// checks if an input array is a `magic square'
#include<iostream.h>

const int maxsquare = 15, TRUE=1, FALSE=0;

void readmagsq(int& size, int ms[][maxsquare]);
/*pre: size the array size;
 post: ms contains size by size array*/


void writesq(int size, int ms[][maxsquare], int& isms);
/*pre: size the array size; isms true if a Magic Square
 post: the array written with a message*/


void checkrows(int sum, int size, int ms[][maxsquare], int& isms);
/* pre: isms true; sum has value; ms has values
 post: isms true only if all rows sum to sum*/


void checkcols(int sum, int size, int ms[][maxsquare], int& isms);
/*pre: isms true; sum has value; msType has values
 post: isms true only if all cols sum to sum*/


void checkdiags(int sum, int size, int ms[][maxsquare], int& isms);
/*pre: isms true; Sum has value; msType has values
 post: isms true only if both diagonals sum to sum*/


int main()
{int size, sum, j, magic, ms[maxsquare][maxsquare];

 cout << "input square size ( <" << maxsquare << ") >";
 cin >> size;
 readmagsq(size,ms);
 sum = 0;
 for (j = 0; j < size; j++)
  sum = sum + ms[1][j];
 magic = TRUE;
 checkrows(sum,size,ms,magic);
 if (magic)
     checkcols(sum,size,ms,magic);
 if (magic)
     checkdiags(sum,size,ms,magic);
 writesq(size,ms,magic);
 return (0);

}


void readmagsq(int& size, int ms[][maxsquare])

{int i, j;

  cout << "Type in " << size << " rows of " << size << " integers\n";
  for (i = 0; i < size; i++)
   {
    for (j = 0; j < size; j++)
     cin >> ms[i][j] ;
   };/*for i*/
  cout << endl;
}/*ReadMagSq*/

void writesq(int size, int ms[][maxsquare], int& isms)

{int i,j;

  if (isms)
    cout << "The square below is a Latin square\n\n";
  else
    cout << "The square below is not a Latin square\n\n";

  for (i = 0; i < size; i++)
   {
    for (j = 0; j < size; j++)
     {cout.width(3);
      cout <<  ms[i][j];};
    cout << endl ;
   };//for i
 }//WriteMagSq

void checkrows(int sum, int size, int ms[][maxsquare], int& isms)

{int rowsum, i, j;

   i = 2;
   while ((i <= size)&&(isms))
    {
     rowsum = 0;
     for (j = 0; j < size; j++)
       rowsum = rowsum + ms[i][j];
     if (rowsum != sum) isms = FALSE;
     i++;
    };//while
}//Checkrows

void checkcols(int sum, int size, int ms[][maxsquare], int& isms)

{int colsum, i, j;

   j = 0;
   while ((j <= size)&&(isms))
    {
     colsum = 0;
     for (i = 0; i<= size;i++)
       colsum = colsum + ms[i][j];
     if (colsum != sum) isms = FALSE;
     j++;
    };//while
};/*CheckCols*/

void checkdiags(int sum, int size, int ms[][maxsquare], int& isms)
{int diagsum, i;

    diagsum = 0;
    for (i = 0; i < size; i++)
       diagsum = diagsum + ms[i][i];
    if (diagsum != sum) isms = FALSE;
    if (isms)
      {
       diagsum = 0;
       for (i = 0; i < size; i++)
        diagsum = diagsum + ms[size + 1 - i][i];
       if (diagsum != sum) isms = FALSE;
     };//if isms
}//Checkdiags