The definition for binary search tree should be the one used in classClass definition: A BST is a binary tree that (if not empty) also follows two storage rules regarding its nodes’ items: ♯For any node n of the tree, every item in n’s left subtree (LST), if not empty, is less than the item in n♯ ♯For any node n of the tree, every item in n’s right subtree (RST), if not empty, is greater than the item in n●bst_insert must be iterative (NOT recursive).●bst_remove and bst_remove_max must use the algorithm described by the suggested book authors In btNode.h: provide prototypes for bst_insert, bst_remove and bst_remove_max. ●In btNode.cpp: provide definition (implementation) for bst_insert, bst_remove and bst_remove_ma#ifndef BT_NODE_H#define BT_NODE_Hstruct btNode{ int data; btNode* left; btNode* right;};// pre: bst_root is root pointer of a binary search tree (may be 0 for// empty tree) and portArray has the base address of an array large// enough to hold all the data items in the binary search tree// post: The binary search tree has been traversed in-order and the data// values are written (as they are encountered) to portArray in// increasing positional order starting from the first elementvoid portToArrayInOrder(btNode* bst_root, int* portArray);void portToArrayInOrderAux(btNode* bst_root, int* portArray, int& portIndex);// pre: (none)// post: dynamic memory of all the nodes of the tree rooted at root has been// freed up (returned back to heap/freestore) and the tree is now empty// (root pointer contains the null address)void tree_clear(btNode*& root);// pre: (none)// post: # of nodes contained in tree rooted at root is returnedint bst_size(btNode* bst_root);// pre: bst_root is root pointer of a binary search tree (may be 0 for// empty tree)// post: If no node in the binary search tree has data equals insInt, a// node with data insInt has been created and inserted at the proper// location in the tree to maintain binary search tree property.// If a node with data equals insInt is found, the node's data field// has been overwritten with insInt; no new node has been created.// (Latter case seems odd but it's to mimick update of key-associated// data that exists in more general/real-world situations.)// write prototype for bst_insert here// pre: bst_root is root pointer of a binary search tree (may be 0 for// empty tree)// post: If remInt was in the tree, then remInt has been removed, bst_root// now points to the root of the new (smaller) binary search tree,// and the function returns true. Otherwise, if remInt was not in the// tree, then the tree is unchanged, and the function returns false.// write prototype for bst_remove here// pre: bst_root is root pointer of a non-empty binary search tree// post: The largest item in the binary search tree has been removed, and// bst_root now points to the root of the new (smaller) binary search// tree. The reference parameter, removed, has been set to a copy of// the removed item.// write prototype for bst_remove_max here#endif==============================test case 1 of 990000attempt to remove 5 values below:(sequential order) -2 8 -4 0 1 (value-sort order) -4 -2 0 1 8 from 8 values below:-8 -7 -6 -2 -1 0 1 2 gives (with 3 values successfully removed)-8 -7 -6 -1 2 ==============================test case 2 of 990000attempt to remove 7 values below:(sequential order) 8 -3 -5 -4 5 6 4 (value-sort order) -5 -4 -3 4 5 6 8 from 6 values below:-8 -5 -4 -3 -2 3 gives (with 3 values successfully removed)-8 -2 3 ==============================test case 3 of 990000attempt to remove 5 values below:(sequential order) 4 -6 -4 -1 6 (value-sort order) -6 -4 -1 4 6 from 11 values below:-8 -7 -6 -5 -4 -2 -1 0 5 6 7 gives (with 4 values successfully removed)-8 -7 -5 -2 0 5 7 ==============================test case 4 of 990000attempt to remove 1 values below:(sequential order) 8 (value-sort order) 8 from 12 values below:-9 -8 -7 -6 -4 -3 -1 1 3 4 5 9 gives (with 0 values successfully removed)-9 -8 -7 -6 -4 -3 -1 1 3 4 5 9 ============================== int bst_size(btNode* bst_root){}if (bst_root == 0) return 0;return 1 + bst_size(bst_root-left) + bst_size(bst_root-right); 1 #include "btNode.h"23456789101112131415161718192021222324252627282930313233// write definition for bst_insert here// write definition for bst_remove here// write definition for bst_remove_max herevoid portToArrayInOrder (btNode* bst_root, int* portArray){if (bst_root == 0) return;int portIndex = 0;portToArrayInOrder Aux (bst_root, portArray, portIndex);}void portToArrayInOrder Aux (btNode* bst_root, int* portArray, int& portIndex){}if (bst_root0) return;portToArrayInOrder Aux (bst_root-left, portArray, portIndex);portArray[portIndex++] = bst_root-data;portToArrayInOrderAux (bst_root-right, portArray, portIndex);==}void tree_clear (btNode*& root){if (root == 0) return;tree_clear (root-left);tree_clear (root-right);delete root;root = 0;

