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Data Structures
  • Data Structures Manual
  • Arrays
    • Array ADT
    • Linear Search
    • Binary Search
    • Some More Basic Operations
    • Reversing an Array
    • Operations in a Sorted Array
    • Merging Two Arrays
    • Set Operations
    • Finding Missing Elements
    • Duplicates in an Array
    • Getting a Pair whose Sum = K
    • Finding Max & Min in Single Scan
  • Strings
    • Finding the Length of a String
    • Changing Cases in a String
    • Finding Number of Vowels, Consonants & Words
    • Reversing a String
    • Checking for Palindrome
    • Duplicates in a String
    • Checking if Strings are Anagrams
    • Permutations of a String
  • Singly Linked List
    • Displaying the Nodes
    • Counting the Nodes
    • Sum of all Nodes
    • Finding the Maximum Element
    • Searching in a Node
    • Inserting a Node
    • Inserting a Node in Sorted List
    • Deleting a Node
    • Checking if List is Sorted
    • Removing Duplicates from a List
    • Reversing a Linked List
    • Concatenating Two Lists
    • Detecting a Loop in Linked List
    • Merge Two Sorted Lists
    • Finding the Middle Node
  • Cirular Linked List
    • Displaying the Nodes
    • Inserting a Node
    • Deleting a Node
  • Doubly Linked List
    • Inserting a Node
    • Deleting a Node
    • Reversing a Doubly Linked List
    • Circular Doubly Linked List
  • Stack
    • Stack Using Array
    • Stack Using Linked List
    • Balancing Parenthesis
    • Infix to Postfix
    • Evaluation of Postfix Expression
  • Queue
    • Queue using Array
    • Queue using Linked List
    • Double Ended Queue
  • Binary Tree
    • Creating a Binary Tree using Queue
    • Recursive Tree Traversals
    • Iterative Tree Traversals
    • Level Order Traversal
    • Counting Nodes in a Binary Tree
    • Finding the Height of Tree
    • Finding Sum of All Nodes
  • Binary Search Tree
    • Searching in a BST
    • Inserting in a BST
    • Deleting in a BST
  • AVL Tree
    • Inserting in an AVL Tree
    • AVL Tree Rotations
    • Deleting in an AVL Tree
  • Heap
    • Inserting in a Heap
    • Deleting in a Heap
    • Heapify
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  1. AVL Tree

Deleting in an AVL Tree

Procedure :

  • Perform the same steps as deleting in a binary search tree.

  • After that, assign new height to the node.

  • Check the balance factor of the node.

  • According to the balance of the node and it's left/right child, perform rotation in order to balance the balance the tree

struct Node *deleteNode(struct Node *ptr , int key) {
  
 		// If there's no node to be deleted
	if (ptr == NULL) 
		return NULL;

	// If the node is a leaf node
	if (ptr -> left == NULL && ptr -> right == NULL) {
		// If it's the root node, make root NULL after deletion
		if (ptr == root) 
			root = NULL;
		// Free the memory
		free(ptr);
		return NULL;
	}

	// If value to be deleted is lesser, go to left subtree
	if (key < ptr -> data) 
		ptr -> left = deleteNode(ptr -> left, key);

	// If value to be deleted is greater, go to right subtree
	else if (key > ptr -> data)
		ptr -> right = deleteNode(ptr -> right, key);
	
	// Deleting the node once it's found
	else {
		// Delete from the subtree which has greater height
		if (nodeHeight(ptr -> left) > nodeHeight(ptr -> right)) {

			// Find the inorder predecessor for left subtree
			struct Node *inPre = inorderPredecessor(ptr -> left);
			ptr -> data  = inPre -> data;
			ptr -> left = deleteNode(ptr -> left, inPre -> data);
		
		} else {

			// Find the inorder successor for right subtree
			struct Node *inSuc = inorderSuccessor(ptr -> right);
			ptr -> data  = inSuc -> data;
			ptr -> right = deleteNode(ptr -> right, inSuc -> data);
		
