In this assignment, you are given several classes in the cpp file BTree.cpp. Your task is to

complete the implementation of the classes specified as below. You need to submit a single cpp file

that contains everything about your source code. It must be compilable and executable. Do not

submit things irrelevant (such as .exe).

1 Your Task

You are given a class TNode that contains one integer value, and three pointers one to the

parent, one to the left child, and one to the right child. You need to complete the class BTree

and two other functions specified in the cpp file.

Task 1: Write a function isValidBT that given inputs as a binary tree in the array form, and

outputs whether the array forms a correct binary tree. The inputs contain a pointer p to an array,

and an integer n denoting the number of slots used in the array representation. Here the array has

size n, and we use p[0] to store the empty symbol for the binary tree as discussed in the class. For

this representation, the tree has size n 1.

Task 2: Implement the constructors (default and copy) of BTree, and the destructor. You need

to make sure that the copy constructor makes a separate copy of the list.

In addition to the normal copy constructor, here we ask you to implement a special copy

constructor that takes input a binary tree of the array form. The inputs have the same format

as Task 1, and you need to copy the binary tree, and convert the array form/to the pointer-based

construction.

Task 3: Implement the function convertpos that takes input an integer position, and returns the

TNode pointer that points to the position-th node in the tree. We discussed about how to do this

in the class.

Task 4: Implement the add2left, add2right functions. The functionalities are just as the names.

Here you need to consider how to handle different input of positions, i.e. places that you want to

add the node/tree to. Task 2 can be useful in this case.

Task 5: Write the removeleaf function. You need to first check whether the input is a leaf or not.

If that is a leaf, then remove it. Otherwise do nothing.

Task 6: Write a function Toarray that converts the BTree into the array form. You can start by

determining the size to the reference n, and new an array of size n. Then you need to produce the

correct array according to your BTree.

Task 7: Write swapnodes and the three tree traversal algorithms. For the traversal algorithm,

you can just print the notes according to the order. Here you just need to swap the values for the

swapnodes. This task should be very simple.

Task 8: Write a function isValidBST that checks whether the binary tree is a valid binary search

tree.

Task 9: Test the above tasks.

#include

using namespace std;

class TNode

{

public:

int val;

TNode(){}

TNode(int v){val = v;}

TNode * left;

TNode * right;

TNode * parent;

};

class BTree

{

public:

//constructors and destructor

BTree();

BTree(TNode *r);// initialize BTree with the root r. r is the only node.

BTree(const BTree & t); // copy constructor

BTree(const int *p, const int n);// similar to the copy constructor, but your input is of the array form.

// input is given an array that denotes a tree that uses up to n slots. The size of the tree is not given directly as input.

// the array is pointed by p and has size n, where p[0] is used to store the empty symbol.

//the function converts the array representation into a linked-list representation, i.e. BTree

~BTree();

int size;

TNode *root;

TNode * convertpos(int position);// find the pointer where the position points to

void add2left(TNode *newnode, TNode *p);

void add2right(TNode *newnode, TNode *p);

void add2left(TNode *newnode, int position);

void add2right(TNode *newnode, int position);

void add2left(BTree *newsubtree, int position);

void add2right(BTree *newsubtree, int position);

void removeleaf(int position);

void removeleaf(TNode *p);

void swapnodes(TNode *n1, TNode *n2);//swap-the-values is fine

int * Toarray(int &n);// convert the BT into the array form. Determine what n should be, and new an array of size n+1, and store the empty symbol at array[0]. Convert the BT into the array form and retrun the array pointer. The size of the array will be given to the variable n.

void print_pre_order();// print the node as you traverse according to the order.

void print_in_order();

void print_post_order();

bool isValidBST(); // return whether this BT is a valid BST

};

bool isValidBT(const int *p, const int n);

//Determine whether the array forms a valid BT.

// the input format is the same as the above

int main()

{

return 0;

}