I ve done a program that take an number n as input and then return a square matrix n*n with the property that all row, columns, and diagonals have the same sum.
The project works without problem, and I tried to optimize it as much as i can, from the algorithm to uses the specific data type for this(in my case unsigned short, cause i didn t need a bigger storage).
After all i tried to see the performance and i wanted to try it with a bigger number like 100,200, so on; But when i tried to change the storage of matrix the program didn t work properly and returned a matrix with 0 and the sum was strange.
I don t understand from where is this bug.
#include <stdio.h>
#include <stdlib.h>
unsigned short a[100][100], i = 0, j = 0, n, suma[100];
void next_b(unsigned short *i, unsigned short *j); // find the properly i and j
void completare(unsigned short i, unsigned short j); // completes the matrix after i find the i and j
void tipar(); // print the matrix
int suma_linie(unsigned short x); //sum of a row
int suma_coloana(unsigned short y); //sum of a column
int suma_diagonala_principala(); //first diagonal
int suma_diagonala_secundara(); //second one
int main()
{
scanf("%hu", &n);
system("cls");
j = n / 2 - 1;
a[0][j] = 4;
a[0][j + 1] = 1;
a[1][j] = 2;
a[1][j + 1] = 3;
suma[0] = 5;
suma[1] = 5;
suma[n + j] = 6;
suma[n + j + 1] = 4;
for (int x = 2; x <= (n / 2) * (n / 2); x++)
{
next_b(&i, &j);
a[i][j] = x;
completare(i, j);
}
tipar();
//for(int x=0;x<n;x++){
//
// printf("suma de pe linia %d este: %d\n",x,suma_linie(x));
// printf("suma de pe coloana %d este: %d\n\n",x,suma_coloana(x));
//}
//printf("suma de pe daig principala este: %d\n\n",suma_diagonala_principala());
// printf("suma de pe daig secundara este: %d\n\n",suma_diagonala_secundara());
for (int x = 0; x < 2 * n + 2; x++)
{
if (x < n)
{
printf("suma de pe linia %d este %hu\n", x, suma[x]);
}
else if (x < 2 * n)
{
printf("suma de pe coloana %d este %hu\n", x % n, suma[x]);
}
else if (x == 2 * n)
{
printf("suma de pe diag principala este %hu\n", suma[x]);
}
else
{
printf("suma de pe diag secundara este %hu\n", suma[x]);
}
}
return 0;
}
void tipar()
{
for (int k = 0; k < n; k++)
{
for (int l = 0; l < n; l++)
{
if (a[k][l] < 10)
{
printf(" %d |", a[k][l]);
}
else if (a[k][l] <= 99)
{
printf(" %d |", a[k][l]);
}
else if (a[k][l] < 1000)
{
printf(" %d |", a[k][l]);
}
else if (a[k][l] < 10000)
{
printf("%d ", a[k][l]);
}
}
printf("\n");
for (int z = 0; z <= 6 * n - 1; z++)
{
printf("-");
}
printf("\n");
}
printf("\n");
}
void next_b(unsigned short *i, unsigned short *j)
{
if (*i - 2 < 0)
{
if (a[n - 2][*j + 2] == 0 && *j + 2 <= n - 2)
{
// printf("cazul 2\n");
*i = n - 2;
*j += 2;
return;
}
else if (a[*i - 2][*j] == 0)
{
// printf("cazul 7\n");
*i += 2;
return;
}
}
else
{
if (*j == n - 2)
{ //printf("cazul 3\n");
*i -= 2;
*j = 0;
return;
}
else if (a[*i - 2][*j + 2] != 0)
{
//printf("cazul 4\n");
*i += 2;
}
else if (a[*i - 2][*j + 2] == 0)
{
// printf("cazul 5\n");
*i -= 2;
*j += 2;
}
}
}
void completare(unsigned short i, unsigned short j)
{
if (i <= n / 2)
{ //////////// l
if (i == n / 2 - 1 && j == n / 2 - 1)
{
a[i][j + 1] = 4 * a[i][j];
a[i + 1][j] = 4 * a[i][j] - 2;
a[i + 1][j + 1] = 4 * a[i][j] - 1;
a[i][j] = 4 * a[i][j] - 3;
}
else
{
a[i][j] = 4 * a[i][j];
a[i][j + 1] = a[i][j] - 3;
a[i + 1][j] = a[i][j] - 2;
a[i + 1][j + 1] = a[i][j] - 1;
}
}
else if (i == n / 2 + 1)
{ ///////////// u
if (j == n / 2 - 1)
{
a[i][j] = 4 * a[i][j];
a[i][j + 1] = a[i][j] - 3;
a[i + 1][j] = a[i][j] - 2;
a[i + 1][j + 1] = a[i][j] - 1;
}
else
{
a[i][j + 1] = 4 * a[i][j];
a[i + 1][j] = 4 * a[i][j] - 2;
a[i + 1][j + 1] = 4 * a[i][j] - 1;
a[i][j] = 4 * a[i][j] - 3;
}
}
else
{ ///////x
a[i][j + 1] = 4 * a[i][j];
a[i + 1][j + 1] = 4 * a[i][j] - 2;
a[i + 1][j] = 4 * a[i][j] - 1;
a[i][j] = 4 * a[i][j] - 3;
}
suma[i] += a[i][j] + a[i][j + 1];
suma[i + 1] += a[i + 1][j] + a[i + 1][j + 1];
suma[n + j] += a[i][j] + a[i + 1][j];
suma[n + j + 1] += a[i][j + 1] + a[i + 1][j + 1];
if (i == j)
{
suma[2 * n] += a[i][j] + a[i + 1][j + 1];
}
if (i + j + 1 == n - 1)
{
suma[2 * n + 1] += a[i + 1][j] + a[i][j + 1];
}
}
int suma_linie(unsigned short x)
{
int s = 0;
for (int y = 0; y < n; y++)
{
s += a[x][y];
}
return s;
}
int suma_coloana(unsigned short y)
{
int s = 0;
for (int x = 0; x < n; x++)
{
s += a[x][y];
}
return s;
}
int suma_diagonala_principala()
{
int s = 0;
for (int x = 0; x < n; x++)
{
s += a[x][x];
}
return s;
}
int suma_diagonala_secundara()
{
int s = 0;
for (int x = 0; x < n; x++)
{
s += a[x][n - x - 1];
}
return s;
}
The code is solve with an algorithm that i found on Wikipedia-Magic Square.
In the above cod if i try to change suma size to 200 for example or any other value, the program works strange and returns stupid things.
It s valid even i set a size higher.
I used two ways to see the sum, one with a predefined functions and the other adding the matrix element to suma, the functions used int and the other method utilize unsigned short if its matters.
I checked your code and found some problems. I tried with n = 90.
for(int x=2; x<=(n/2)*(n/2); x++)
{
next_b(&i,&j);
a[i][j]=x;
completare(i,j);
}
If you check this code then you can see when the value of i, j become 0, 2 accordingly then it goes to next_b(i, j) method. And there are some lines which are trying to access negative indexes. So it throws exception.
Like -
else if(a[*i-2][*j]==0) // here
{
// printf("cazul 7\n");
*i+=2;
return;
}
.............................................
if(*j==n-2)
{
//printf("cazul 3\n");
*i-=2;
*j=0;
return;
}
else if (a[*i-2][*j+2]!=0) // here
{
//printf("cazul 4\n");
*i+=2;
}
else if(a[*i-2][*j+2]==0) // here
{
//printf("cazul 5\n");
*i-=2;
*j+=2;
}
Try to fix these negative indexing and then it should work (Assuming your approach is correct).