Climb Stairs With Minimum Moves

1. You are given a number n, representing the number of stairs in a staircase.

2. You are on the 0th step and are required to climb to the top.

3. You are given n numbers, where ith element's value represents - till how far from the step you 

     could jump to in a single move.  You can of-course fewer number of steps in the move.

4. You are required to print the number of minimum moves in which you can reach the top of 

     staircase.

Note -> If there is no path through the staircase print null.

Input Format

A number n

.. n more elements

Output Format

A number representing the number of ways to climb the stairs from 0 to top.

Constraints

0 <= n <= 20

0 <= n1, n2, .. <= 20

Sample Input

10

3

3

0

2

1

2

4

2

0

0

Sample Output

4

Solution:

import java.io.*;

import java.util.*;

public class Main {

    public static void main(String[] args) throws Exception {

        // write your code here

        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        int[] A = new int[n];

        for(int i=0;i<n;i++)

            A[i] = sc.nextInt();

        System.out.println(minClimb(n,A));

    }

    public static int minClimb(int n,int[] A){

        if(n <= 0) return 0;

        Integer[] arr = new Integer[n+1];

        arr[n] = 0;

        for(int i=n-1;i>=0;i--){

            if(A[i] == 0) continue;

            int min = 25;

            for(int j=A[i];j>0;j--){

                if((i+j>n) || (arr[i+j] == null)) continue;

                min = Math.min(min,arr[i+j]);

                

            }

            if(min != 25)

                arr[i] = min + 1;

        }

        return arr[0];

    }

}