Climbing Stairs 题解
题目来源: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 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
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);
}
};
解题描述
这道题题意是,给出一个数代表台阶数,每次可以上1个或2个台阶,求总共有多少种上台阶的办法。事实上这道题是数学问题,根据不同的上2格台阶的次数,求这些2格台阶所处的位置可用组合数。第一次提交的解法是WA是出现了溢出,所以把与最终计算结果有关的数字类型都改成了long long
。