magic_square_sum_24_v1.c

/*

    magic_square_sum_24_v1.c

    Task:
    https://www.facebook.com/groups/1941400139499670/posts/2686570531649290/

    Put the numbers 4,5,6,7,8,9,10,11,12 in the squares
    (don't repeat the numbers, one number has to be in one square),
    such that three numbers added to get 24,
    this must get in rows, columns and diagonal (two senses).

    Sum of the 3 numbers in each row, column and diagonal should be 24.
    All numbers are different, from range 4 to 12.

    24                24                indexes of array:

        x1  x2  x3  =   24              0   1   2

        x4  x5  x6  =   24              3   4   5

        x7  x8  x9  =   24              6   7   8

        "   "   "
  24    24  24  24     24


    Algorithm with permutations.

    https://www.codesdope.com/blog/article/generating-permutations-of-all-elements-of-an-arra/


    You can find all my C programs at Dragan Milicev's pastebin:

    https://pastebin.com/u/dmilicev

*/

#include <stdio.h>

#define SUM 24

int number_of_solutions=0;
unsigned number_of_attempts=0;

//function to print the array of n integers
void print_array(int arr[], int n)
{
    number_of_attempts++;

    if( arr[0] + arr[1] + arr[2] == SUM &&
        arr[3] + arr[4] + arr[5] == SUM &&
        arr[6] + arr[7] + arr[8] == SUM &&
        arr[0] + arr[3] + arr[6] == SUM &&
        arr[1] + arr[4] + arr[7] == SUM &&
        arr[2] + arr[5] + arr[8] == SUM &&
        arr[0] + arr[4] + arr[8] == SUM &&
        arr[2] + arr[4] + arr[6] == SUM     )
    {
            number_of_solutions++;  // number_of_solutions and display them
            printf("\n---%3d. solution: --------\n\n", number_of_solutions);
            printf(" %3d %3d %3d \n", arr[0], arr[1], arr[2] );
            printf(" %3d %3d %3d \n", arr[3], arr[4], arr[5] );
            printf(" %3d %3d %3d \n", arr[6], arr[7], arr[8] );
    }
} // print_array()

// function to swap the variables a and b
void swap(int *a, int *b)
{
    int temp;
    temp = *a;
    *a = *b;
    *b = temp;
}

// recursive function to generate permutation
void permutation(int *arr, int start, int end)
{
    int i;

    if(start==end)
    {
        print_array(arr, end+1);        // this is one permutation
        return;
    }

    for( i=start; i<=end; i++ )         // fixing one first digit,
    {
        swap((arr+i), (arr+start));     // swapping numbers
        permutation(arr, start+1, end); // and calling permutation on the rest of the digits
        swap((arr+i), (arr+start));     // swapping numbers
    }
} // permutation()


int main(void)
{
    int i;

    int arr[9]={4,5,6,7,8,9,10,11,12};  // array of 9 permutation elements

    permutation(arr, 0, 8);     //calling recursive function to generate permutations

    printf("\n Number of attempts is 9! = %ld \n", number_of_attempts);
    printf("\n There are %d solutions. \n", number_of_solutions);

    return 0;
} // main()

/*

---  1. solution: --------

   5  10   9
  12   8   4
   7   6  11

---  2. solution: --------

   5  12   7
  10   8   6
   9   4  11

---  3. solution: --------

   7   6  11
  12   8   4
   5  10   9

---  4. solution: --------

   7  12   5
   6   8  10
  11   4   9

---  5. solution: --------

   9   4  11
  10   8   6
   5  12   7

---  6. solution: --------

   9  10   5
   4   8  12
  11   6   7

---  7. solution: --------

  11   6   7
   4   8  12
   9  10   5

---  8. solution: --------

  11   4   9
   6   8  10
   7  12   5

 Number of attempts is 9! = 362880

 There are 8 solutions.

*/