Square Subsequence

Question

A string is called a square string if it can be obtained by concatenating two copies of the same string. For example, \"abab\", \"aa\" are square strings, while \"aaa\", \"a

Answer 1

Here's a solution using LINQ:

IEnumerable input = new[] {"a","a","a"};

// The next line assumes the existence of a "PowerSet" method for IEnumerable.
// I'll provide my implementation of the method later.
IEnumerable> powerSet = input.PowerSet();

// Once you have the power set of all subsequences, select only those that are "square".
IEnumerable> squares = powerSet.Where(x => x.Take(x.Count()/2).SequenceEqual(x.Skip(x.Count()/2)));

Console.WriteLine(squares);

And here is my PowerSet extension method, along with a "Choose" extension method that is required by PowerSet:

public static class CombinatorialExtensionMethods
{
    public static IEnumerable> Choose(this IEnumerable seq, int k)
    {
        // Use "Select With Index" to create IEnumerable
        var indexedSeq = seq.Select((Value, Index) => new {Value, Index});

        // Create k copies of the sequence to join
        var sequences = Enumerable.Repeat(indexedSeq,k);

        // Create IEnumerable containing one empty sequence
        /// To create an empty sequence of the same anonymous type as indexedSeq, allow the compiler to infer the type from a query expression
        var emptySequence =
            from item in indexedSeq
            where false
            select item;
        var emptyProduct = Enumerable.Repeat(emptySequence,1);

        // Select "Choose" permutations, using Index to order the items
        var indexChoose = sequences.Aggregate( 
            emptyProduct,
            (accumulator, sequence) =>  
            from accseq in accumulator  
            from item in sequence
            where accseq.All(accitem => accitem.Index < item.Index)
            select accseq.Concat(new[] { item }));

        // Select just the Value from each permutation
        IEnumerable> result = 
            from item in indexChoose
            select item.Select((x) => x.Value);

        return result;
    }

    public static IEnumerable> PowerSet(this IEnumerable seq)
    {
        IEnumerable> result = new[] { Enumerable.Empty() };
        for (int i=1; i<=seq.Count(); i++)
        {
            result = result.Concat(seq.Choose(i));
        }
        return result;
    }
}