Data Structures Tutorial

Data Structures Tutorial Asymptotic Notation Structure and Union Array Data Structure Linked list Data Structure Type of Linked list Advantages and Disadvantages of linked list Queue Data Structure Implementation of Queue Stack Data Structure Implementation of Stack Sorting Insertion sort Quick sort Selection sort Heap sort Merge sort Bucket sort Count sort Radix sort Shell sort Tree Traversal of the binary tree Binary search tree Graph Spanning tree Linear Search Binary Search Hashing Collision Resolution Techniques

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Priority Queue in Data Structure Deque in Data Structure Difference Between Linear And Non Linear Data Structures Queue Operations In Data Structure About Data Structures Data Structures Algorithms Types of Data Structures Big O Notations Introduction to Arrays Introduction to 1D-Arrays Operations on 1D-Arrays Introduction to 2D-Arrays Operations on 2D-Arrays Strings in Data Structures String Operations Application of 2D array Bubble Sort Insertion Sort Sorting Algorithms What is DFS Algorithm What Is Graph Data Structure What is the difference between Tree and Graph What is the difference between DFS and BFS Bucket Sort Dijkstra’s vs Bellman-Ford Algorithm Linear Queue Data Structure in C Stack Using Array Stack Using Linked List Recursion in Fibonacci Stack vs Array What is Skewed Binary Tree Primitive Data Structure in C Dynamic memory allocation of structure in C Application of Stack in Data Structures Binary Tree in Data Structures Heap Data Structure Recursion - Factorial and Fibonacci What is B tree what is B+ tree Huffman tree in Data Structures Insertion Sort vs Bubble Sort Adding one to the number represented an array of digits Bitwise Operators and their Important Tricks Blowfish algorithm Bubble Sort vs Selection Sort Hashing and its Applications Heap Sort vs Merge Sort Insertion Sort vs Selection Sort Merge Conflicts and ways to handle them Difference between Stack and Queue AVL tree in data structure c++ Bubble sort algorithm using Javascript Buffer overflow attack with examples Find out the area between two concentric circles Lowest common ancestor in a binary search tree Number of visible boxes putting one inside another Program to calculate the area of the circumcircle of an equilateral triangle Red-black Tree in Data Structures Strictly binary tree in Data Structures 2-3 Trees and Basic Operations on them Asynchronous advantage actor-critic (A3C) Algorithm Bubble Sort vs Heap Sort Digital Search Tree in Data Structures Minimum Spanning Tree Permutation Sort or Bogo Sort Quick Sort vs Merge Sort

Binary Search Tree

Binary Search Tree: A binary search tree is a type of tree in which every node is organized in the sorted order. It is also called an ordered binary tree.

Properties of BST

  1. The left sub-tree value is less than the root node.
  2. Similarly, the right sub-tree value is higher than the root node.
  3. This rule is reapplied to all left and right sub-trees of the root.
Binary Search Tree

Operations of the BST

There are three types of operations in the BST.

  1. Search operation
  2. Insertion operation
  3. Delete operation

Search operation:

The search operation is used to search a particular node in a BST. Whenever any node in BST is searched, that node is first compared with the root node. If the node is less than the root node, it is searched in the left subtree. If the node is greater than the root node, it is searched in the correct subtree.

Algorithm of the Search operation

struct node* search(int data)
{    
struct node *current = root;   
 printf("Visiting elements: ");                
while(current->data != data)
{           
 if(current != NULL) 
 { 
 printf("%d ",current->data);  
 }   
     //go to left tree                  
 if(current->data > data) 
          { 
             current = current->leftChild;
           } 
       //else go to right tree   
   Else  
  {      
  current = current->rightChild;   
 }          
 if(current == NULL){  
  return NULL;     
 }   
 }    
    }    
   return current;
 }

Insertion Operation

It is used to add a new node to a particular location in a specific situation. Whenever a new node is inserted in the BST, the location of that node is first searched. The new node is first compared with the root node. If the new node is less than the root node, search the null location in the left subtree and insert that node. If the node is greater than the root node, search the null location in the right subtree and insert that node.

Algorithm of the Insertion operation

TreeNode insert (int data, TreeNode T) 
{         
if T is NULL     
      {   
                T = (TreeNode *)malloc(sizeof (Struct TreeNode));         
          (Allocate Memory of new node and load the data into it)               
    T ? data = data;                   T ? left   = NULL;                   T ? right = NULL;           }                  
  else if T is less than T ? left     
      {              
    T ? left = insert(data, T ? left);    
               (Then node needs to be inserted in the left sub-tree. So, 
                  recursively traverse left sub-tree to find the place         
          where the new node needs to be inserted)     
      }           
     else if T is greater than T ? right    
       {                
    T ? right = insert(data, T ? right);     
               (Then node needs to be inserted in right sub-tree     
               So, recursively traverse right sub-tree to find the               
     place where the new node needs to be inserted.)    
      }    
      return T; 
}

Delete operation

This operation is used to delete a node in a specific situation. A node can be deleted from the following locations.

  1. Leaf node
  2. One child node
  3. Two child nodes

Leaf node: In this case, it simply removes the leaf node in the tree. This case is much simpler than other cases.

For example, remove the 6 in this BST.

Binary Search Tree

One child node: In this case, first, the original node is replaced with the child node, and then the node is removed. For example, remove the 9 in this BST.

Binary Search Tree



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