How to make simmetric matrix in C language - c

Question

For a school project of the features asked is to build a symmetric matrix using random number in [1,100], I know how to build a matrix and how to do it using the rand() function in C however I'm not being able to do a symmetric one, this is my code:
int size, num;
fflush(stdin);
system("cls");
printf("Build a simmetric matrix using random numbers\n\n");
printf("Insert matrix size: ");
scanf("%d", &size);
int matrix[size-1][size-1];
for(int i=0;i<size;i++){
for(int j=0;j<size;j++){
num = rand()%100+1;
matrix[i][j]=num;
matrix[j][i]=num;
}
}
for(int i=0;i<size;i++){
printf("\n\t");
for(int j=0;j<size;j++){
printf("%03d ", matrix[i][j]);
}
}
printf("\n\nPress Enter to continue...");
system("pause >nul /nobreak");
It builds a square matrix as requested but it isn't symmetric.
I would appreciate and be thankful for any help with the code to do it or pointing me to the right direction.

Answer 1

You are not getting symmetric matrix because you are accessing the index of matrix not properly. Let me explain in a bit detail.
The matrix that you are using is of size size-1 x size-1, so if size=5 then the matrix that you are allocating is of size 4x4, so you effectively have only 16 elements in your matrix. (And you actually want 25 elements).
But when traversing the matrix to populate it, you are accessing index like[4,4] which means your matrix should (logically) have 25 elements. (But it is not having).
So there are two ways to get rid of this mistake:
You can change your for loop to for(int i=0;i<size-1;i++) so you don't access elements in an unexpected way.
You can increase the size of your array to size x size instead of size-1 x size-1.
The final code will look something like this (I'm posting only the core part):
int matrix[size][size];
for(int i=0;i<size;i++){
for(int j=i;j<size;j++){
num = rand()%100+1;
matrix[i][j]=num;
matrix[j][i]=num;
}
}
As an optimization you can avoid re-writing the values by putting starting the inner-loop for j from i itself, so that the values in the upper triangle of matrix are generated by random number and the lower triangle values are filled by the value in the corresponding symmetric cell in the upper triangle.
I think your intention for asking the question is to learn and get better, so I answered in detail with some extra comments. I hope this was helpful. :)

Answer 2

Two mistakes:
off-by-one error in the matrix size: accesses will go to wrong place
you overwrite all columns in all lines, instead of filling just a triangle
Corrected code:
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
int main(int argc, char **argv) {
(void) argc;
(void) argv;
int size;
printf("Build a symmetric matrix using random numbers\n\n");
printf("Insert matrix size: ");
scanf("%d", &size);
/* ensure different result every time program is executed */
srand(time(NULL));
int matrix[size][size];
for (int i = 0; i < size; i++) {
for (int j = 0; j < i + 1; j++) {
int num = rand() % 100 + 1;
matrix[i][j] = num;
matrix[j][i] = num;
}
}
for (int i = 0; i < size; i++) {
printf("\n\t");
for (int j = 0; j < size; j++) {
printf("%03d ", matrix[i][j]);
}
}
printf("\n");
return(0);
}
Example output:
Build a symmetric matrix using random numbers
Insert matrix size: 5
084 087 016 087 063
087 078 094 093 028
016 094 036 050 091
087 093 050 022 060
063 028 091 060 064

Answer 3

Line #7:
use
int matrix[size][size];