70. Climbing Stairs*

​​https://leetcode.com/problems/climbing-stairs/​​

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.
4. 1 step + 1 step + 1 step
5. 1 step + 2 steps
6. 2 steps + 1 step

C++ 实现 1

使用迭代的方法. 假设爬 ​​n​​​ 楼的方法有 ​​Tn​​​ 种, 那么有可能是爬到 ​​n - 1​​​ 楼之后, 再走 1 步到达 ​​n​​​ 楼, 有 ​​Tn-1​​​ 种方法; 或者是爬到 ​​n-2​​​ 楼之后, 再走 2 步达到 ​​n​​​ 楼, 这有 ​​Tn-2​​​ 种方法; 因此达到 ​​n​​ 楼的方法有:

Tn = Tn-1 + Tn-2

类似于 ​​1137. N-th Tribonacci Number*​​ 这题.

代码如下:

class Solution {
public:
    int climbStairs(int n) {
        if (n <= 1) return 1;
        int a = 1, b = 1;
        n -= 1;
        while (n --) {
            int c = a + b;
            a = b;
            b = c;
        }
        return b;
    }
};

C++ 实现 2

更简洁的写法:

class Solution {
public:
    int climbStairs(int n) {
        if (n <= 1) return 1;
        int a = 1, b = 1;
        while (-- n) {
            b = a + b;
            a = b - a;
        }
        return b;
    }
};