Leetcode 70. Climbing Stairs 爬楼梯

70. Climbing Stairs 爬楼梯

题目描述

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.

示例:

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

解答

这是典型DP问题，令dp[i] 为爬到第i个台阶有多少种方法，则dp[i] = dp[i - 1] + dp[i - 2]。考虑到计算dp[i] 只需要i - 1 和i - 2我们可以用两个变量prev 和 cur来代替dp[i - 1] 和dp[i - 2]。

代码如下。

代码

class Solution {
     
public:
    int climbStairs(int n) {
     
        if (n < 3) {
     
        	return n;
        }
        int sum = 0;
        int prev = 1;
        int cur = 2;
        for (int i = 3; i <= n; i++) {
     
        	sum = prev + cur;
        	prev = cur;
        	cur = sum;

        }
        return cur;
    }
};