算法分析与设计作业

最新推荐文章于 2021-03-17 16:19:31 发布

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本文探讨了经典的爬楼梯问题，给出了一个通过动态规划解决该问题的C++代码实现。问题要求计算出达到楼梯顶部的不同方式数量，输入为正整数n，表示楼梯的阶数。文章提供了详细的代码解释，并通过实例说明了算法的工作原理。

算法分析与设计作业题
作业来源

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

class Solution {
public:
    int climbStairs(int n) {
        if(n<=2)
            return n;
        else{
            vector<int> ways;
            ways.push_back(1);
            ways.push_back(2);
            for(int i = 2; i< n; i++){
                int way = ways[i-1]+ways[i-2];
                ways.push_back(way);
            }
            return ways[n-1];
        }
    }
};