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.

 1 public class Solution {
 2     public int climbStairs(int n) {
 3         if (n < 1)
 4             return 0;
 5         int[] dp = new int[3];
 6         dp[0] = 1;
 7         dp[1] = 1;
 8         for (int i = 2; i <= n; i++) {
 9             dp[2] = dp[0] + dp[1];
10             dp[0] = dp[1];
11             dp[1] = dp[2];
12         }
13         return dp[1];
14     }
15 }