Number of different binary string with k flips

Question

I am trying a problem where we are given binary string of length N(<10^5), and we are allowed exactly X(<10^5) flips on it, we are asked how many different string is p

Answer 1

This is in c#. See if it helps.

static class Program
{
    static void Main(string[] args)
    {
        string bnryStr = "111111";
        int x = 4;

        //here in this string merely the poistions of the binary string numbers are placed
        //if the binary string is "1111111", this fakeStr will hold "0123456"
        string fakeStr = String.Empty;
        for (int i = 0; i < bnryStr.Length; i++)
        {
            fakeStr += i.ToString();
        }
        char[] arr = fakeStr.ToCharArray();

        // gets all combinations of the input string altered in x ways
        IEnumerable> result = Combinations(arr, x);

        // this holds all the combinations of positions of the binary string at which flips will be made
        List places = new List();
        foreach (IEnumerable elements in result)
        {
            string str = string.Empty;
            foreach (var item in elements)
            {
                str += item;
            }
            places.Add(str);
        }

        List results = GetFlippedCombos(bnryStr, places);
        Console.WriteLine("The number of all possible combinations are: " + results.Count);
        foreach (var item in results)
        {
            Console.WriteLine(item);
        }
        Console.Read();
    }

    /// 

    /// Gets a list of flipped strings
    /// 
    /// binary string
    /// List of strings containing positions of binary string at which flips will be made
    /// list of all possible combinations of flipped strings
    private static List GetFlippedCombos(string bnryStr, List placeList)
    {
        List rtrnList = new List();
        foreach (var item in placeList)
        {
            rtrnList.Add(Flip(bnryStr, item));
        }
        return rtrnList;
    }

    /// 

    /// Flips all the positions (specified in 'places') of a binary string  from 1 to 0 or vice versa
    /// 
    /// binary string
    /// string holding the position values at which flips are made
    /// a flipped string
    private static string Flip(string bnryStr, string places)
    {
        StringBuilder str = new StringBuilder(bnryStr);
        foreach (char place in places)
        {
            int i = int.Parse(place.ToString());
            char ch = str[i];
            str.Replace(ch, '0' == ch ? '1' : '0', i, 1);
        }
        return str.ToString();
    }

    /// 

    /// Gets all combinations of k items from a  collection with n elements 
    /// 
    /// collection having n elements
    /// no of combinations
    /// all possible combinations of k items chosen from n elements
    private static IEnumerable> Combinations(this IEnumerable elements, int k)
    {
        if (k == 0)
        {
            return new[] { new T[0] };
        }
        else
        {
            IEnumerable elements1 = elements as IList ?? elements.ToList();
            IEnumerable> enumerable = elements1.SelectMany((e, i) =>
            {
                IEnumerable enumerable1 = elements as IList ?? elements1.ToList();
                return enumerable1.Skip(i + 1).Combinations(k - 1).Select(c => (new[] { e }).Concat(c));
            });
            return enumerable;
        }
    }
}






Result:
Binary String: 111111
No. of Flips: 4
The number of all possible combinations are: 15
000011
000101
000110
001001
001010
001100
010001
010010
010100
011000
100001
100010
100100
101000
110000