Added the solution for Count ways to N'th Stair. issue #1455

Java/cp/Staircase_problem.java

@@ -0,0 +1,38 @@
+// This program finds the total number of possible combinations that can be used to
+// climb statirs . EG : for 3 stairs ,combination and output will be 1,1,1 , 1,2 , 2,1 i.e 3 . 
+import java.util.Scanner;
+
+class Staircase_problem{
+    public static void main(String args[]){
+        int count_stairs=0;
+        Scanner input = new Scanner(System.in);
+        //Asking for number of steps to find combination.
+        System.out.println("Enter total number of Stairs:"); 
+        count_stairs = input.nextInt();
+        Staircase_problem sp = new Staircase_problem();
+        // Making object of this class and passing stair number to  the function.
+        int final_steps = sp.possibilities_count(count_stairs); 
+        //Printing the number of combination which is given by the function.
+        System.out.println("Total Number of possible Combinations = "+final_steps);
+    }
+
+    int possibilities_count(int a){
+        int result = a;
+        //Using Recursion to find the total number of stairs as f(a) = f(a-1) + a(a-2) 
+        // where f(a) is the final result 
+        if(result <= 1){
+            result =  1;
+        }else{
+            result = possibilities_count(a-1) + possibilities_count(a-2);
+        }
+        return result;
+    }
+}
+/* Output 
+Enter total number of Stairs:
+4
+Total Number of possible Combinations = 5
+*/
+// Time Complexity : O(2^n)
+// Space Complexity :O(1)
+// Created by Shubham Patel on 16-12-2020 on WoC