[Leetcode] 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?

思路：动态规划。

class Solution {
public:
    int climbStairs(int n) {
        vector<int> count(3);
        count[0] = 1;
        count[1] = 1;
        for (int i = 2; i <= n; ++i) {
            count[i%3] = count[(i-1)%3] + count[(i-2)%3];
        }
        return count[n%3];
    }
};

总结：注意压缩空间，每一个状态只和它的前两个状态相关。复杂度O(n).