题目描述

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?

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

题目思路

• 裴波那契数的变体用法
• 面试题10(1): 裴波那契数列
• 面试题10(2): 青蛙跳台阶问题
• 面试题10(3): 青蛙变态跳台阶问题

代码 C++

• 思路一、循环

class Solution {
public:
    int climbStairs(int n) {
        if(n == 1 || n ==2){
            return n;
        } 
        
        int result = 0;
        int a = 1;
        int b = 2;
        
        for(int i=3; i <= n; i++){
            result = a + b;
            a = b;
            b = result;
        }
        return result;
    }
};

• 思路二、递归，但是 leetcode 超时

class Solution {
public:
    int climbStairs(int n) {
        if(n == 1){
            return 1;
        }
        else if(n == 2){
            return 2;
        }
        else{
            return climbStairs(n-1) + climbStairs(n-2);
        }
    }
};

总结展望

• 递归，循环，用递归解决的问题最好用循环吧