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?

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解法一:
思路：n级台阶可以看成n-1级台阶直接一步跨上去，或者n-2步台阶，跨两步上去，由于n-1和n-2的起点不同，终点相同，所以n-1的方式和n-2的方式一定没有重复的，所以S(n)=S(n-1)+S(n-2)

class Solution {
public:
    int climbStairs(int n) {
        if(n<=2)
            return n;
        else{
            vector<int> ways;
            ways.push_back(1);
            ways.push_back(2);
            for(int i = 2; i< n; i++){
                int way = ways[i-1]+ways[i-2];
                ways.push_back(way);
            }
            return ways[n-1];
        }
    }
};

其他解法暂时先留着。