C# Program for Count ways to reach the n\’th stair

There are n stairs, a person standing at the bottom wants to reach the top. The person can climb either 1 stair or 2 stairs at a time. Count the number of ways, the person can reach the top. Consider the example shown in diagram. The value of n is 3. There are 3 ways to reach the top. The diagram is taken from Easier Fibonacci puzzles

C#

// C# program to count the
// number of ways to reach
// n'th stair
using System;

class GFG {
    // A simple recursive
    // program to find n'th
    // fibonacci number
    static int fib(int n)
    {
        if (n <= 1)
            return n;
        return fib(n - 1) + fib(n - 2);
    }

    // Returns number of ways
    // to reach s'th stair
    static int countWays(int s)
    {
        return fib(s + 1);
    }

    // Driver Code
    static public void Main()
    {
        int s = 4;
        Console.WriteLine("Number of ways = " + countWays(s));
    }
}

// This code is contributed
// by akt_mit

Output:

Number of ways = 5

The time complexity of the above implementation is exponential (golden ratio raised to power n). It can be optimized to work in O(Logn) time using the previously discussed Fibonacci function optimizations. 

C#

// C# program to Count ways to reach
// the n’th stair
using System;

class GFG {

    // A recursive function used by
    // countWays
    static int countWaysUtil(int n, int m)
    {
        if (n <= 1)
            return n;
        int res = 0;

        for (int i = 1; i <= m && i <= n; i++)
            res += countWaysUtil(n - i, m);
        return res;
    }

    // Returns number of ways to reach
    // s'th stair
    static int countWays(int s, int m)
    {
        return countWaysUtil(s + 1, m);
    }

    /* Driver program to test above function */
    public static void Main()
    {
        int s = 4, m = 2;
        Console.Write("Number of ways = "
                      + countWays(s, m));
    }
}

// This code is contributed by nitin mittal.

Output:

Number of ways = 5

Time complexity: O(2ⁿ)
Auxiliary Space: O(n)

C#

// C# program to count number
// of ways to reach n't stair when
// a person can climb 1, 2, ..m
// stairs at a time
using System;
class GFG {

    // A recursive function
    // used by countWays
    static int countWaysUtil(int n, int m)
    {
        int[] res = new int[n];
        res[0] = 1;
        res[1] = 1;
        for (int i = 2; i < n; i++) {
            res[i] = 0;
            for (int j = 1; j <= m && j <= i; j++)
                res[i] += res[i - j];
        }
        return res[n - 1];
    }

    // Returns number of ways
    // to reach s'th stair
    static int countWays(int s, int m)
    {
        return countWaysUtil(s + 1, m);
    }

    // Driver Code
    public static void Main()
    {
        int s = 4, m = 2;
        Console.WriteLine("Number of ways = " + countWays(s, m));
    }
}

// This code is contributed by anuj_67.

Output:

Number of ways = 5

Time Complexity: O(m*n)

Auxiliary Space: O(n)

Please refer complete article on Count ways to reach the n’th stair for more details!