[LeetCode] 70. Climbing Stairs

题目链接：传送门

Description

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 step + 1 step
2 steps

Example 2:

Input: 3
Output:  3
Explanation:  There are three ways to climb to the top.

1 step + 1 step + 1 step
1 step + 2 steps
2 steps + 1 step

Solution

题意：

有n阶楼梯，每次可以爬1阶或2阶，问爬完n阶有几种爬法

思路：

令 \(dp[i]\) 为 i 阶楼梯的方案数，显然 \(dp[i]=dp[i-1]+dp[i-2]\)，初始值 \(dp[1]=1, dp[2]=2\)

其实就是一个Fibonacci，用矩阵快速幂加速可解，但似乎直接扫一遍也不会TLE

class Solution {
public:
    int climbStairs(int n) {
        if (n == 1)  return 1;
        if (n == 2)  return 2;
        int x = 1, y = 2, z;
        for (int i = 3; i <= n; i++) {
            z = x + y;
            x = y;
            y = z;
        }
        return z;
    }
};