Complete the implementation of all functions in BinarySearchTree.h$.$

main.cpp code:

#include

#include

#include

#include "BinarySearchTree.h$"$

using namespace std;

$//$ Do not modify the contents of this file

int main$()\{$

BinarySearchTree tree;

tree.insert$(5)$;

tree.insert$(3)$;

tree.insert$(4)$;

tree.insert$(1)$;

tree.insert$(7)$;

tree.draw$()$;

BinarySearchTree backup $=$ tree;

tree.insert$(8)$;

tree.draw$()$;

backup.draw$()$;

backup.remove$($backup$.$search$(5))$;

backup.draw$()$;

backup.remove$($backup$.$search$(7))$;

backup.draw$()$;

return $0$;

$\}$

BinarySearchTree.h code:

#ifndef BST$\_$H

#define BST$\_$H

#include

struct Node$\{$

int data;

Node$*$ left;

Node$*$ right;

Node$($int x$)\{$

data $=$ x;

left $=$ nullptr;

right $=$ nullptr;

$\}$

$\}$;

class BinarySearchTree$\{$

Node$*$ root;

public:

BinarySearchTree$()\{$

$\}$

BinarySearchTree$($const BinarySearchTree& other$)\{$

$\}$

void insert$($int x$)\{$

$\}$

void traverse$()\{$

$\}$

Node$*$ search$($int x$)\{$

$\}$

Node$*$ min$()\{$

$\}$

Node$*$ max$()\{$

$\}$

Node$*$ successor$($Node$*$ start$)\{$

$\}$

Node$*$ findParent$($Node$*$ start$)\{$

$\}$

void remove$($Node$*$ node$)\{$

$\}$

$//$ A function to display the tree graphically

void displayTree$($Node$*$ r$,$ int level, int direction$)\{$

$//$ Don't worry about this function, just use it

if $($r $!=$ NULL$)\{$

displayTree$($r$->$right, level$+1,1)$;

for $($int i $=0$; i $<$ level$-1$; i$++)\{$

std::cout $<<""$;

$\}$

if $($level $>0)\{$

if $($direction $==1)\{$

std::cout $<<"/--"$;

$\}$

else$\{$

std::cout $<<"\backslash \backslash --"$;

$\}$

$\}$

std::cout $<<$ r$->$data;

std::cout $<<$ std::endl;

level$++$;

displayTree$($r$->$left, level, $-1)$;

$\}$

$\}$

$//$ Call the function to display the tree and leave some space afterwards

void draw$()\{$

displayTree$($root$,0,0)$;

std::cout $<<$ std::endl $<<$ std::endl;

$\}$

$\}$;

#endif