Climbing Stairs 題解

題目來源：https://leetcode.com/problems/climbing-stairs/description/

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

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

Solution

class Solution {
private:
    long
 
 long combinatorial(int m, int n) {
        long long res = 1, a = m - n + 1, b = 1;
        long long times = static_cast<long long>(n);
        while (b <= times) {
            res *= a;
            res /= b;
            a++;
            b++;
        }
        return res;
    }
public:
    int
 
 climbStairs(int n) {
        int count2 = n / 2;
        long long res = 1;
        for (int i = 1; i <= count2; i++) {
            res += combinatorial(n - i, i);
        }
        return static_cast<int>(res);
    }
};

解題描述

這道題題意是，給出一個數代表臺階數，每次可以上1個或2個臺階，求總共有多少種上臺階的辦法。事實上這道題是數學問題，根據不同的上2格臺階的次數，求這些2格臺階所處的位置可用組合數。第一次提交的解法是WA是出現了溢出，所以把與最終計算結果有關的數字類型都改成了long long。

[Leetcode] Climbing Stairs