Climbing Stairs 解答

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];
     }
 }