AVL with duplicate keys
Please refer below post before reading about AVL tree handling of duplicates.
How to handle duplicates in Binary Search Tree?
This 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++
// C++ program of AVL tree that// handles duplicates#include <bits/stdc++.h>using namespace std;// An AVL tree nodestruct node { int key; struct node* left; struct node* right; int height; int count;};// A utility function to get maximum of two integersint max(int a, int b);// A utility function to get height of the treeint height(struct node* N){ if (N == NULL) return 0; return N->height;}// A utility function to get maximum of two integersint 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 Nint 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, increment 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 NULL; } // 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 and update the count root->key = temp->key; root->count = temp->count; temp->count = 1; // 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 nodevoid preOrder(struct node* root){ if (root != NULL) { cout << root->key << "("<<root->count << ")"<< " "; preOrder(root->left); preOrder(root->right); }}/* Driver 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); cout <<"Pre order traversal of the constructed AVL tree is \n"; preOrder(root); cout <<"\nPre order traversal after deletion of 9 \n"; preOrder(root); return 0;}// this code is contributed by shivanisinghss2110 |
C
// C++ program of AVL tree that// handles duplicates#include <stdio.h>#include <stdlib.h>// An AVL tree nodestruct node { int key; struct node* left; struct node* right; int height; int count;};// A utility function to get maximum of two integersint max(int a, int b);// A utility function to get height of the treeint height(struct node* N){ if (N == NULL) return 0; return N->height;}// A utility function to get maximum of two integersint 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 Nint 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, increment 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 NULL; } // 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 and update the count root->key = temp->key; root->count = temp->count; temp->count = 1; // 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 nodevoid preOrder(struct node* root){ if (root != NULL) { printf("%d(%d) ", root->key, root->count); preOrder(root->left); preOrder(root->right); }}/* Driver 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 9 \n"); preOrder(root); return 0;} |
Java
// Java program of AVL tree that handles duplicatesimport 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, increment 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 and update the count root.key = temp.key; root.count = temp.count; temp.count = 1; // 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); } } /* Driver program to test above function*/ public static void main(String args[]) { 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); System.out.printf("Pre order traversal of the constructed AVL tree is \n"); preOrder(root); deleteNode(root, 9); System.out.printf("\nPre order traversal after deletion of 9 \n"); preOrder(root); }}// contributed by Arnab Kundu |
C#
// C# program of AVL tree that// handles duplicatesusing 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, // increment 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 and update the count root.key = temp.key; root.count = temp.count; temp.count = 1; // 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; /* 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); Console.Write("Pre order traversal of " + "the constructed AVL tree is \n"); preOrder(root); deleteNode(root, 9); Console.Write("\nPre order traversal after " + "deletion of 9 \n"); preOrder(root); }}// This code is contributed by Arnab Kundu |
Python3
# Python code to delete a node in AVL tree# Generic tree node classclass TreeNode(): def __init__(self, val): self.count = 1 # assigning count variable so that during insertion in will be incremented for duplicate values # and during deletion, it will be decremented if has multiple copies. self.height = 1 self.val = val self.left = None self.right = None# only insertion and deletion will be affected. if multiple copies are there, entry(count) will be printed during traversal.# AVL tree class which supports insertion,# deletion operationsclass AVL_Tree(object): def insert(self, root, key): # Step 1 - Perform normal BST if not root: return TreeNode(key) else if key < root.val: root.left = self.insert(root.left, key) else if key > root.val: root.right = self.insert(root.right, key) else: root.count += 1 # incrementing count if same entry is inserted. # Step 2 - Update the height of the # ancestor node root.height = 1 + max(self.getHeight(root.left), self.getHeight(root.right)) # Step 3 - Get the balance factor balance = self.getBalance(root) # Step 4 - If the node is unbalanced, # then try out the 4 cases # Case 1 - Left Left if balance > 1 and key < root.left.val: return self.rightRotate(root) # Case 2 - Right Right if balance < -1 and key > root.right.val: return self.leftRotate(root) # Case 3 - Left Right if balance > 1 and key > root.left.val: root.left = self.leftRotate(root.left) return self.rightRotate(root) # Case 4 - Right Left if balance < -1 and key < root.right.val: root.right = self.rightRotate(root.right) return self.leftRotate(root) return root # Recursive function to delete a node with # given key from subtree with given root. # It returns root of the modified subtree. def delete(self, root, key): # Step 1 - Perform