Question

The definition for binary search tree should be the one used in classClass definition:                                                                    A BST is a binary tree that (if not empty) also follows two storage rules regarding its nodes’ items:   ♯For any node n of the tree, every item in n’s left subtree (LST), if not empty, is less than the item in n♯   ♯For any node n of the tree, every item in n’s right subtree (RST), if not empty, is greater than the item in n●bst_insert must be iterative (NOT recursive).●bst_remove and bst_remove_max must use the algorithm described by the suggested book authors In btNode.h: provide prototypes for bst_insert, bst_remove and bst_remove_max. ●In btNode.cpp: provide definition (implementation) for bst_insert, bst_remove and bst_remove_ma#ifndef BT_NODE_H#define BT_NODE_Hstruct btNode{   int data;   btNode* left;   btNode* right;};// pre:  bst_root is root pointer of a binary search tree (may be 0 for//       empty tree) and portArray has the base address of an array large//       enough to hold all the data items in the binary search tree// post: The binary search tree has been traversed in-order and the data//       values are written (as they are encountered) to portArray in//       increasing positional order starting from the first elementvoid portToArrayInOrder(btNode* bst_root, int* portArray);void portToArrayInOrderAux(btNode* bst_root, int* portArray, int& portIndex);// pre:  (none)// post: dynamic memory of all the nodes of the tree rooted at root has been//       freed up (returned back to heap/freestore) and the tree is now empty//       (root pointer contains the null address)void tree_clear(btNode*& root);// pre:  (none)// post: # of nodes contained in tree rooted at root is returnedint bst_size(btNode* bst_root);// pre:  bst_root is root pointer of a binary search tree (may be 0 for//       empty tree)// post: If no node in the binary search tree has data equals insInt, a//       node with data insInt has been created and inserted at the proper//       location in the tree to maintain binary search tree property.//       If a node with data equals insInt is found, the node's data field//       has been overwritten with insInt; no new node has been created.//       (Latter case seems odd but it's to mimick update of key-associated//       data that exists in more general/real-world situations.)// write prototype for bst_insert here// pre:  bst_root is root pointer of a binary search tree (may be 0 for//       empty tree)// post: If remInt was in the tree, then remInt has been removed, bst_root//       now points to the root of the new (smaller) binary search tree,//       and the function returns true. Otherwise, if remInt was not in the//       tree, then the tree is unchanged, and the function returns false.// write prototype for bst_remove here// pre:  bst_root is root pointer of a non-empty binary search tree// post: The largest item in the binary search tree has been removed, and//       bst_root now points to the root of the new (smaller) binary search//       tree. The reference parameter, removed, has been set to a copy of//       the removed item.// write prototype for bst_remove_max here#endif==============================test case 1 of 990000attempt to remove 5 values below:(sequential order) -2 8 -4 0 1 (value-sort order) -4 -2 0 1 8 from 8 values below:-8 -7 -6 -2 -1 0 1 2 gives (with 3 values successfully removed)-8 -7 -6 -1 2 ==============================test case 2 of 990000attempt to remove 7 values below:(sequential order) 8 -3 -5 -4 5 6 4 (value-sort order) -5 -4 -3 4 5 6 8 from 6 values below:-8 -5 -4 -3 -2 3 gives (with 3 values successfully removed)-8 -2 3 ==============================test case 3 of 990000attempt to remove 5 values below:(sequential order) 4 -6 -4 -1 6 (value-sort order) -6 -4 -1 4 6 from 11 values below:-8 -7 -6 -5 -4 -2 -1 0 5 6 7 gives (with 4 values successfully removed)-8 -7 -5 -2 0 5 7 ==============================test case 4 of 990000attempt to remove 1 values below:(sequential order) 8 (value-sort order) 8 from 12 values below:-9 -8 -7 -6 -4 -3 -1 1 3 4 5 9 gives (with 0 values successfully removed)-9 -8 -7 -6 -4 -3 -1 1 3 4 5 9 ============================== int bst_size(btNode* bst_root){}if (bst_root == 0) return 0;return 1 + bst_size(bst_root->left) + bst_size(bst_root->right); 1 #include &#34;btNode.h&#34;23456789101112131415161718192021222324252627282930313233// write definition for bst_insert here// write definition for bst_remove here// write definition for bst_remove_max herevoid portToArrayInOrder (btNode* bst_root, int* portArray){if (bst_root == 0) return;int portIndex = 0;portToArrayInOrder Aux (bst_root, portArray, portIndex);}void portToArrayInOrder Aux (btNode* bst_root, int* portArray, int& portIndex){}if (bst_root0) return;portToArrayInOrder Aux (bst_root->left, portArray, portIndex);portArray[portIndex++] = bst_root->data;portToArrayInOrderAux (bst_root->right, portArray, portIndex);==}void tree_clear (btNode*& root){if (root == 0) return;tree_clear (root->left);tree_clear (root->right);delete root;root = 0;

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