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string combinatorics, generate  nCr strings from n strings

Posted on 2011-09-22
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Last Modified: 2012-05-12
I have a set of n strings. I would like to extract all combinations of strings from these n strings . (all nCr combinations). How can  I do this programmatically.
For example :
Input : a,b,c,d,e
Output :
a,b,c,d
a,b,c,e
a,b,d,e
a,c,d,e
b,c,d,e
a,b,c
a,c,d
a,d,e
......and so on till

a,b
b,a
and so on till
a
b
c
d
e
Please help thanks
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Comment
Question by:TrialUser
  • 5
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8 Comments
 
LVL 37

Expert Comment

by:TommySzalapski
ID: 36580129
The best way is to make a function that finds all string combinations of length N and use that recursively.
Then you just call it for each length.

  
ArrayList FindAllStrings(string input)
{
  ArrayList strings;

  for(int i = 0; i<=input.Length(); i++)
  AddStrings(strings, input, i, "");
}

AddStrings(ArrayList strings, string input, int N, string leading = "")
{
  if(N == 0)
    strings.Add(leading);
  else
  {
    for(int i = 0; i + N < input.Length(); i++)
      addStrings(strings, input.SubString(i+1), N-1, leading + input[i]);
  }

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LVL 37

Accepted Solution

by:
TommySzalapski earned 2000 total points
ID: 36580206
Tested and fixed
        private ArrayList FindAllStrings(string input)
        {
            ArrayList strings = new ArrayList();

            for (int i = 0; i <= input.Length; i++)
                AddStrings(strings, input, i, "");

            return strings;
        }

        private void AddStrings(ArrayList strings, string input, int N, string leading = "")
        {
            if (N == 0)
                strings.Add(leading);
            else
            {
                for (int i = 0; i + N <= input.Length; i++)
                    AddStrings(strings, input.Substring(i + 1), N - 1, leading + input[i]);
            }
        }

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LVL 37

Expert Comment

by:TommySzalapski
ID: 36580224
If you want the commas, change line 18 to
AddStrings(strings, input.Substring(i + 1), N - 1, leading + (leading.Length > 0 ? ",":"") + input[ i]);
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LVL 86

Expert Comment

by:Mike Tomlinson
ID: 36581969
Use the libaray here written by Adrian Akison:
http://www.codeproject.com/KB/recipes/Combinatorics.aspx

Simple Demo: Idle-Mind-502573.flv

Click on Project --> Add Reference --> Browse --> Facet.Combinatorics.dll

Then you want to use the Variations class like this:
using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;

namespace WindowsFormsApplication1
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        private void button1_Click(object sender, EventArgs e)
        {
            listBox1.DataSource = Variations(textBox1.Text);
        }

        private List<string> Variations(string input)
        {
            List<string> values = new List<string>();
            for (int i=0; i < input.Length; i++)
            {
                values.Add(input.Substring(i,1));
            }

            List<string> results = new List<string>();
            for (int i = input.Length; i >= 1; i--)
            {
                Facet.Combinatorics.Variations<string> vars = new Facet.Combinatorics.Variations<string>(values.AsReadOnly(), i);
                foreach (IList<string> set in vars)
                {
                    results.Add(String.Join(",", set));
                }
            }
            return results;
        }
    }
}

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Here's the output:
a,b,c,d
a,b,d,c
a,c,b,d
a,d,b,c
a,c,d,b
a,d,c,b
b,a,c,d
b,a,d,c
c,a,b,d
d,a,b,c
c,a,d,b
d,a,c,b
b,c,a,d
b,d,a,c
c,b,a,d
d,b,a,c
c,d,a,b
d,c,a,b
b,c,d,a
b,d,c,a
c,b,d,a
d,b,c,a
c,d,b,a
d,c,b,a
a,b,c
a,b,d
a,c,b
a,d,b
a,c,d
a,d,c
b,a,c
b,a,d
c,a,b
d,a,b
c,a,d
d,a,c
b,c,a
b,d,a
c,b,a
d,b,a
c,d,a
d,c,a
b,c,d
b,d,c
c,b,d
d,b,c
c,d,b
d,c,b
a,b
a,c
a,d
b,a
c,a
d,a
b,c
b,d
c,b
d,b
c,d
d,c
a
b
c
d

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LVL 37

Expert Comment

by:TommySzalapski
ID: 36582051
Idle_Mind, that does all the possible permutations of all the possible combinations. It's also using another library and even then, the code looks just about as long as mine.

TrialUser, I assume your inclusion of both a,b and b,a was accidental and you just wanted the combinations. To do all permutations in mine you would just change
input.Substring(i + 1)
to
input.Substring(0,i) + input.Substring(i + 1)
0
 
LVL 37

Expert Comment

by:TommySzalapski
ID: 36582067
You do need to make sure to have
using System.Collections
at the top to use the ArrayList or you could modify the code to use whatever collection type you prefer.
0
 
LVL 86

Expert Comment

by:Mike Tomlinson
ID: 36582072
The library can also do Permuations and Combinations as well...it's pretty flexible.
0
 
LVL 13

Expert Comment

by:Ryan
ID: 36904484
Just last week I was solving a Permutation problem on ProjectEuler.net and came across this website. http://www.bearcave.com/random_hacks/permute.html

In particular, I found this graphic interesting, http://www.bearcave.com/random_hacks/permute_diagram.jpg

Merely implementing that, with an otter loop that iterates through removing letters solves it.
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