sparse matrix multiplication

#include <stdio.h>
#include <stdlib.h>

typedef struct _matrix {
    int size;       //number of elements
    int ord;       //order of matrix
    int* val;
    int* col;
    int* row;
} matrix;

matrix fill_matrix (int ord)
{
    int i, j, size = ord * ord / 3;
    matrix new_matrix;

    new_matrix.val = malloc(sizeof(int) * size);
    new_matrix.row = malloc(sizeof(int) * size);
    new_matrix.col = malloc(sizeof(int) * size);
    new_matrix.ord = ord;
    new_matrix.size = size;

    j = 1;
    for (i = 0; i < size; i++) {
        new_matrix.val[i] = rand() % 9 + 1;
        new_matrix.col[i] = rand() % j + 1;
        new_matrix.row[i] = rand() % j + 1;
        j++;
    }
    printf("\n=====array:=====\n");
    for (i = 0; i < size; i++) printf("%d ", new_matrix.val[i]);
    printf("\n");
    for (i = 0; i < size; i++) printf("%d ", new_matrix.row[i]);
    printf("\n");
    for (i = 0; i < size; i++) printf("%d ", new_matrix.col[i]);

    return new_matrix;
}

void print_matrix (matrix m)
{
    int i, j, k, flag, ord = m.ord, size = m.size;

    for (i = 1; i <= ord; i++) {
        for (j = 1; j <= ord; j++) {
            flag = 0;
            for (k = 0; k < size; k++) {
                if (m.row[k] == i && m.col[k] == j){
                    flag = 1;
                    printf("%d ", m.val[k]);
                    break;
                }
            }
            if (flag == 0) printf(". ");
        }
        printf("\n");
    }
}

matrix transpose (matrix m)
{
    int i, size = m.size, ord = m.ord;
    matrix mt;

    mt.val = malloc(sizeof(int) * size);
    mt.row = malloc(sizeof(int) * size);
    mt.col = malloc(sizeof(int) * size);
    mt.ord = ord;
    mt.size = size;

    for (i = 0; i < size; i++) {
        mt.val[i] = m.val[i];
        mt.row[i] = m.col[i];
        mt.col[i] = m.row[i];
    }
    return mt;
}

matrix mul (matrix A, matrix B)
{
    int i, j, k, a, b, r = 0, curr_row_a, curr_row_b, curr_col_b, r_col, sum = 0, size = A.size, ord = A.ord;

    matrix BT;
    BT = transpose(B);
    printf("\n-----mtxBT-----\n");
    print_matrix(BT);

    matrix R;
    R.val = malloc(sizeof(int) * size);
    R.row = malloc(sizeof(int) * size);
    R.col = malloc(sizeof(int) * size);
    R.ord = ord;
    R.size = size;

    for (a = 1; a <= ord; a++) {
        //printf(" a=%d\n", a);
        for (b = 1; b <= ord; b++) {
            //printf("  b=%d\n", b);
            sum = 0;
            for (i = 0; i < size; i++) {
                curr_row_a = a;
                curr_row_b = b;
                curr_col_b = A.col[i];
                if (A.row[i] == a) {
                    for(j = 0; j < size; j++) {
                        if (BT.col[j] == curr_col_b && BT.row[j] == curr_row_b) {
                            sum += A.val[i] * BT.val[j];
                            r_col = BT.col[j];
                            break;
                        }
                    }
                }
            }
            if (0 != sum) {
                //printf("%d\n", sum);
                R.val[r] = sum;
                R.row[r] = a;
                R.col[r] = b;
                r++;
            }
        }
    }
    printf("\n=====array:=====\n");
    for (i = 0; i < size; i++) printf("%d ", R.val[i]);
    printf("\n");
    for (i = 0; i < size; i++) printf("%d  ", R.row[i]);
    printf("\n");
    for (i = 0; i < size; i++) printf("%d  ", R.col[i]);

    return R;
}

int main()
{
    matrix A, B, C;
    int n = 3;
    printf("insert order:");
    scanf("%d", &n);
    A = fill_matrix(n);
    B = fill_matrix(n);

    printf("\n-----mtrxA-----\n");
    print_matrix(A);

    //printf("\n-----mtrxB-----\n");
    //print_matrix(B);


    C = mul(A, B);

    printf("\n-----mtrxC-----\n");
    print_matrix(C);

    return 0;
}