leetcode70-Climbing Stairs(斐波那契数列)

问题描述：

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?

问题求解：

设ways[n]表示登完n个台阶的方法。考虑最后一步：

（1）登一个阶梯。ways[n]=ways[n-1] （2）登2个阶梯。ways[n]=ways[n-2]

因此，得到状态转移方程：ways[n] = ways[n-1]+ways[n-2],
ways[1]=1, ways[2]=2.
代码：

class Solution {
public:
    int climbStairs(int n) {
        if(n <= 2) return n;
        int ways[n];
        ways[1]=1;
        ways[2]=2;
        for(int i=3;i<=n;i++)
        {
            ways[i] = ways[i-1]+ways[i-2];
        }
        return ways[n];
    }
};