Codeforces 10E. Greedy Change 科学设计硬币

最新推荐文章于 2023-01-06 15:53:13 发布

三级头不怕通

最新推荐文章于 2023-01-06 15:53:13 发布

阅读量343

点赞数

CC 4.0 BY-SA版权

分类专栏： codeforces不懂

本文链接：https://blog.youkuaiyun.com/u011535421/article/details/79310010

codeforces不懂专栏收录该内容

2 篇文章

订阅专栏

博客探讨了在不同生活领域应用贪婪算法的问题，特别是关于找零问题。当有不同面值的硬币且不限数量时，任务是用最少的硬币数凑出指定金额x。虽然贪婪算法通常会优先选择最大面值的硬币，但并不总是最优解。例如，面对值为{1, 3, 4}的情况，凑出6元时，贪婪算法会选择4+1+1，而最优解是3+3。文章通过给出硬币面值，判断是否存在使贪婪算法非最优的总金额，并找出这样的最小非最优总金额。" 113895208,9317827,Kali Linux中RsaCtfTool的安装步骤与问题解决,"['Linux', 'CTF工具', '软件安装', '系统管理', '信息安全']

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

Billy investigates the question of applying greedy algorithm to different spheres of life. At the moment he is studying the application of greedy algorithm to the problem about change. There is an amount of n coins of different face values, and the coins of each value are not limited in number. The task is to collect the sum x with the minimum amount of coins. Greedy algorithm with each its step takes the coin of the highest face value, not exceeding x. Obviously, if among the coins' face values exists the face value 1, any sum x can be collected with the help of greedy algorithm. However, greedy algorithm does not always give the optimal representation of the sum, i.e. the representation with the minimum amount of coins. For example, if there are face values {1, 3, 4} and it is asked to collect the sum 6, greedy algorithm will represent the sum as 4 + 1 + 1, while the optimal representation is 3 + 3, containing one coin less. By the given set of face values find out if there exist such a sum x that greedy algorithm will collect in a non-optimal way. If such a sum exists, find out the smallest of these sums.

Input

The first line contains an integer n (1 ≤ n ≤ 400) — the amount of the coins' face values. The second line contains n integers a_i(1 ≤ a_i ≤ 10⁹), describing the face values. It is guaranteed that a₁ > a₂ > ... > a_n and a_n = 1.

Output

If greedy algorithm collects any sum in an optimal way, output -1. Otherwise output the smallest sum that greedy algorithm collects in a non-optimal way.

Examples

input
5
25 10 5 2 1

output
-1

input
3
4 3 1

output
6

不用dp太难了吧啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊看不懂啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊先记着吧

#include <iostream>  
using namespace std;  
int n,i,j,k,c[411],x,y,z,o,ans;  
int main()  
{  
    ans=1 << 30;  
    cin >> n;  
    for (i=1;i<=n;i++) cin >> c[i];  
    for (i=2;i<=n;i++)  
    for (j=i;j<=n;j++)  
    {  
        x=c[i-1]-1;  
        y=0;  
        for (k=i;k<=j;k++)  
        {  
            z=x/c[k];  
            x-=z*c[k];  
            y+=z;  
        }  
        x=c[i-1]-1-x+c[j];  
        o=x;  
        y++;  
        if (x<ans)  
        {  
           for (k=1;k<=n;k++)  
           {  
               z=x/c[k];  
               x-=z*c[k];  
               y-=z;  
           }  
           if (y<0) ans=o;  
        }  
    }  
    if (ans==1 << 30) cout << -1;  
    else              cout << ans;  
    return 0;  
}

啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊啊

dp的就是naq17

http://cs.ecs.baylor.edu/~hamerly/icpc/qualifier_2017/naq17_slides.pdf