Non-recursive combination algorithm to generate distinct character strings - c

Question

This problem has been irritating me for too long. I need a non-recursive algorithm in C to generate non-distinct character strings. For instance, if a given character string is 26 characters long, and the string is of length 2, then there are 26^2 non-distinct characters.
Please note that these are distinct combinations, aab is not the same as baa or aba. I've searched S.O., and most solutions produce non-distinct combinations. Also, I do not need permutations.
The algorithm can't rely on a libraries. I'm going to translate this C code into cuda where standard C libraries don't work (at least not efficiently).
Before I show you what I started, let me explain an aspect of the program. It is multithreaded on a GPU, so I initialize the beginning string with a few characters, aa in this case. To create a combination, I add one or more characters depending on the desired length.
Here's one method that I have attempted:
int main(void){
//Declarations
char final[12] = {0};
char b[3] = "aa";
char charSet[27] = "abcdefghijklmnopqrstuvwxyz";
int max = 4; //Set for demonstration purposes
int ul = 1;
int k,i;
//This program is multithreaded on a GPU. Each thread is initialized
//to a starting value for the string. In this case, it is aa
//Set final with a starting prefix
int pref = strlen(b);
memcpy(final, b, pref+1);
//Determine the number of non-distinct combinations
for(int j = 0; j < length; j++) ul *= strlen(charSet);
//Start concatenating characters to the current character string
for(k = 0; k < ul; k++)
{
final[pref+1] = charSet[k];
//Do some work with the string
}
...
It should be obvious that this program does nothing useful, accept if I'm only appending one character from charSet.
My professor suggested that I try using a mapping (this isn't homework; I asked him about possible ways to generate distinct combinations without recursion).
His suggestion is similar to what I started above. Using the number of combinations calculated, he suggested to decompose it according to mod 10. However, I realized it wouldn't work.
For example, say I need to append two characters. This gives me 676 combinations using the character set above. If I am on the 523rd combination, the decomposition he demonstrated would yield
523 % 10 = 3
52 % 10 = 2
5 % 10 = 5
It should be obvious that this doesn't work. For one, it yields three characters, and two, if my character set is larger than 10 characters, the mapping ignores those above index 9.
Still, I believe a mapping is key to the solution.
The other method I explored utilized for loops:
//Psuedocode
c = charset;
for(i = 0; i <length(charset); i++){
concat string
for(j = 0; i <length(charset); i++){
concat string
for...
However, this hardcodes the length of the string I want to compute. I could use an if statement with a goto to break it, but I would like to avoid this method.
Any constructive input is appreciated.

Answer 1

Given a string, to find the next possible string in the sequence:
Find the last character in the string which is not the last character in the alphabet.
Replace it with the next character in the alphabet.
Change every character to the right of that character with the first character in the alphabet.
Start with a string which is a repetition of the first character of the alphabet. When step 1 fails (because the string is all the last character of the alphabet) then you're done.
Example: the alphabet is "ajxz".
Start with aaaa.
First iteration: the rightmost character which is not z is the last one. Change it to the next character: aaaj
Second iteration. Ditto. aaax
Third iteration: Again. aaaz
Four iteration: Now the rightmost non-z character is the second last one. Advance it and change all characters to the right to a: aaja
Etc.

Answer 2

First, thanks for everyone's input; it was helpful. Being that I am translating this algorithm into cuda, I need it to be as efficient as possible on a GPU. The methods proposed certainly work, but not necessarily optimal for GPU architecture. I came up with a different solution using modular arithmetic that takes advantage of the base of my character set. Here's an example program, primarily in C with a mix of C++ for output, and it's fairly fast.
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <iostream>
using namespace std;
typedef unsigned long long ull;
int main(void){
//Declarations
int init = 2;
char final[12] = {'a', 'a'};
char charSet[27] = "abcdefghijklmnopqrstuvwxyz";
ull max = 2; //Modify as need be
int base = strlen(charSet);
int placeHolder; //Maps to character in charset (result of %)
ull quotient; //Quotient after division by base
ull nComb = 1;
char comb[max+1]; //Array to hold combinations
int c = 0;
ull i,j;
//Compute the number of distinct combinations ((size of charset)^length)
for(j = 0; j < max; j++) nComb *= strlen(charSet);
//Begin computing combinations
for(i = 0; i < nComb; i++){
quotient = i;
for(j = 0; j < max; j++){ //No need to check whether the quotient is zero
placeHolder = quotient % base;
final[init+j] = charSet[placeHolder]; //Copy the indicated character
quotient /= base; //Divide the number by its base to calculate the next character
}
string str(final);
c++;
//Print combinations
cout << final << "\n";
}
cout << "\n\n" << c << " combinations calculated";
getchar();
}