Find all combinations of a given set of numbers

Question

say I have a set of numbers \'0\', \'1\', \'2\', ..., \'9\'. I want to find all numbers that contain exactly one of each of the numbers in my set.

The problem is: Be

Answer 1

Here is my C# 3.0 implementation of permutations you can find useful

public static class PermutationExpressions
    {
        public static IEnumerable<IEnumerable<T>> Permutations<T>(this IEnumerable<T> list)
        {
            return list.Permutations((uint)list.Count());
        }

        public static IEnumerable<IEnumerable<T>> Permutations<T>(this IList<T> list)
        {
            return list.Permutations((uint)list.Count);
        }

        private static IEnumerable<IEnumerable<T>> Permutations<T>(this IEnumerable<T> list, uint n)
        {
            if (n < 2) yield return list;
            else
            {
                var ie = list.GetEnumerator();
                for (var i = 0; i < n; i++)
                {
                    ie.MoveNext();
                    var item = ie.Current;

                    var i1 = i;
                    var sub_list = list.Where((excluded, j) => j != i1).ToList();

                    var sub_permutations = sub_list.Permutations(n - 1);

                    foreach (var sub_permutation in sub_permutations)
                    {
                        yield return
                            Enumerable.Repeat(item, 1)
                                .Concat(sub_permutation);
                    }
                }
            }
        }
        }

[TestFixture]
    public class TestPermutations
    {
        [Test]
        public void Permutation_Returns_Permutations()
        {
            var permutations = PermutationExpressions.Permutations(new[] { "a", "b", "c" }.AsEnumerable());
            foreach (var permutation in permutations)
            {
                Console.WriteLine(string.Join("", permutation.ToArray()));
            }
            Assert.AreEqual("abc_acb_bac_bca_cab_cba", permutations.Select(perm => perm.joinToString("")).joinToString("_"));
        }
    }

Answer 2

Nothing to do with dynamic programming; unless you want to wear underpants outside your trousers and paint a symbol on your chest.

Simple way to do it is maintain an array of 0-9 of integers, then run through the numbers one by one and increment array[num]. The result, once you've processed all digits, is to see if any element of the array is non-zero or one. (That indicates a repeated digit.) Of course, it's trivial to take a number and then iterate through digit by digit using modulus and divisor.

Answer 3

You're looking to find all permutations of a given set of values.

One article on "doing" permutations in Java is here: http://www.bearcave.com/random_hacks/permute.html

You want to skip the first couple of sections until you get to the heading Permutation algorithms (of course).