## Stumped Need Help 15 Puzzle

I've been trying to figure out how to implement a way to save this board state throughout a user's inputted path. At the end, I need the output to print out the board states (user's path) of how he or she got the puzzle solved. This puzzle is the 15 Puzzle; but we have it to change by the user's input on what size they want to play (3x3 to 5x5). I need help figuring out how to save the board state of each user input, then print those out in order from beginning to solved puzzle state. Subsequently, I would also need some help on transferring the board state to change with using a vector to store the size based on user input. Yes, this is college work; and I have turned this in last week late. I need help on figuring out how to fix last week's problems to proceed with this week's homework assignment, which is using a first search to solve the puzzle from the current board's state.

calculations.h
Code:
```/*Calculations set as a header to keep compiling simple and faster*/

#ifndef calculations
#define calculations

int solved[5][5];

void initialize(int board[][5], int);
void slide(int board[][5],int move,int);
bool isBoardSolved(int board[][5],int);

/*Configure and Setup the 15-Puzzle Game*/
void initialize(int board[][5], int amt)
{
int i = 1;
for(int row = 0; row <= amt; row++)
{
for(int column = 0; column <= amt; column++)
{
board[row][column] = i;
solved[row][column] = i;
i++;
}
board[amt][amt] = 0;
solved[amt][amt] = 0;
}
}

/*Results of moving the blank space*/
void slide(int board[][5],int move, int amt)
{
int emptyRow;
int emptyCol;
bool legalMoves[4] = {1,1,1,1}; //array of possible moves, [0] = left, [1] = right, [2] = up, [3] = down. (1) represents a possible move to be accessible.
for(int rows = 0; rows <= amt; rows++)
{
for(int columns = 0; columns <= amt; columns++)
{
if(board[rows][columns] == 0) //Find location of empty space
{

emptyRow = rows;
emptyCol = columns;
}
}
}
if(emptyRow + 1 > amt) //Able to move up?
legalMoves[2] = false; //If false, set move flag to false
else if(emptyRow - 1 < 0) //Able to move down?
legalMoves[3] = false;

if(emptyCol - 1 < 0) //Able to move right?
legalMoves[1] = false; //If false, set move flag to false
else if(emptyCol + 1 > amt) //Able to move left?
legalMoves[0] = false;

switch(move) //Replace zero space with space to the left right up or down.
{
case 0:
if(legalMoves[move])
{
board[emptyRow][emptyCol] = board[emptyRow][emptyCol + 1];
board[emptyRow][emptyCol + 1] = 0;
emptyCol = emptyCol+1;
}
break;
case 1:
if(legalMoves[move])
{
board[emptyRow][emptyCol] = board[emptyRow][emptyCol - 1];
board[emptyRow][emptyCol- 1] = 0;
emptyCol = emptyCol-1;
}
break;
case 2:
if(legalMoves[move])
{
board[emptyRow][emptyCol] = board[emptyRow+1][emptyCol];
board[emptyRow+1][emptyCol] = 0;
emptyRow = emptyRow+1;
}
break;
case 3:
if(legalMoves[move])
{
board[emptyRow][emptyCol] = board[emptyRow-1][emptyCol];
board[emptyRow-1][emptyCol] = 0;
emptyRow = emptyRow-1;
}
break;
}

}
bool isBoardSolved(int board[][5], int amt)
{
bool boardSolved = true;
int row = 0;
int col = 0;
while(boardSolved && row<=amt)
{
if(solved[row][col] == board[row][col]) //Compares to make sure if the puzzle is solved
//and sets numbers to green if they are in the correct position
{
col++;
if(col == amt)
{
row++;
col = 0;
}
}
else //If there is any hinderance on solving the puzzle, break the loop by setting it to false
boardSolved = false;
}
return boardSolved;
}

#endif```
main.cpp
Code:
```/*Advance AI for Game & Sim Dsgn w/L
Professor:  Marty Geier
By: Cody Bennett
References:	1) http://xoax.net/cpp/crs/console/lessons/Lesson29/
2) http://www.cplusplus.com/forum/beginner/11636/
This program is designed to have the user able to play the 15-Puzzle game. Although,
the user is also able to make a choice from 3x3(9) and 5x5(25) puzzle as well. Once
the puzzle is solved, the user has their amount of moves and time displayed.*/

#include <iostream>
#include <string>
#include <conio.h>
#include <stdio.h>
#include <ctime>
#include <vector>
#include <array>
#include <new>
#include <calculations.h>
#include <Windows.h>

using namespace std;

