Code to generate Permutations for a given set of numbers efficiently C#

Not sure how efficient these are, but here are some options:

• http://www.codeproject.com/KB/recipes/Combinatorics.aspx
• http://www.codeproject.com/KB/recipes/premutations.aspx
• A C# implementation of Knuth's solution

A little bit too late... Just as reference...

According to my tests, my implementation of Heap's algorithm seems to give fastest performance I've seen (tested against 2 assumed very fast algorithms).

Advantages:

• Heap's algorithm (Single swap per permutation)
• No multiplication (like some implementations seen on the web)
• Inlined swap
• Generic
• No unsafe code
• In place (very low memory usage)
• No modulo (only first bit compare)

My implementation of Heap's algorithm:

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Runtime.CompilerServices;

namespace WpfPermutations
{
    /// <summary>
    /// EO: 2016-04-14
    /// Generator of all permutations of an array of anything.
    /// Base on Heap's Algorithm. See: https://en.wikipedia.org/wiki/Heap%27s_algorithm#cite_note-3
    /// </summary>
    public static class Permutations
    {
        /// <summary>
        /// Heap's algorithm to find all pmermutations. Non recursive, more efficient.
        /// </summary>
        /// <param name="items">Items to permute in each possible ways</param>
        /// <param name="funcExecuteAndTellIfShouldStop"></param>
        /// <returns>Return true if cancelled</returns> 
        public static bool ForAllPermutation<T>(T[] items, Func<T[], bool> funcExecuteAndTellIfShouldStop)
        {
            int countOfItem = items.Length;

            if (countOfItem <= 1)
            {
                return funcExecuteAndTellIfShouldStop(items);
            }

            var indexes = new int[countOfItem];
            for (int i = 0; i < countOfItem; i++)
            {
                indexes[i] = 0;
            }

            if (funcExecuteAndTellIfShouldStop(items))
            {
                return true;
            }

            for (int i = 1; i < countOfItem;)
            {
                if (indexes[i] < i)
                { // On the web there is an implementation with a multiplication which should be less efficient.
                    if ((i & 1) == 1) // if (i % 2 == 1)  ... more efficient ??? At least the same.
                    {
                        Swap(ref items[i], ref items[indexes[i]]);
                    }
                    else
                    {
                        Swap(ref items[i], ref items[0]);
                    }

                    if (funcExecuteAndTellIfShouldStop(items))
                    {
                        return true;
                    }

                    indexes[i]++;
                    i = 1;
                }
                else
                {
                    indexes[i++] = 0;
                }
            }

            return false;
        }

        /// <summary>
        /// This function is to show a linq way but is far less efficient
        /// From: StackOverflow user: Pengyang : http://stackoverflow.com/questions/756055/listing-all-permutations-of-a-string-integer
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="list"></param>
        /// <param name="length"></param>
        /// <returns></returns>
        static IEnumerable<IEnumerable<T>> GetPermutations<T>(IEnumerable<T> list, int length)
        {
            if (length == 1) return list.Select(t => new T[] { t });

            return GetPermutations(list, length - 1)
                .SelectMany(t => list.Where(e => !t.Contains(e)),
                    (t1, t2) => t1.Concat(new T[] { t2 }));
        }

        /// <summary>
        /// Swap 2 elements of same type
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="a"></param>
        /// <param name="b"></param>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static void Swap<T>(ref T a, ref T b)
        {
            T temp = a;
            a = b;
            b = temp;
        }

        /// <summary>
        /// Func to show how to call. It does a little test for an array of 4 items.
        /// </summary>
        public static void Test()
        {
            ForAllPermutation("123".ToCharArray(), (vals) =>
            {
                Console.WriteLine(String.Join("", vals));
                return false;
            });

            int[] values = new int[] { 0, 1, 2, 4 };

            Console.WriteLine("Ouellet heap's algorithm implementation");
            ForAllPermutation(values, (vals) =>
            {
                Console.WriteLine(String.Join("", vals));
                return false;
            });

            Console.WriteLine("Linq algorithm");
            foreach (var v in GetPermutations(values, values.Length))
            {
                Console.WriteLine(String.Join("", v));
            }

            // Performance Heap's against Linq version : huge differences
            int count = 0;

            values = new int[10];
            for (int n = 0; n < values.Length; n++)
            {
                values[n] = n;
            }

            Stopwatch stopWatch = new Stopwatch();

            ForAllPermutation(values, (vals) =>
            {
                foreach (var v in vals)
                {
                    count++;
                }
                return false;
            });

            stopWatch.Stop();
            Console.WriteLine($"Ouellet heap's algorithm implementation {count} items in {stopWatch.ElapsedMilliseconds} millisecs");

            count = 0;
            stopWatch.Reset();
            stopWatch.Start();

            foreach (var vals in GetPermutations(values, values.Length))
            {
                foreach (var v in vals)
                {
                    count++;
                }
            }

            stopWatch.Stop();
            Console.WriteLine($"Linq {count} items in {stopWatch.ElapsedMilliseconds} millisecs");
        }
    }
}

Usage examples:

ForAllPermutation("123".ToCharArray(), (vals) =>
    {
        Console.WriteLine(String.Join("", vals));
        return false;
    });

int[] values = new int[] { 0, 1, 2, 4 };
ForAllPermutation(values, (vals) =>
        {
            Console.WriteLine(String.Join("", vals));
            return false;
        });

    public static IEnumerable<T[]> Permute<T>(T[] array)
    {
        for(int i=0; i<array.Length; i++)
        {
            if (array.Length <= 1)
            {
                yield return array;
            }
            else
            {
                T[] except = new T[array.Length - 1];
                Array.Copy(array, except, i);
                Array.Copy(array, i + 1, except, i, array.Length - i - 1);
                foreach (T[] sub in Permute(except))
                {
                    T[] answer = new T[sub.Length + 1];
                    Array.Copy(sub, 0, answer, 1, sub.Length);
                    answer[0] = array[i];
                    yield return answer;
                }
            }
        }
    }