/* Use like 
 *   g++ -o sigmaStar sigmaStar.C
 *   sigmaStar > o

 *    Looking for strings with an odd number of symbols.

 *   egrep '^(ab|aa|ba|bb)*(a|b)$' o |more
 *      or
 *   egrep '^(ab|aa|ba|bb)*[ab]$' o |more

 *      or
 *   sigmaStar | egrep '^(ab|aa|ba|bb)*(a|b)$' o |more
 */

#include <iostream>
#include <string>
#include <math.h>
using namespace std;

int main()
{
   string alphabet[] = {"a", "b"};
   int numalpha = 2;

   const int MAXLENGTH = 8;
   string strings[static_cast<int>(pow(numalpha,MAXLENGTH+1))];
   int num=0;

   // length 0 string
   strings[num++] = "";		// null string
   cout << strings[num-1] << endl;

   // length n strings
   for (int is = 0; is < num; is++) {
      for (int ia = 0; ia < numalpha; ia++) {
         strings[num++] = strings[is] + alphabet[ia];
         if (strings[num-1].length() > MAXLENGTH) 
            return 0;
         cout << strings[num-1] << endl;
      }
   }
}