Question

output all possible combinations of N boolean variables

Asked by: substand

For example, if I have:

int main()
{

     ouputCombos(3);
}

the program should output:

TTT
TTF
TFT
TFF
FTT
FTF
FFT
FFF

I've been able to write a recursive function that basically traverses the "tree", but I think I've just been looking at it too long and can't think of how to get it to remember and actually output the whole line.

Here's what I have so far:

#include <iostream.h>
#include <stdlib.h>

void tf(int n)
{
     if (n<1)  // in case someone puts in something less than one to begin with
     {
        ;
     }
     if (n==1)
     {
        cout << "T" << endl;
        cout << "F" << endl;

     }
     else
     {
        cout << "T" ;
        tf(n-1);
        cout << "F" ;
        tf(n-1);

     }
}

int main()
{     char ch;
      tf(3);
      cin >> ch;

      return 0;
}

I realize the cout and crap is c++, but its just quicker that typing printf and such.

Yes, this is for school, but no its not an assignment.  I'm doing it to try and get back in the swing of things (I was out of school for 1 and a half years) so I'd appreciate any insight.  Solution can be in any language, including pseudo code.

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Asked On
2006-01-22 at 13:41:53ID21705905
Tags

combinations

,

possible

,

c

,

program

Topic

C Programming Language

Participating Experts
5
Points
500
Comments
12

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Answers

 

by: amit_gPosted on 2006-01-22 at 14:00:20ID: 15762197

#include <stdio.h>

void ouputCombos(int HowMany, char* Combo)
{
      if (HowMany == 0)
      {
            printf("%s\n", Combo);
            return;
      }

      HowMany--;

      Combo[HowMany] = 'T';
      ouputCombos(HowMany, Combo);

      Combo[HowMany] = 'F';
      ouputCombos(HowMany, Combo);
}

int main()
{
      const MAX_CHARS = 10;

      int HowMany = 3;
      char Combo[MAX_CHARS + 1];

      Combo[HowMany] = '\0';
    ouputCombos(HowMany, Combo);

      return 0;
}

 

by: Infinity08Posted on 2006-01-22 at 14:02:33ID: 15762207

I'll not give you complete source code. Even though it's not homework, i'm convinced you'll learn more by finding out yourself ...

Here's some pointers to get you started :

How about passing a char array (or pointer) that contains the string uptill now ? ie. the following call chain :

main()
  tf("", 3)
    tf("T", 2)
      tf("TT", 1)
        printf("TTT")
        printf("TTF")
      tf("TF", 1)
        printf("TFT")
        printf("TFF")
    tf("F", 2)
      tf("FT", 1)
        printf("FTT")
        printf("FTF")
      tf("FF", 1)
        printf("FFT")
        printf("FFF")

I'd be happy to take a look at any code you make and give further pointers !

 

by: ozoPosted on 2006-01-22 at 14:11:49ID: 15762240

Does the solution need to be recursive?

 

by: pallospPosted on 2006-01-22 at 14:27:31ID: 15762315

The following code is fast and works up to 32 bits.
If you use unsigned long long instead of unsigned, it can be increased to 64 bits.

void outputCombos(unsigned n) {
    char s[65];
    unsigned i, j, max;
    max = (1<<n)-1;
    s[n] = 0;
    for (i=0; i<=max; i++) {
        for (j=0; j<n; j++)
            s[j] = (i & (1<<j)) ? 'F' : 'T';
        printf("%s\n", s);
    }
}

 

by: substandPosted on 2006-01-22 at 14:31:45ID: 15762344

amit, thanks but what happens when n=100?  I need to increase max chars, right?

ozo: no, not really... it just occurred to me when I thought out the process of how I would write it down, that my own process was sort of recursive.  In fact, if I could think of several ways to do it, I'd be even happier, so if you have non-recursive solutions, please show me!

Infinity: I did think of that (and in fact took out my poor attempt at it before posting the question).  

