LeetCode 70. 爬楼梯

70. Climbing Stairs

You are climbing a staircase. It takes?n?steps to reach the top.

Each time you can either climb?1?or?2?steps. In how many distinct ways can you climb to the top?

Example 1:

Input: n = 2

Output: 2

Explanation: There are two ways to climb to the top.

1. 1 step + 1 step
2. 2 steps

Example 2:

Input: n = 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

Constraints:

• 1 <= n <= 45

解法思路：

// 懵逼的时候:

// 暴力？基本情况？

// 找 最近 重复子问题

// if else

// for while, recursion

// 1: 1

// 2: 2

// 3: f(1) + f(2) 第三个台阶必须从第二个台阶跨一步上去 或者 从第一个台阶跨两步上去

// 4: f(2) + f(3)

// f(n) = f(n-1) + f(n-2) : Fibonacii

class Solution {
    public int climbStairs(int n) {
        // recursion (超时)
        // if (n <= 2) return n;
        // return climbStairs(n-1) + climbStairs(n-2);

        if (n <= 2) return n;
        int first = 1;
        int second = 2;
        int res = 0;
        for (int i = 3; i <= n; i++) {
            res = first + second;
            first = second;
            second = res;
        }
        return res;
    }
}