Count number of cycles in permutation
Unless you use a very old compiler, I suggest you to declare (and initialize) variables as late as possible and limit their scope. This prevents potential mistakes like

return current; /* whoops, meant counter! */


in countCyclesHelper.

Next, unless you got invalid input, only array[first] may be -1, otherwise one of your nodes in your (implicit) graph has two incoming edges and the original file didn't contain a valid permutation.

If we take both suggestions into account, we end up with the following countCyclesHelper:

int countCyclesHelper(int* array, int N) {
  int total_cycles = 0;

  for (int i = 0; i &lt; N; i++) {
    const int first = i;
    int current = first;

    if (array[current] == -1) {
      /* already counted this cycle */
      continue;
    }

    while (1) {
      const int temp = array[current] - 1;
      array[current] = -1;
      current = temp;
      if (current == first) {
        counter++;
        break;
      }
    }
  } 
  return total_cycles; 
}


While I kept first, it's possible to replace it with i.



As you can see, I've added const at various places. If we don't intend to change a value it's usually a good idea to prevent it with const. This holds for example for your name in countCycles. We don't want to accidentally change the file name:

int countCycles(const char *name, int N)


Next, fread(buffer, sizeof(buffer), …) is&mdash;unfortunately&mdash;wrong, since buffer is a pointer. You end up with fread(buffer, sizeof(char*), …). Therefore, your program contained undefined behaviour, unless N &lt;= sizeof(char*).

That being said, countCycles is an overkill, since you handle only single digit permutation indices. For any  N >= 10the content ofarraywon't be a permutation. With this in mind, we can simplifycountCycles` a lot:

enum { MAXIMUM_DIGITS = 9 };

int countCycles(const char *name, int N) {
  if(N &lt;= 0 || N &gt; MAXIMUM_DIGITS) {
    return -1;
  }

  char buffer[MAXIMUM_DIGITS];

  FILE *fp = fopen(name, "rb");
  if(fread(buffer, N, 1, fp) != N) {
    fclose(fp);
    return -1;
  }
  fclose(fp);

  int array[MAXIMUM_DIGITS];

  for (int i = 0; i &lt; N; i++) {
    array[i] = buffer[i] - '0';
  }
  return countCyclesHelper(array, N);
}


If MAXIMUM_DIGITS gets larger at some point, you probably need to switch to malloc again, but simple arrays with a static size work well enough for your use case.