70 Climbing Stairs

1 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?

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

2 尝试解

2.1 分析

爬n级的楼梯，每次可以爬1级或者2级，问有多少种爬楼梯的方法。

对于n>2的阶梯，既可以从n-1级爬1级上来，也可以从n-2级爬2级上来，所以f(n) = f(n-1) + f(n-2)，其中f(1)=1，f(2)=2。

2.2 代码

class Solution {
public:
    int climbStairs(int n) {
        if(n == 1) return 1;
        int first = 1;
        int second = 2;
        int result = 2;
        for(int i = 3; i <= n ; i++){
            result = first + second;
            first = second;
            second = result;
        }
        return result;
    }
};

3 标准解

int climbStairs(int n) {
    int a = 1, b = 1;
    while (n--)
        a = (b += a) - a;
    return a;
}