One of my goals was just to have this as one algorithm whose only input was "n".  So any char arrays and the like need to be self contained within the tf / outputCombos (whatever you want to call it) function.

My thought was to use a "static" array dynamically allocated based on the size of n.  But it's been quite a while since I've used C or done anything of this "academic" nature, that I couldn't even remember how to do that and when I looked it up, I didn't think it would work anyway.

 

by: pallospPosted on 2006-01-22 at 14:57:11ID: 15762472

If you choose only n=32, the program outputs 132 GB data.
For n=100 the program never ends.

 

by: amit_gPosted on 2006-01-22 at 22:05:30ID: 15763892

Change the main to ...

int main()
{
      int HowMany = 3;
      char* Combo = new char[HowMany + 1];

      Combo[HowMany] = '\0';
      ouputCombos(HowMany, Combo);

      delete [] Combo;

      return 0;
}

and then there is no limit from program's side. However, the physical hardware and the time required would pose a practical limit.

 

by: Infinity08Posted on 2006-01-23 at 00:23:13ID: 15764266

>> One of my goals was just to have this as one algorithm whose only input was "n".  So any char arrays and the like need to be self contained within the tf / outputCombos (whatever you want to call it) function.

As you say, you could use either a static array within the recursive function or a global array.

Something along these lines :

void tf(int n) {
  static char *str = 0;
  static int pos = 0;
  static char *vals = "TF";
  int i;

  if (str == 0) str = (char*) calloc(n + 1, sizeof(char));

  for (i = 0; i < strlen(vals); i++) {
    str[pos++] = vals[i];
    if (n == 1) {
      fprintf(stdout, "%s\n", str);
    }
    else {
      tf(n - 1);
    }
    pos--;
  }
  return;
}

well, i did show complete code in the end heh ... but i'm sure you'll get something out of it :)

 

by: Infinity08Posted on 2006-01-23 at 00:25:55ID: 15764276

oh, and of course, don't forget to free() the allocated array !!!, ie. just before returning, check for pos == 0, and if so, free(). ie., place this line, just before the return statement :

  if (pos == 0) free(str);

 

by: PaulCaswellPosted on 2006-01-23 at 01:25:25ID: 15764497

substand,

There are three main ways of printing out from a recursive function.

1. Keep a buffer thats shared between invocations.

Like you have now. Something like :

void tf(int level, int limit, char * buffer)
{
 if ( level < limit )
 {
   buffer[level] = 'T';
   tf(level+1,limit,buffer);
   buffer[level] = 'F';
   tf(level+1,limit,buffer);
 }
 else if (level == limit )
 {
   buffer[level+1] = '\0';
   printf ( "%s\n", buffer );
 }
}

2. Print 'On the fly'

Too early in the morning for one of these.

3. Like '1' but make it a linked-list on the stack.

This is better for slightly more complex structure.

Each has its merits. Have you any further requirements in you code that might help us suggest the best option?

Paul

 

by: substandPosted on 2006-01-23 at 08:58:33ID: 15768052

>> If you choose only n=32, the program outputs 132 GB data.
>> For n=100 the program never ends.

I am aware that there will be 2^n combinations so the increase is quick, however the point was just to find a single algorithm that would take care of the problem for any n, regardless of space requirements (but hopefully find the best algorithm regarding time).

PaulCaswell- I'm interested in seeing the "print 'on the fly'" method you talked about if you have time in the afternoon =).

pallosp- can you explain your code a bit?  I've forgotten in particular what the left/right shift operators are doing and why you are using them.

I'm off to class and will be back tommorrow.  I thank you all for your help!

 

by: ozoPosted on 2006-01-23 at 23:14:08ID: 15773584

#include <string.h>
#include <stdio.h>
int main(){
#define HowMany 3
  char str[HowMany+1];
  char *p;
  memset(str,'T',HowMany);
  str[HowMany]='\0';
  while( puts(str),p=strrchr(str,'T') ){
    *p='F';
    memset(p+1,'T',str+HowMany-1-p);
  }
}

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