Below there are some basic processing functions of strings in C. The implementations are approached with the pointers of C, thus creating faster and more compact code.

You should know that the implementation of the algorithms does not take into account issues of data input validation or proper management of dynamic memory (e.g. avoiding memory leaks) because it is only necessary to highlight the logic of the algorithms.

Calculating string length:

size_t
strlen (const char * s) {
  const char * z = s;
  while (*z++) ;
  return z-s-1;
}

Copy a string: 

char *
strcpy (char * s1, const char * s2) {
  char * z = s1;
  while (*s1++ = *s2++) ;
  return z;
}

Compare strings: 

int
strcmp (const char * s1, const char * s2) {
  while (*s1++ == *s2++)
  if (*(s1-1) == 0)
    return 0;

  return *(s1-1) - *(s2-1);
}

Compare strings (prefix): 

int
strncmp (const char * s1, const char * s2, size_t n) {
  int i = 0;

  while (i < n && *s1 != 0) {
    if (*s1 != *s2)
      return *s1 - *s2;

    i++, s1++, s2++;
  }

  return 0;
}

Append string:

char *
strcat (char * s1, const char * s2) {
  return strcpy (s1 + strlen (s1), s2);
}