[c] How does one represent the empty char?

To represent the fact that the value is not present you have two choices:

1) If the whole char range is meaningful and you cannot reserve any value, then use char* instead of char:

char** c = new char*[N];
c[0] = NULL; // no character
*c[1] = ' '; // ordinary character
*c[2] = 'a'; // ordinary character
*c[3] = '\0' // zero-code character

Then you'll have c[i] == NULL for when character is not present and otherwise *c[i] for ordinary characters.

2) If you don't need some values representable in char then reserve one for indicating that value is not present, for example the '\0' character.

char* c = new char[N];
c[0] = '\0'; // no character
c[1] = ' '; // ordinary character
c[2] = 'a'; // ordinary character

Then you'll have c[i] == '\0' for when character is not present and ordinary characters otherwise.