Question

c++

Write a class that will create a binary tree that can hold values of string data type, define and implement insert, delete, search, functions, and a constructor and a destructor. Demonstrate the insertion, searching, and deletion functions in a program.

Answer 1

Binary Search Tree, is a node-based binary tree data structure which has the following properties:

• The left subtree of a node contains only nodes with keys lesser than the node’s key.
• The right subtree of a node contains only nodes with keys greater than the node’s key.
• The left and right subtree each must also be a binary search tree.
  There must be no duplicate nodes.

The above properties of Binary Search Tree provide an ordering among keys so that the operations like search, minimum and maximum can be done fast. If there is no ordering, then we may have to compare every key to search a given key.

Searching a key
To search a given key in Binary Search Tree, we first compare it with root, if the key is present at root, we return root. If key is greater than root’s key, we recur for right subtree of root node. Otherwise we recur for left subtree.

struct node* search(struct node* root, int key)

{

    // Base Cases: root is null or key is present at root

    if (root == NULL || root->key == key)

       return root;

     

    // Key is greater than root's key

    if (root->key < key)

       return search(root->right, key);

  

    // Key is smaller than root's key

    return search(root->left, key);

}

Insertion of a key
A new key is always inserted at leaf. We start searching a key from root till we hit a leaf node. Once a leaf node is found, the new node is added as a child of the leaf node.

#include<stdio.h>

#include<stdlib.h>

   

struct node

{

    int key;

    struct node *left, *right;

};

   

// A utility function to create a new BST node

struct node *newNode(int item)

{

    struct node *temp = (struct node *)malloc(sizeof(struct node));

    temp->key = item;

    temp->left = temp->right = NULL;

    return temp;

}

   

// A utility function to do inorder traversal of BST

void inorder(struct node *root)

{

    if (root != NULL)

    {

        inorder(root->left);

        printf("%d \n", root->key);

        inorder(root->right);

    }

}

   

/* A utility function to insert a new node with given key in BST */

struct node* insert(struct node* node, int key)

{

    /* If the tree is empty, return a new node */

    if (node == NULL) return newNode(key);

  

    /* Otherwise, recur down the tree */

    if (key < node->key)

        node->left = insert(node->left, key);

    else if (key > node->key)

        node->right = insert(node->right, key);   

  

    /* return the (unchanged) node pointer */

    return node;

}

Deletion

Node to be deleted is leaf: Simply remove from the tree.

Node to be deleted has only one child: Copy the child to the node and delete the child

Node to be deleted has two children: Find inorder successor of the node. Copy contents of the inorder successor to the node and delete the inorder successor. Note that inorder predecessor can also be used.

#include<stdio.h>

#include<stdlib.h>

  

struct node

{

    int key;

    struct node *left, *right;

};

  

// A utility function to create a new BST node

struct node *newNode(int item)

{

    struct node *temp = (struct node *)malloc(sizeof(struct node));

    temp->key = item;

    temp->left = temp->right = NULL;

    return temp;

}

  

// A utility function to do inorder traversal of BST

void inorder(struct node *root)

{

    if (root != NULL)

    {

        inorder(root->left);

        printf("%d ", root->key);

        inorder(root->right);

    }

}

  

/* A utility function to insert a new node with given key in BST */

struct node* insert(struct node* node, int key)

{

    /* If the tree is empty, return a new node */

    if (node == NULL) return newNode(key);

  

    /* Otherwise, recur down the tree */

    if (key < node->key)

        node->left = insert(node->left, key);

    else

        node->right = insert(node->right, key);

  

    /* 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 && current->left != NULL)

        current = current->left;

  

    return current;

}

  

/* Given a binary search tree and a key, this function deletes the key

   and returns the new root */

struct node* deleteNode(struct node* root, int key)

{

    // base case

    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

    {

        // node with only one child or no child

        if (root->left == NULL)

        {

            struct node *temp = root->right;

            free(root);

            return temp;

        }

        else if (root->right == NULL)

        {

            struct node *temp = root->left;

            free(root);

            return temp;

        }

  

        // node with two children: Get the inorder successor (smallest

        // in the right subtree)

        struct node* temp = minValueNode(root->right);

  

        // Copy the inorder successor's content to this node

        root->key = temp->key;

  

        // Delete the inorder successor

        root->right = deleteNode(root->right, temp->key);

    }

    return root;

}