Listing all permutations of a string/integer

Question

A common task in programming interviews (not from my experience of interviews though) is to take a string or an integer and list every possible permutation.

Is there

Answer 1

Slightly modified version in C# that yields needed permutations in an array of ANY type.

    // USAGE: create an array of any type, and call Permutations()
    var vals = new[] {"a", "bb", "ccc"};
    foreach (var v in Permutations(vals))
        Console.WriteLine(string.Join(",", v)); // Print values separated by comma


public static IEnumerable<T[]> Permutations<T>(T[] values, int fromInd = 0)
{
    if (fromInd + 1 == values.Length)
        yield return values;
    else
    {
        foreach (var v in Permutations(values, fromInd + 1))
            yield return v;

        for (var i = fromInd + 1; i < values.Length; i++)
        {
            SwapValues(values, fromInd, i);
            foreach (var v in Permutations(values, fromInd + 1))
                yield return v;
            SwapValues(values, fromInd, i);
        }
    }
}

private static void SwapValues<T>(T[] values, int pos1, int pos2)
{
    if (pos1 != pos2)
    {
        T tmp = values[pos1];
        values[pos1] = values[pos2];
        values[pos2] = tmp;
    }
}

Answer 2

class Permutation
{
    public static List<string> Permutate(string seed, List<string> lstsList)
    {
        loopCounter = 0;
        // string s="\w{0,2}";
        var lstStrs = PermuateRecursive(seed);

        Trace.WriteLine("Loop counter :" + loopCounter);
        return lstStrs;
    }

    // Recursive function to find permutation
    private static List<string> PermuateRecursive(string seed)
    {
        List<string> lstStrs = new List<string>();

        if (seed.Length > 2)
        {
            for (int i = 0; i < seed.Length; i++)
            {
                str = Swap(seed, 0, i);

                PermuateRecursive(str.Substring(1, str.Length - 1)).ForEach(
                    s =>
                    {
                        lstStrs.Add(str[0] + s);
                        loopCounter++;
                    });
                ;
            }
        }
        else
        {
            lstStrs.Add(seed);
            lstStrs.Add(Swap(seed, 0, 1));
        }
        return lstStrs;
    }
    //Loop counter variable to count total number of loop execution in various functions
    private static int loopCounter = 0;

    //Non recursive  version of permuation function
    public static List<string> Permutate(string seed)
    {
        loopCounter = 0;
        List<string> strList = new List<string>();
        strList.Add(seed);
        for (int i = 0; i < seed.Length; i++)
        {
            int count = strList.Count;
            for (int j = i + 1; j < seed.Length; j++)
            {
                for (int k = 0; k < count; k++)
                {
                    strList.Add(Swap(strList[k], i, j));
                    loopCounter++;
                }
            }
        }
        Trace.WriteLine("Loop counter :" + loopCounter);
        return strList;
    }

    private static string Swap(string seed, int p, int p2)
    {
        Char[] chars = seed.ToCharArray();
        char temp = chars[p2];
        chars[p2] = chars[p];
        chars[p] = temp;
        return new string(chars);
    }
}

Answer 3

Here's a good article covering three algorithms for finding all permutations, including one to find the next permutation.

http://www.cut-the-knot.org/do_you_know/AllPerm.shtml

C++ and Python have built-in next_permutation and itertools.permutations functions respectively.

Answer 4

Here is the simplest solution I can think of:

let rec distribute e = function
  | [] -> [[e]]
  | x::xs' as xs -> (e::xs)::[for xs in distribute e xs' -> x::xs]

let permute xs = Seq.fold (fun ps x -> List.collect (distribute x) ps) [[]] xs

The distribute function takes a new element e and an n-element list and returns a list of n+1 lists each of which has e inserted at a different place. For example, inserting 10 at each of the four possible places in the list [1;2;3]:

> distribute 10 [1..3];;
val it : int list list =
  [[10; 1; 2; 3]; [1; 10; 2; 3]; [1; 2; 10; 3]; [1; 2; 3; 10]]

The permute function folds over each element in turn distributing over the permutations accumulated so far, culminating in all permutations. For example, the 6 permutations of the list [1;2;3]:

> permute [1;2;3];;
val it : int list list =
  [[3; 2; 1]; [2; 3; 1]; [2; 1; 3]; [3; 1; 2]; [1; 3; 2]; [1; 2; 3]]

Changing the fold to a scan in order to keep the intermediate accumulators sheds some light on how the permutations are generated an element at a time:

> Seq.scan (fun ps x -> List.collect (distribute x) ps) [[]] [1..3];;
val it : seq<int list list> =
  seq
    [[[]]; [[1]]; [[2; 1]; [1; 2]];
     [[3; 2; 1]; [2; 3; 1]; [2; 1; 3]; [3; 1; 2]; [1; 3; 2]; [1; 2; 3]]]

Answer 5

Lists permutations of a string. Avoids duplication when characters are repeated:

using System;
using System.Collections;

class Permutation{
  static IEnumerable Permutations(string word){
    if (word == null || word.Length <= 1) {
      yield return word;
      yield break;
    }

    char firstChar = word[0];
    foreach( string subPermute in Permutations (word.Substring (1)) ) {
      int indexOfFirstChar = subPermute.IndexOf (firstChar);
      if (indexOfFirstChar == -1) indexOfFirstChar = subPermute.Length;

      for( int index = 0; index <= indexOfFirstChar; index++ )
        yield return subPermute.Insert (index, new string (firstChar, 1));
    }
  }

  static void Main(){
    foreach( var permutation in Permutations ("aab") )
      Console.WriteLine (permutation);
  }
}

Answer 6

Here is the function which will print all permutations recursively.

public void Permutations(string input, StringBuilder sb)
    {
        if (sb.Length == input.Length)
        {
            Console.WriteLine(sb.ToString());
            return;
        }

        char[] inChar = input.ToCharArray();

        for (int i = 0; i < input.Length; i++)
        {
            if (!sb.ToString().Contains(inChar[i]))
            {
                sb.Append(inChar[i]);
                Permutations(input, sb);    
                RemoveChar(sb, inChar[i]);
            }
        }
    }

private bool RemoveChar(StringBuilder input, char toRemove)
    {
        int index = input.ToString().IndexOf(toRemove);
        if (index >= 0)
        {
            input.Remove(index, 1);
            return true;
        }
        return false;
    }