In c$++,$please complete the following functions implementing a Hash Table for Quadratic Probing closed hashing table in a Snake Game. Your hash table will be used to keep a small collection of selected treasures from the ItemBin as the $$bingo condition$$for each player instance, and upon collecting each treasure, the matched treasure will be lazy$-$deleted from the hash table. As soon as one of the player instances reaches a hash table load factor lambda $=0,$the player completes the bingo condition and wins the game. Refer to attached image for function requirements. Below is the objPosDoubleHashing class $($that needs filling based on the attached image requirements$)$ and header files.

#include "objPosDoubleHashing.h$"$

$//$#include "MacUILib.h$"$

#include

using namespace std;

objPosDoubleHashing::objPosDoubleHashing$()$

$\{$

$//$Instantiate the objPos Hash Table of the default size TABLE$\_$SIZE defined in the objPosHashTable abstract class

$//$Should also initialize tableSize field with the default size TABLE$\_$SIZE

$\}$

objPosDoubleHashing::objPosDoubleHashing$($int size$)$

$\{$

$//$Instantiate the objPos Hash Table of the specified size

$//$Should also initialize tableSize field with specified size

$\}$

objPosDoubleHashing::~objPosDoubleHashing$()$

$\{$

$//$delete the Hash Table

$\}$

int objPosDoubleHashing::calculateHashing$($int prefix, int number$)$const $//$hashing function

$\{$

$//$Implementing the primary hashing function

$//$Add all the decimal integer digits of the Prefix ASCII char and the Number together

$//$For example, given objPos.prefix $=\text{'}$A$\text{'}(65)$and objPos.number $=98,$then$...$

$//$ h$($x$)=$sum of all decimal digits of prefix and number $=6+5+9+8=28$

$//$return the sum as the hashing key.

$\}$

int objPosDoubleHashing::calculateSecondaryHashing$($int input$)$const

$\{$

$//$Implementing the secondary hashing function

$//1.$Sum up all digits of input

$//2.$return $5-($sum mod $5)$

$//$e$.$g$.$ input $=18$

$//$ sum $=1+8=9$

$//$ return value $=5-(9\%5)=5-4=1$

$$

$\}$

bool objPosDoubleHashing::insert$($const objPos &thisPos$)$

$\{$

$//$Algorithm similar to the one discussed in class

$//1.$Calculate the initial hashing key using calculateHashing$()$private helper function $($i$.$e$.$the h$1($x$))$

$//2.$Check symbol field to see whether the indexed slot is empty

$//$ If yes, insert data, set symbol to $\text{'}$v$\text{'},$then return true $($indicating successful insertion$)$

$//$ Otherwise, proceed to collision resolution

$//3.$Collision resolution strategy $-$Double Probing

$//$ h$($x$)=($h$1($x$)+$i$*$h$2($x$))$mod tableSize $($i is the probing count$)$

$//$ where h$2($x$)=5-($sum of all digits of h$1($x$))$mod $5)$

$//4.$For every newly calculated key using quadratic probing, check for empty slot for insertion

$//$ If empty slot is found, insert data, set symbol to $\text{'}$v$\text{'},$then return true $($indicating successful insertion$)$

$//$ If element is already inserted, return false $($indicating failed insertion$)$

$//$ If probing count exceeds MAX$\_$PROBING$\_$COUNT defined in objPosHash.h$,$return false

$//($too many probing attempts, may lead to integer overflow$)$

$\}$

#ifndef OBJPOS$\_$DOUBLE$\_$HASHING$\_$H

#define OBJPOS$\_$DOUBLE$\_$HASHING$\_$H

#include "objPosHash.h$"$

#include "objPos.h$"$

class objPos;

class objPosDoubleHashing : public objPosHashTable

$\{$

$$ private:

$$ objPos$*$myHashTable;

$$ int calculateHashing$($int prefix, int number$)$const; $//$hashing function

$$ int calculateSecondaryHashing$($int input$)$const; $//$secondary hashing function

$//$signature subject to change

$$ public:

$$ objPosDoubleHashing$()$;

$$ objPosDoubleHashing$($int$)$;

$$ virtual ~objPosDoubleHashing$()$;

$$ bool insert$($const objPos &thisPos$)$;

$$ bool remove$($const objPos &thisPos$)$; $//$lazy delete

$$ bool isInTable$($const objPos &thisPos$)$const;

$$ double getLambda$()$const;

$$ void printMe$()$const;

$\}$;

#endif