// To use the arrow keys instead of letters

#define UP 72
#define LEFT 75
#define RIGHT 77
#define DOWN 80

vector< vector<int> > board;
board matrix(m);

void print(int board[][5], int);
void initialize(int board[][5], int);
void slide(int board[][5],int move,int);
bool isBoardSolved(int board[][5],int);
void scramble(int board[][5],int);
void WaitKey();

int main()
{
int boardAmount = 0;
int moves = 0;
int shuffleCount = 0;

do
{
system("CLS");
cout << endl << endl << endl << "\t\tEnter designated size for sliding puzzle. (3 to 5)";
cout << endl << endl << "\t\t\t\t\t";
cin >> boardAmount;
if(boardAmount <3 || boardAmount > 5)
cout << "\t\t\tSorry, this program is unable to allow playing with that size specified. Please, enter another size." << endl << endl;
Sleep(1300);
}while (boardAmount <3 || boardAmount > 5);

int gameBoard[5][5];

char input;
string direction;
bool invalid = false;
boardAmount--; /* Use this method in order to keep from having to
subtract 1 from the checking to make sure the blank space
doesn't go outside the boundaries of the board.*/
initialize(gameBoard,boardAmount);
print(gameBoard,boardAmount);
cout << boolalpha;
cout<<"isBoardSolved(): "<<isBoardSolved(gameBoard,boardAmount)<<endl;
cout<<"How many times would you like to shuffle the board?" << endl;
cin >> shuffleCount;
cout<<"Press enter to continue to shuffle the board"<<endl;
WaitKey();
cout<<"Scrambling is commencing..."<<endl;
scramble(gameBoard, boardAmount);
cout<<"Scrambling is completed, please press enter to continue"<<endl;
cin.get();
system("CLS");

print(gameBoard,boardAmount);
cout<<endl<<endl;
clock_t begin = clock ();
cout<<"Use arrow keys to move the blank in the desired direction" << endl;
cout<<"in order to move the tiles!"<<endl;
cout<<"Input: ";
while(!isBoardSolved(gameBoard, boardAmount))
{
input = _getch();
system("CLS");

switch(input)
{
case DOWN:
slide(gameBoard,2,boardAmount);
direction = "Up";
moves++;
break;
case RIGHT:
slide(gameBoard,0,boardAmount);
direction = "Left";
moves++;
break;
case UP:
slide(gameBoard,3,boardAmount);
direction = "Down";
moves++;
break;
case LEFT:
slide(gameBoard,1,boardAmount);
direction = "Right";
moves++;
break;
default:
invalid = true;

}
print(gameBoard,boardAmount);
cout<<endl<<endl;
cout<<"Use arrow keys to move the blank space in the direction that you want."<<endl;
if(invalid)
invalid = false;
else
cout<<"Last User Input: "<<direction;
}
cout << endl;
clock_t end = clock();
double elasped_secs = double(end - begin)/ CLOCKS_PER_SEC;
cout << "Congratulations!!! You've Won!" << endl;
cout << "RESULTS:" << endl;
cout << "Moves made: " << moves << endl;
cout << "Your time to solve the puzzle is: " << elasped_secs << " seconds" << endl;
cout << "Please any key to print your moves below:" << endl;
system ("PAUSE");

}

/* Print board and replace zero with a character 177 */
void print(int board[][5], int amt)
{
HANDLE hConsole;
hConsole = GetStdHandle(STD_OUTPUT_HANDLE);
for(int row = 0; row <= amt; row++)
{
for(int column = 0; column <= amt; column++)
{
if(board[row][column] == 0)
{
SetConsoleTextAttribute(hConsole, 7); //Default color
cout << "\xB1\xB1 ";
}
else
{
if(board[row][column] == solved[row][column]) //Change the numbers as they are crossed over their correct positions
//They are compared to the solved solution
SetConsoleTextAttribute(hConsole, 10);
else
SetConsoleTextAttribute(hConsole, 12); //If the numbers are not in the right position, turn their color red
if (board[row][column]<10) // Print a 0 first if # < 10
cout<<"0";
cout<<board[row][column] << " ";
}
}
cout<<endl;
}
SetConsoleTextAttribute(hConsole, 7);
}

void scramble(int board[][5], int shuffleCount)
{
time_t t;
srand((unsigned) time(&t));
int move;
while(isBoardSolved(board,shuffleCount))// Shuffle the board based on the user input
{
for(int i = 0; i < 50;i++) //Shuffle the board with random tiles moved
{
move = rand() % 4;
slide(board,move,shuffleCount);
}
}
}

void WaitKey()
{
while (_kbhit()) _getch(); // Empty the input buffer
_getch(); // Wait for a key
while (_kbhit()) _getch(); // Empty the input buffer (some keys sends two messages)
}```
I would appreciate any quick responses. I've spent a long time trying to figure this out myself; but as the title states, I'm stumped.