		}
	}
 	
 	// Set new height
    ptr->height = nodeHeight(ptr);
 
 	// Rotate as per balance factor
    if(balanceFactor(ptr) == 2 && balanceFactor(ptr -> left) == 1)
    	return LLRotation(ptr);		//L 1 Rotation
    else if(balanceFactor(ptr) == 2 && balanceFactor(ptr -> left)==-1)
    	return LRRotation(ptr);		//L -1 Rotation
    else if(balanceFactor(ptr) == 2 && balanceFactor(ptr -> left) == 0)
    	return LLRotation(ptr);		//L 0 Rotation
    else if(balanceFactor(ptr) == 2 && balanceFactor(ptr -> right) == 1)
    	return RRRotation(ptr);  	//R 1 Rotation
    else if(balanceFactor(ptr) == 2 && balanceFactor(ptr -> right) == -1)
    	return RLRotation(ptr); 	//R-1 Rotation
    else if(balanceFactor(ptr) == 2 && balanceFactor(ptr -> right) == 0)
    	return RRRotation(ptr);  	//R 0 Rotation
 
    return ptr;

}

Utility Functions :

// Node height function
int nodeHeight(struct Node *ptr) {
	
	int leftHeight, rightHeight;
	leftHeight = ptr && ptr -> left ? ptr -> left -> height : 0;
	rightHeight = ptr && ptr -> right ? ptr -> right -> height : 0;
	return leftHeight > rightHeight ? leftHeight + 1 : rightHeight + 1;

}

// Balance factor function
int balanceFactor(struct Node *ptr) {

	int leftHeight, rightHeight;
	leftHeight = ptr && ptr -> left ? ptr -> left -> height : 0;
	rightHeight = ptr && ptr -> right ? ptr -> right -> height : 0;
	return leftHeight - rightHeight;

}

// LL Rotation
struct Node *LLRotation(struct Node *ptr) {

	struct Node *ptrL = ptr -> left;
	struct Node *ptrLR = ptrL -> right;

	ptrL -> right = ptr;
	ptr -> left = ptrLR;

	ptr -> height = nodeHeight(ptr);
	ptrL -> height = nodeHeight(ptr -> left);

	if (ptr == root) 
		root = ptrL;

	return ptrL;

}

// LR Rotation
struct Node *LRRotation(struct Node *ptr) {

	struct Node *ptrL = ptr -> left;
	struct Node *ptrLR = ptrL -> right;

	ptrL -> right = ptrLR -> left;
	ptr -> left = ptrLR -> right;
	ptrLR -> left = ptrL;
	ptrLR -> right = ptr;

	ptr -> height = nodeHeight(ptr);
	ptrL -> height = nodeHeight(ptrL);
	ptrLR -> height = nodeHeight(ptrLR);

	if (ptr == root)
		root = ptrLR;

	return ptrLR;

}

// RR Rotation
struct Node *RRRotation(struct Node *ptr) {
	
	struct Node *ptrR = ptr -> right;
	struct Node *ptrRL = ptrR -> left;

	ptrR -> left = ptr;
	ptr -> right = ptrRL;

	ptr -> height = nodeHeight(ptr);
	ptrR -> height = nodeHeight(ptr -> right);

	if (ptr == root) 
		root = ptrR;

	return ptrR;

}

// RL Rotation
struct Node *RLRotation(struct Node *ptr) {
	
	struct Node *ptrR = ptr -> right;
	struct Node *ptrRL = ptrR -> left;

	ptrR -> left = ptrRL -> right;
	ptr -> right = ptrRL -> left;
	ptrRL -> left = ptr;
	ptrRL -> right = ptrR;

	ptr -> height = nodeHeight(ptr);
	ptrR -> height = nodeHeight(ptrR);
	ptrRL -> height = nodeHeight(ptrRL);

	if (ptr == root)
		root = ptrRL;

	return ptrRL;

}

Contributed by Nitin Ranganath

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Last updated 4 years ago

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