Question

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Solution

Classic DP problem. When we climb n steps, we have two choices for last step, either one step or two steps. To save space, we can further improve the solution using O(1) space.

 public class Solution {

     public int climbStairs(int n) {

         if (n < 1)

             return 0;

         int[] dp = new int[3];

         dp[0] = 1;

         dp[1] = 1;

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

             dp[2] = dp[0] + dp[1];

             dp[0] = dp[1];

             dp[1] = dp[2];

         }

         return dp[1];

     }

 }