70. Climbing Stairs

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?

Note: Given n will be a positive integer.

Example 1:

Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Example 2:

Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step


DP经典入门题,但是没想到第一次还超时了,因为直接递归的话肯定超时;
优化1: 用数组来存每一个步骤,减少计算量
优化2: 经过发现n只需要n-1和n-2这两个状态嘛,而且这三个值是连续的,也就是说数组的空间可以再优化成三个变量,当然看起来要费尽一点

class Solution {
public:
    int climbStairs(int n) {
        if(n<3)return n;
        int step1=1,step2=2,res=0;
        for(int i=2;i<n;++i)
        {
            res=step1+step2;
            step1=step2;
            step2=res;
        }
        return res;
    }
};