HDU 1114Piggy-Bank(完全背包) 解题报告

本文探讨了一个经典的计算机科学问题——如何通过已知重量的硬币组合来达到特定总重量的同时实现价值最小化。文章详细解释了使用完全背包算法解决这一问题的方法,并附带了一段实现该算法的C++代码。

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Problem Description
Before ACM can do anything, a budget must be prepared and the necessary financial support obtained. The main income for this action comes from Irreversibly Bound Money (IBM). The idea behind is simple. Whenever some ACM member has any small money, he takes all the coins and throws them into a piggy-bank. You know that this process is irreversible, the coins cannot be removed without breaking the pig. After a sufficiently long time, there should be enough cash in the piggy-bank to pay everything that needs to be paid. 

But there is a big problem with piggy-banks. It is not possible to determine how much money is inside. So we might break the pig into pieces only to find out that there is not enough money. Clearly, we want to avoid this unpleasant situation. The only possibility is to weigh the piggy-bank and try to guess how many coins are inside. Assume that we are able to determine the weight of the pig exactly and that we know the weights of all coins of a given currency. Then there is some minimum amount of money in the piggy-bank that we can guarantee. Your task is to find out this worst case and determine the minimum amount of cash inside the piggy-bank. We need your help. No more prematurely broken pigs! 
 

Input
The input consists of T test cases. The number of them (T) is given on the first line of the input file. Each test case begins with a line containing two integers E and F. They indicate the weight of an empty pig and of the pig filled with coins. Both weights are given in grams. No pig will weigh more than 10 kg, that means 1 <= E <= F <= 10000. On the second line of each test case, there is an integer number N (1 <= N <= 500) that gives the number of various coins used in the given currency. Following this are exactly N lines, each specifying one coin type. These lines contain two integers each, Pand W (1 <= P <= 50000, 1 <= W <=10000). P is the value of the coin in monetary units, W is it's weight in grams. 
 

Output
Print exactly one line of output for each test case. The line must contain the sentence "The minimum amount of money in the piggy-bank is X." where X is the minimum amount of money that can be achieved using coins with the given total weight. If the weight cannot be reached exactly, print a line "This is impossible.". 
 

Sample Input
3 10 110 2 1 1 30 50 10 110 2 1 1 50 30 1 6 2 10 3 20 4
 

Sample Output
The minimum amount of money in the piggy-bank is 60. The minimum amount of money in the piggy-bank is 100. This is impossible.
这两天看了背包九讲的前几讲,总算对背包有点了解。 01背包更新状态时从V(背包的容积)开始更新。 而完全背包则可以直接从当前物品(v【i】)开始更新。原因是完全背包的特点恰是每种物品可选无限件,所以在考虑“加选一件第i种物品”这种策略时,需要一个可能已选入第i种物品的子结果f[i][v-c[i]],所以就可以并且必须采用v=0..V的顺序循环。
下面是我的代码:
#include<iostream>
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#include<algorithm>
using namespace std;
const int INF=500000005;
int a[10005],p,w;
int min(int a,int b)
{
	return a>b?b:a;
}
int main()
{
//	freopen("in.txt","r",stdin);
	int i,j,n,t,e,f;
	scanf("%d",&t);
	while(t--)
	{
		for(i=0;i<=10000;i++) a[i]=INF;
		scanf("%d%d",&e,&f);
		f-=e;
		scanf("%d",&n);
		a[0]=0;
		for(i=0;i<n;i++)
		{
			scanf("%d%d",&p,&w);
			for(j=w;j<=f;j++)
			{
				a[j]=min(a[j],a[j-w]+p);
			}
		}
		if(a[f]==INF)
			printf("This is impossible.\n");
		else
			printf("The minimum amount of money in the piggy-bank is %d.\n",a[f]);
	}
	return 0;
}

内容概要:本文档详细介绍了一个基于MATLAB实现的跨尺度注意力机制(CSA)结合Transformer编码器的多变量时间序列预测项目。项目旨在精准捕捉多尺度时间序列特征,提升多变量时间序列的预测性能,降低模型计算复杂度与训练时间,增强模型的解释性和可视化能力。通过跨尺度注意力机制,模型可以同时捕获局部细节和全局趋势,显著提升预测精度和泛化能力。文档还探讨了项目面临的挑战,如多尺度特征融合、多变量复杂依赖关系、计算资源瓶颈等问题,并提出了相应的解决方案。此外,项目模型架构包括跨尺度注意力机制模块、Transformer编码器层和输出预测层,文档最后提供了部分MATLAB代码示例。 适合人群:具备一定编程基础,尤其是熟悉MATLAB和深度学习的科研人员、工程师和研究生。 使用场景及目标:①需要处理多变量、多尺度时间序列数据的研究和应用场景,如金融市场分析、气象预测、工业设备监控、交通流量预测等;②希望深入了解跨尺度注意力机制和Transformer编码器在时间序列预测中的应用;③希望通过MATLAB实现高效的多变量时间序列预测模型,提升预测精度和模型解释性。 其他说明:此项目不仅提供了一种新的技术路径来处理复杂的时间序列数据,还推动了多领域多变量时间序列应用的创新。文档中的代码示例和详细的模型描述有助于读者快速理解和复现该项目,促进学术和技术交流。建议读者在实践中结合自己的数据集进行调试和优化,以达到最佳的预测效果。
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