Question

IN C++

Write a program that uses a 3x3 array and randomly places each integer from 1 to 9 into the nine squares. The program calculates the "magic number" by adding all the numbers in the array and then dividing the sum by 3. The 3x3 array is said to be a "magic square" if the sum of each row, each column, and each diagonal is equal to the magic number.

Your program must use at least the following functions: a function to randomly fill the array with the numbers and a function to determine if the array is a magic square. Run these functions 10000 times and report the number of times the array is a magic square.

Answer 1

C++ Code:

#include <iostream>

#include <cstdlib>

#include <iomanip>

using namespace std;

const int ROWS = 3;

const int COLS = 3;

void fillBoard(int b[][COLS]);

void showBoard(int b[][COLS]);

bool isMagicSquare(int b[][COLS], int rows);

int main()

{

   int board[ROWS][COLS];

long long count = 0;

long long numOfTrials;

cout << "Enter the number of times to test magic square: ";

cin >> numOfTrials;

cout << endl;

for (long long i = 0; i < numOfTrials; i++)

{

fillBoard(board);

if (isMagicSquare(board, ROWS))

{

showBoard(board);

count++;

}

}

cout << "Number of times magic square occurred: " << count << endl;

   return 0;

}

void fillBoard(int b[][COLS])

{

int row;

int col;

int num = 1;

bool placedNum;

for (int i = 0; i < ROWS; i++)

for (int j = 0; j < COLS; j++)

b[i][j] = -1;

for (int i = 0; i < ROWS * COLS; i++)

{

placedNum = false;

while (!placedNum)

{

row = rand() % ROWS;

col = rand() % COLS;

if (b[row][col] == -1)

{

b[row][col] = num;

placedNum = true;

}

}

num++;

}

}

void showBoard(int b[][COLS])

{

for (int i = 0; i < ROWS; i++)

{

for (int j = 0; j < COLS; j++)

cout << setw(4) << b[i][j];

cout << endl;

}

cout << endl;

}

bool isMagicSquare(int b[][COLS], int rows)

{

int magicNum;

int sum = 0;

bool isMagic = true;

for (int i = 0; i < rows; i++)

for (int j = 0; j < COLS; j++)

sum = sum + b[i][j];

magicNum = sum / rows;;

for (int i = 0; i < rows; i++)

{

sum = 0;

for (int j = 0; j < COLS; j++)

sum = sum + b[i][j];

if (sum != magicNum)

{

isMagic = false;

break;

}

}

if (isMagic)

{

for (int j = 0; j < COLS; j++)

{

sum = 0;

for (int i = 0; i < rows; i++)

sum = sum + b[i][j];

if (sum != magicNum)

{

isMagic = false;

break;

}

}

}

if (isMagic)

{

sum = 0;

for (int i = 0; i < rows; i++)

sum = sum + b[i][i];

isMagic = false;

}

if (isMagic)

{

sum = 0;

for (int i = 0; i < rows; i++)

sum = sum + b[i][rows - 1 - i];

isMagic = false;

}

return isMagic;

}