C++: Write a program that uses a 3 X 3 array and randomly place each integer fro

Question

C++: Write a program that uses a 3 X 3 array and randomly place 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 3 X 3 array is a magic square if the sum of each row, each column, and each diagonal is equal to the magic number. Your program must contain 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 for some large number of times, say 1,000, 10,000, or 1,000,000 times and see the number of times the array is a magic square.

Explanation / Answer

#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;
}

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