here are all the info you will need:

Using the binary search tree implementation posted on Blackboard, please complete the

following methods:

1. Write a recursive method that checks whether a given binary tree is a BST or not.

2. Write a method that searches the given value and returns the address of the node if it is

found, otherwise returns NULL.

3. Write a method that finds k

th smallest element in a BST.

4. Write a method that finds the minimum absolute difference in a BST.

5. Write a method that prints nodes in top view of a BST.

#include <iostream> using namespace std; struct node{ int data; struct node* left; struct node* right; }; struct node* newNode(int data){ struct node* anode = new struct node; anode->data = data; anode->left = NULL; anode->right = NULL; return anode; } void insert(struct node** rootRef, int data){ if(*rootRef == NULL){ //there is no right/left children *rootRef = newNode(data); }else{ if(data < (*rootRef)->data ){ //if data is less than root insert(&(*rootRef)->left, data); }else{ insert(&(*rootRef)->right, data); //if data is greater than root } } } void printInOrder(struct node* root){ if(root == NULL) return; printInOrder(root->left); cout << root->data << " "; printInOrder(root->right); } void printPostOrder(struct node* root){ if(root == NULL) return; printInOrder(root->left); printInOrder(root->right); cout << root->data << " "; } void printPreOrder(struct node* root){ if(root == NULL) return; cout << root->data << " "; printInOrder(root->left); printInOrder(root->right); } int size(struct node* root){ if(root == NULL) return 0; return (size(root->left)+size(root->right)+1); } int height(struct node* root){ if(root == NULL) return 0; return (1+max(height(root->left), height(root->right))); } //Find the smallest value in BST (With a loop) int findMinValueLoop(struct node* root){ if(root == NULL){ return 0; }else{ struct node* current = root; while(current->left != NULL){ current = current->left; } return current->data; } } //Find the smallest value in BST (Recursively) int findMinValueRec(struct node* root){ if(root == NULL){ return 0; }else{ if(root->left == NULL){ return root->data; } return findMinValueRec(root->left); } } //Find the maximum value in BST (Recursively) int findMaxValueRec(struct node* root){ if(root == NULL){ return 0; }else{ if(root->right == NULL){ return root->data; } return findMaxValueRec(root->right); } } struct node **getSuccessor(struct node** root){ struct node **temp = root; while( (*temp) -> right != NULL){ temp = &(*temp)->right; } return temp; } void deleteNode(struct node** root, int target){ if(*root != NULL){ if(target == (*root)->data){ if((*root)->right == NULL){ *root = (*root)->left; }else if((*root)->left == NULL){ *root = (*root)->right; }else{ struct node **successor = getSuccessor(&(*root)->left); (*root)->data = (*successor)->data; deleteNode(successor,(*successor)->data); } }else if(target < (*root)->data){ deleteNode(&(*root)->left, target); }else{ //if (target > (*root)->data) deleteNode(&(*root)->right, target); } } } int main() { struct node* root = NULL; insert(&root, 30); insert(&root, 50); insert(&root, 70); insert(&root, 10); insert(&root, 90); insert(&root, 40); insert(&root, 80); cout << "In-order: "; printInOrder(root); cout << endl; cout << "Pre-order: " ; printPreOrder(root); cout << endl; cout << "Post-order: "; printPostOrder(root); cout << endl; cout << "The size of the BST: " << size(root) << endl; cout << "The height of the BST: " << height(root) << endl; cout << "The smallest value of BST: " << findMinValueRec(root) << endl; deleteNode(&root, 90); cout << "Delete 90 " << endl; cout << "Maximum: " << findMaxValueRec(root) << endl; cout << "Minimum: " << findMinValueRec(root) << endl; return 0; }

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