Ladder

 Ladder : A person is at level 0 and he has options to take 1 step or 2 steps at a time. To reach level 'n', how many number of ways he has ?

Explanation:

For step 0, number of ways =1

For step 1, number of ways =1

For step 2, number of ways =2

For step 3, number of ways =3

For step 4, number of ways =5

For step 5, number of ways =8

and so on...

For step n, number of ways = number(n-1)+number(n-2), let's see the code below:

package abc;

import java.util.Arrays;

import java.util.Scanner;

public class Ladder {

       public static void main(String[] args) {

             Scanner scanner = new Scanner(System.in);

             System.out.println("Enter the value = ");

             int userInput = scanner.nextInt();

             int n=userInput ;

             int[] total = new int[n];

             int forLoopLimit = n-1;

             for(int i =2;i<=forLoopLimit;i++) {

                    total[0] = 1;

                    total[1] = 1;

//                  total[2] = 2;

//                  total[3] = 3;

//                  total[4] = 5;

                    total[i] = total[i-1]+total[i-2];

                    System.out.println("The number of ways for step "+i+" = "+total[i]);

             }

                                 if(n==0 || n==1) {

                                        int[] num = {1};

                                        System.out.println("return 1, which is: "+Arrays.toString(num));

                                 } else {

//                                      int finalVal = n-1;

                                        int[] num = {total[forLoopLimit]};//last value of i=forLoopLimit

                                        System.out.println("return (n-1)+(n-2), which is: "+total[forLoopLimit]+" OR "+Arrays.toString(num));

                                 }

       }

}

 Output 1:

Enter the value = 

7

The number of ways for step 2 = 2

The number of ways for step 3 = 3

The number of ways for step 4 = 5

The number of ways for step 5 = 8

The number of ways for step 6 = 13

return (i-1)+(i-2), which is: 13 OR [13]

Output 2:

Enter the value = 

1

return 1, which is: [1]