HDOJ 题目1963 Investment（完全背包）

Investment

Time Limit: 5000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 550    Accepted Submission(s): 234

Problem Description

John never knew he had a grand-uncle, until he received the notary’s letter. He learned that his late grand-uncle had gathered a lot of money, somewhere in South-America, and that John was the only inheritor.

John did not need that much money for the moment. But he realized that it would be a good idea to store this capital in a safe place, and have it grow until he decided to retire. The bank convinced him that a certain kind of bond was interesting for him. 

This kind of bond has a fixed value, and gives a fixed amount of yearly interest, payed to the owner at the end of each year. The bond has no fixed term. Bonds are available in different sizes. The larger ones usually give a better interest. Soon John realized that the optimal set of bonds to buy was not trivial to figure out. Moreover, after a few years his capital would have grown, and the schedule had to be re-evaluated.

Assume the following bonds are available:
Value Annual interest
4000   400
3000   250

With a capital of  10000onecouldbuytwobondsof 4 000, giving a yearly interest of  800.Buyingtwobondsof 3 000, and one of  4000isabetteridea,asitgivesayearlyinterestof 900. After two years the capital has grown to  11800,anditmakessensetosella 3 000 one and buy a  4000one,sotheannualinterestgrowsto 1 050. This is where this story grows unlikely: the bank does not charge for buying and selling bonds. Next year the total sum is  12850,whichallowsforthreetimes 4 000, giving a yearly interest of $1 200. 

Here is your problem: given an amount to begin with, a number of years, and a set of bonds with their values and interests, find out how big the amount may grow in the given period, using the best schedule for buying and selling bonds.

 

Input

The first line contains a single positive integer N which is the number of test cases. The test cases follow. 

The first line of a test case contains two positive integers: the amount to start with (at most  1000000),andthenumberofyearsthecapitalmaygrow(atmost40).Thefollowinglinecontainsasinglenumber:thenumberd(1<=d<=10)ofavailablebonds.Thenextdlineseachcontainthedescriptionofabond.Thedescriptionofabondconsistsoftwopositiveintegers:thevalueofthebond,andtheyearlyinterestforthatbond.Thevalueofabondisalwaysamultipleof 1 000. The interest of a bond is never more than 10% of its value.

 

Output

For each test case, output – on a separate line – the capital at the end of the period, after an optimal schedule of buying and selling.

 

Sample Input

  

   1
10000 4
2
4000 400
3000 250
  

 

Sample Output

  

   14050
  

 

Source

NWERC2004

 

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题目上说了v【i】是1000的倍数所以可以让他们都整除1000

ac代码

#include<stdio.h>
#include<string.h>
#define max(a,b) (a>b?a:b)
int dp[110100],v[100010],w[100010];
int main()
{
	int t;
	scanf("%d",&t);
	while(t--)
	{
		int m,y,n,i,j,k,temp,sum=0;
		scanf("%d%d%d",&m,&y,&n);
		for(i=0;i<n;i++)
		{
			scanf("%d%d",&v[i],&w[i]);
			v[i]/=1000;
		}
		sum=m;
		for(i=0;i<y;i++)
		{
			temp=sum/1000;
			memset(dp,0,sizeof(dp));
			for(j=0;j<n;j++)
			{
				for(k=v[j];k<=temp;k++)
				{
					dp[k]=max(dp[k],dp[k-v[j]]+w[j]);
				}
			}
			sum+=dp[temp];
		}
		printf("%d\n",sum);
	}
}