Number of Binary Strings of length N with K adjacent Set Bits

// C# program to find the number of Bit Strings
// of length N with K adjacent set bits
using System;

class GFG
{
// Function to find the number of Bit Strings
// of length N with K adjacent set bits
static int waysToKAdjacentSetBits(int n, int k, int currentIndex,
                                  int adjacentSetBits, int lastBit)
{

    /* Base Case when we form bit 
    string of length n */
    if (currentIndex == n) 
    {

        // if f(bit string) = k, count this way
        if (adjacentSetBits == k)
            return 1;
        return 0;
    }

    int noOfWays = 0;

    /* Check if the last bit was set, if it was 
    set then call for next index by incrementing 
    the adjacent bit count else just call the next 
    index with same value of adjacent bit count and 
    either set the bit at current index or let it 
    remain unset */
    if (lastBit == 1) 
    {
        // set the bit at currentIndex
        noOfWays += waysToKAdjacentSetBits(n, k, currentIndex + 1, 
                                            adjacentSetBits + 1, 1);
        // unset the bit at currentIndex
        noOfWays += waysToKAdjacentSetBits(n, k,currentIndex + 1,
                                                adjacentSetBits, 0);
    }
    else if (lastBit != 1) 
    {
        noOfWays += waysToKAdjacentSetBits(n, k, currentIndex + 1,
                                                adjacentSetBits, 1);
        noOfWays += waysToKAdjacentSetBits(n, k, currentIndex + 1, 
                                                adjacentSetBits, 0);
    }

    return noOfWays;
}

// Driver Code
public static void Main()
{
    int n = 5, k = 2;

    /* total ways = (ways by placing 1st bit as 1 + 
                    ways by placing 1st bit as 0) */
    int totalWays = waysToKAdjacentSetBits(n, k, 1, 0, 1) +
                    waysToKAdjacentSetBits(n, k, 1, 0, 0);

    Console.WriteLine("Number of ways = " + totalWays);
}
}

// This code is contributed 
// by Akanksha Rai

using System;
                
// C# program to find the number
// of Bit Strings of length N
// with K adjacent set bits
class GFG
{

static readonly int MAX=1000;

// Function to find the number
// of Bit Strings of length N
// with K adjacent set bits
static int waysToKAdjacentSetBits(int [,,]dp, 
                            int n, int k, 
                            int currentIndex, 
                            int adjacentSetBits,
                            int lastBit)
{
    /* Base Case when we form bit
    string of length n */
    if (currentIndex == n) 
    {

        // if f(bit string) = k, count this way
        if (adjacentSetBits == k)
            return 1;
        return 0;
    }

    if (dp[currentIndex, adjacentSetBits, 
                            lastBit] != -1) 
    {

        return dp[currentIndex,
        adjacentSetBits, lastBit];
    }

    int noOfWays = 0;

    /* Check if the last bit was set,
    if it was set then call for 
    next index by incrementing the
    adjacent bit count else just call
    the next index with same value of
    adjacent bit count and either set the
    bit at current index or let it remain
    unset */

    if (lastBit == 1) 
    {
        
        // set the bit at currentIndex
        noOfWays += waysToKAdjacentSetBits(dp, n,
                                k, currentIndex + 1, 
                                adjacentSetBits + 1, 1);

        // unset the bit at currentIndex
        noOfWays += waysToKAdjacentSetBits(dp, n, 
                                k, currentIndex + 1,
                                adjacentSetBits, 0);
    }

    else if (lastBit==0) 
    {
        noOfWays += waysToKAdjacentSetBits(dp,
                                n, k, currentIndex + 1, 
                                adjacentSetBits, 1);

        noOfWays += waysToKAdjacentSetBits(dp, 
                                n, k, currentIndex + 1, 
                                adjacentSetBits, 0);
    }

    dp[currentIndex,adjacentSetBits,lastBit] = noOfWays;

    return noOfWays;
}

// Driver Code
public static void Main(String []args)
{
    int n = 5, k = 2;

    /* dp[i,j,k] represents bit strings
    of length i with f(bit string) = j 
    and last bit as k */
    int [,,]dp = new int[MAX, MAX, 2];
    
    // initialize the dp
    for(int i = 0; i < MAX; i++)
        for(int j = 0; j < MAX; j++)
            for(int k1 = 0; k1 < 2; k1++)
                dp[i, j, k1]=-1;
        

    /* total ways = (ways by placing 1st bit as 1 + 
                    ways by placing 1st bit as 0) */
    int totalWays = waysToKAdjacentSetBits(dp, n, k, 1, 0, 1)
                    + waysToKAdjacentSetBits(dp, n, k, 1, 0, 0);

    Console.Write( "Number of ways = " + totalWays + "\n");
}
}

// This code is contributed by PrinciRaj1992

using System;

class MainClass {
    static int WaysToKAdjacentSetBits(int n, int k) {
        // dp[i][j][k] represents bit strings of length i
        // with f(bit string) = j and last bit as k
        int[,,] dp = new int[1000, 1000, 2];
        
        // Initializing the base case
        // when length of bit string is 1
        dp[1, 0, 1] = 1;
        dp[1, 0, 0] = 1;
        
        // Filling up the DP Table
        for(int i = 2; i <= n; i++) {
            for(int j = 0; j <= k; j++) {
                dp[i, j, 0] = dp[i-1, j, 0] + dp[i-1, j, 1];
                if(j > 0) {
                    dp[i, j, 1] = dp[i-1, j-1, 0];
                }
                dp[i, j, 1] += dp[i-1, j, 1];
            }
        }
        
        // Total number of ways
        int totalWays = dp[n, k, 0] + dp[n, k, 1];
        return totalWays;
    }

    public static void Main() {
        int n = 5, k = 2;
        int totalWays = WaysToKAdjacentSetBits(n, k);
        Console.WriteLine("Number of ways = " + totalWays);
    }
}