LeetCode(70)题解: climbing-stairs

https://leetcode.com/problems/climbing-stairs/

题目：

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?

1)递归：超时

class Solution {
public:
    int climbStairs(int n) {
        if (n==1)
            return 1;
        if(n==2)
            return 2;
        return climbStairs(n-1)+climbStairs(n-2);
    }
};

2）非递归，避免嵌套调用

递推公式

a_n=a_{n-1}+a_{n-2}.

a_1=1, a_2=2.

问题：给定n求a_n。其实就是斐波那契数列。

AC代码：

 1 class Solution {
 2 public:
 3     int climbStairs(int n) {
 4         if (n==1)
 5             return 1;
 6         if (n==2)
 7             return 2;
 8         int t=2,x=1,y=2,z;
 9         while(t!=n){
10             t++;
11             z=x+y;
12             x=y;
13             y=z;
14         }
15         return z;
16     }
17 };