70. Climbing Stairs*

70. Climbing Stairs*

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

題目描述

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++ 實現 1

使用迭代的方法. 假設爬 n 樓的方法有 Tn 種, 那麼有可能是爬到 n - 1 樓之後, 再走 1 步到達 n 樓, 有 Tn-1 種方法; 或者是爬到 n-2 樓之後, 再走 2 步達到 n 樓, 這有 Tn-2 種方法; 因此達到 n 樓的方法有:

Tn = Tn-1 + Tn-2

類似於 1137. N-th Tribonacci Number* 這題.

代碼如下:

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;
    }
};