9); printf("\nPre order traversal after deletion of 10 \n"); preOrder(root); return 0; } |
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Java
// Java program of AVL tree that handles duplicates import java.util.*; class solution { // An AVL tree node static class node { int key; node left; node right; int height; int count; } // A utility function to get height of the tree static int height( node N) { if (N == null) return 0; return N.height; } // A utility function to get maximum of two integers static int max(int a, int b) { return (a > b)? a : b; } /* Helper function that allocates a new node with the given key and null left and right pointers. */static 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 node.count = 1; return(node); } // A utility function to right rotate subtree rooted with y // See the diagram given above. static 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 new root return x; } // A utility function to left rotate subtree rooted with x // See the diagram given above. static 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 new root return y; } // Get Balance factor of node N static int getBalance( node N) { if (N == null) return 0; return height(N.left) - height(N.right); } static node insert( node node, int key) { /*1. Perform the normal BST rotation */ if (node == null) return (newNode(key)); // If key already exists in BST, icnrement count and return if (key == node.key) { (node.count)++; return node; } /* Otherwise, recur down the tree */ 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 && 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.left.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 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. */ static node minValueNode( node node) { node current = node; /* loop down to find the leftmost leaf */ while (current.left != null) current = current.left; return current; } static node deleteNode( 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 { // If key is present more than once, simply decrement // count and return if (root.count > 1) { (root.count)--; return null; } // ElSE, delete the node // node with only one child or no child if( (root.left == null) || (root.right == null) ) { node temp = root.left!=null ? 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 } else { // node with two children: Get the inorder successor (smallest // in the right subtree) 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 && getBalance(root.left) >= 0) return rightRotate(root); // Left Right Case if (balance > 1 && getBalance(root.left) < 0) { root.left = leftRotate(root.left); return rightRotate(root); } // Right Right Case if (balance < -1 && getBalance(root.right) <= 0) return leftRotate(root); // Right Left Case if (balance < -1 && 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 static void preOrder( node root) { if(root != null) { System.out.printf("%d(%d) ", root.key, root.count); preOrder(root.left); preOrder(root.right); } } /* Drier program to test above function*/public static void main(String args[]) { node root = null; /* Coning tree given in the above figure */ root = insert(root, 9); root = insert(root, 5); root = insert(root, 10); root = insert(root, 5); root = insert(root, 9); root = insert(root, 7); root = insert(root, 17); System.out.printf("Pre order traversal of the coned AVL tree is \n"); preOrder(root); deleteNode(root, 9); System.out.printf("\nPre order traversal after deletion of 10 \n"); preOrder(root); } } //contributed by Arnab Kundu |
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C#
// C# program of AVL tree that // handles duplicates using System; class GFG { // An AVL tree node class node { public int key; public node left; public node right; public int height; public int count; } // A utility function to get // height of the tree static int height(node N) { if (N == null) return 0; return N.height; } // A utility function to get // maximum of two integers static int max(int a, int b) { return (a > b) ? a : b; } /* Helper function that allocates a new node with the given key and null left and right pointers. */static 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 node.count = 1; return(node); } // A utility function to right // rotate subtree rooted with y // See the diagram given above. static 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 new root return x; } // A utility function to left // rotate subtree rooted with x // See the diagram given above. static 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 new root return y; } // Get Balance factor of node N static int getBalance( node N) { if (N == null) return 0; return height(N.left) - height(N.right); } static node insert(node node, int key) { /*1. Perform the normal BST rotation */ if (node == null) return (newNode(key)); // If key already exists in BST, // icnrement count and return if (key == node.key) { (node.count)++; return node; } /* Otherwise, recur down the tree */ 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 && 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.left.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 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. */static node minValueNode( node node) { node current = node; /* loop down to find the leftmost leaf */ while (current.left != null) current = current.left; return current; } static node deleteNode(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 { // If key is present more than // once, simply decrement // count and return if (root.count > 1) { (root.count)--; return null; } // ElSE, delete the node // node with only one child // or no child if( (root.left == null) || (root.right == null) ) { node temp = root.left != null ? 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 } else { // node with two children: Get // the inorder successor (smallest // in the right subtree) 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 && getBalance(root.left) >= 0) return rightRotate(root); // Left Right Case if (balance > 1 && getBalance(root.left) < 0) { root.left = leftRotate(root.left); return rightRotate(root); } // Right Right Case if (balance < -1 && getBalance(root.right) <= 0) return leftRotate(root); // Right Left Case if (balance < -1 && 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 static void preOrder( node root) { if(root != null) { Console.Write(root.key + "(" + root.count + ")"); preOrder(root.left); preOrder(root.right); } } // Driver Code static public void Main(String []args) { node root = null; /* Coning tree given in the above figure */ root = insert(root, 9); root = insert(root, 5); root = insert(root, 10); root = insert(root, 5); root = insert(root, 9); root = insert(root, 7); root = insert(root, 17); Console.WriteLine("Pre order traversal of " + "the coned AVL tree is \n"); preOrder(root); deleteNode(root, 9); Console.WriteLine("\nPre order traversal after " + "deletion of 10 \n"); preOrder(root); } } // This code is contributed by Arnab Kundu |
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Output:
Pre order traversal of the constructed AVL tree is 9(2) 5(2) 7(1) 10(1) 17(1) Pre order traversal after deletion of 10 9(1) 5(2) 7(1) 10(1) 17(1)
Thanks to Rounaq Jhunjhunu Wala for sharing initial code. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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Improved By : andrew1234