Question

Write a C++ program that uses a 4 X 4 array and randomly place each integer from 1 to 16 into the 16 squares. The program calculates the magic number by adding all the numbers in the array and then dividing the sum by 4. The 4 X 4 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) a function to randomly fill the array with the numbers

b) a function to determine if the array is a magic square

Run these functions for 10000 number of times and print the number of times the array is a magic square.

Answer 1

input code:

output:

code:

#include <bits/stdc++.h>
using namespace std;
#define M 4
/*generate the numbers from 1 to 16 and fill into array*/
void generate_array(int array[][M])
{
for(int i=0;i<M;i++)
{
for(int j=0;j<M;j++)
{
array[i][j]=rand()%16+1;
}
}
}

bool Check_magicsquare (int array[][M])
{

int sum = 0, sum2 = 0;
/*find the sum of diagonal */
for (int i = 0; i < M; i++)
{
sum = sum + array[i][i];
}
/*find the sum of second diagonal */
for (int i = 0; i < M; i++)
{
sum2 = sum2 + array[i][M - 1 - i];
}
/*if diagonal sum is not same than return false */
if (sum != sum2)
{
return false;
}

/*find the sum of all rows */
for (int i = 0; i < M; i++)
{

int Rows = 0;
for (int j = 0; j < M; j++)
{
Rows += array[i][j];
}
/*if row sum is not same as diagonal sum than return false */
if (Rows != sum)
{
return false;
}
}

/*find the sum of all cols */
for (int i = 0; i < M; i++)
{

int Cols = 0;
for (int j = 0; j < M; j++)
{
Cols += array[j][i];
}
/*if row sum is not same as diagonal sum than return false*/
if (sum != Cols)
return false;
}
return true;
}

int main ()
{
/*declare array and counter*/
int magicsquare=0;
int array[M][M];
cout<<"Array generating is starting."<<endl;
cout<<"Loading....."<<endl;
cout<<"Loading....."<<endl;
cout<<"Loading....."<<endl;
/*do process for 10000 times*/
for(int i=0;i<10000;i++)
{
/*fill value into array*/
generate_array(array);
  
/*check array is magicsquare or not*/
if(Check_magicsquare(array))
{
magicsquare++;
}
}
/*print Total magicsquare */
cout<<"Total number of magic square is generated is : "<<magicsquare;
return 0;
}