standard BST delete if not root: return root else if key < root.val: root.left = self.delete(root.left, key) else if key > root.val: root.right = self.delete(root.right, key) else: if root.count > 1: # if count is more than one i.e multiple copies are there root.count -= 1 # just decrement count return root # so that one copy will be deleted and return if root.left is None: temp = root.right root = None return temp else if root.right is None: temp = root.left root = None return temp temp = self.getMinValueNode(root.right) root.val = temp.val root.right = self.delete(root.right, temp.val) # If the tree has only one node, # simply return it if root is None: return root # Step 2 - Update the height of the # ancestor node root.height = 1 + max(self.getHeight(root.left), self.getHeight(root.right)) # Step 3 - Get the balance factor balance = self.getBalance(root) # Step 4 - If the node is unbalanced, # then try out the 4 cases # Case 1 - Left Left if balance > 1 and self.getBalance(root.left) >= 0: return self.rightRotate(root) # Case 2 - Right Right if balance < -1 and self.getBalance(root.right) <= 0: return self.leftRotate(root) # Case 3 - Left Right if balance > 1 and self.getBalance(root.left) < 0: root.left = self.leftRotate(root.left) return self.rightRotate(root) # Case 4 - Right Left if balance < -1 and self.getBalance(root.right) > 0: root.right = self.rightRotate(root.right) return self.leftRotate(root) return root def leftRotate(self, z): y = z.right T2 = y.left # Perform rotation y.left = z z.right = T2 # Update heights z.height = 1 + max(self.getHeight(z.left), self.getHeight(z.right)) y.height = 1 + max(self.getHeight(y.left), self.getHeight(y.right)) # Return the new root return y def rightRotate(self, z): y = z.left T3 = y.right # Perform rotation y.right = z z.left = T3 # Update heights z.height = 1 + max(self.getHeight(z.left), self.getHeight(z.right)) y.height = 1 + max(self.getHeight(y.left), self.getHeight(y.right)) # Return the new root return y def getHeight(self, root): if not root: return 0 return root.height def getBalance(self, root): if not root: return 0 return self.getHeight(root.left) - self.getHeight(root.right) def getMinValueNode(self, root): if root is None or root.left is None: return root return self.getMinValueNode(root.left) def preOrder(self, root): if not root: return print("{}({}) ".format(root.val, root.count), end="") self.preOrder(root.left) self.preOrder(root.right)myTree = AVL_Tree()root = Nonenums = [9, 5, 10, 5, 9, 7, 17]for num in nums: root = myTree.insert(root, num)# Preorder Traversalprint("Preorder Traversal after insertion -")myTree.preOrder(root)print()# Deletekey = 10root = myTree.delete(root, key)key = 10root = myTree.delete(root, key)key = -1root = myTree.delete(root, key)key = 0root = myTree.delete(root, key)# Preorder Traversalprint("Preorder Traversal after deletion -")myTree.preOrder(root)print()# This code is contributed by Ajitesh Pathak |
Javascript
<script> // JavaScript program of AVL tree that handles duplicates class Node { constructor() { this.left; this.right; this.key; this.height; this.count; } } // A utility function to get height of the tree function height(N) { if (N == null) return 0; return N.height; } // A utility function to get maximum of two integers function max(a, b) { return (a > b) ? a : b; } /* Helper function that allocates a new node with the given key and null left and right pointers. */ function newNode(key) { let 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. function rightRotate(y) { let x = y.left; let 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. function leftRotate(x) { let y = x.right; let 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 function getBalance(N) { if (N == null) return 0; return height(N.left) - height(N.right); } function insert(node, key) { /*1. Perform the normal BST rotation */ if (node == null) return (newNode(key)); // If key already exists in BST, increment 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 */ let 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. */ function minValueNode(node) { let current = node; /* loop down to find the leftmost leaf */ while (current.left != null) current = current.left; return current; } function deleteNode(root, 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)) { let temp = root.left != null ? root.left : root.right; // No child case if (temp == null) { temp = root; root = null; } else // One child case // Copy the contents of the non-empty child root = temp; } else { // node with two children: Get the // inorder successor (smallest // in the right subtree) let temp = minValueNode(root.right); // Copy the inorder successor's data to // this node and update the count root.key = temp.key; root.count = temp.count; temp.count = 1; // 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) let 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 function preOrder(root) { if (root != null) { document.write(root.key + "(" + root.count + ") "); preOrder(root.left); preOrder(root.right); } } let 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); document.write( "Pre order traversal of the constructed AVL tree is " + "</br>"); preOrder(root); deleteNode(root, 9); document.write( "</br>" + "Pre order traversal after deletion of 9 " + "</br>"); preOrder(root); </script> |
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 9 9(2) 5(2) 7(1) 10(1) 17(1)
Time Complexity: O(N) ,here ‘N’ is for length of the Linked list.
Auxiliary Space: O(1), since no extra space required.
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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