70. Climbing Stairs(动态规划）

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

分析

这道题是斐波那契数列的模型，上第n阶台阶的方法数是f(n)=f(n-1)+f(n-2),因为到第n阶台阶只有从第n-1阶台阶上来或者从第n-2阶上来；

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