Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?
爬楼梯的问题,思路和 Unique Paths问题类似。我们假设到了第i个台阶,因为每次只能走一步和两步,因此到第i个台阶的方式等于到第i-1个台阶的方式和到第i-2个台阶的方式的和,这时i > 1; 递推式为dp[i] = dp[i - 1] + dp[i - 2];实现代码如下:
public class Solution { public int climbStairs(int n) { if(n <= 0) return 0; if(n == 1) return 1; if(n == 2) return 2; int[] dp = new int[n]; dp[0] = 1; dp[1] = 2; for(int i = 2; i < n; i++) { dp[i] = dp[i - 1] + dp[i - 2]; } return dp[n - 1]; } }