HDU 1963 && POJ 2063

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
3000 400
250

With a capital of e10 000 one could buy two bonds of 4000,givingayearlyinterestof800. Buying two bonds of 3000,andoneof4 000 is a better idea, as it gives a yearly interest of 900.Aftertwoyearsthecapitalhasgrownto11 800, and it makes sense to sell a 3000oneandbuya4 000 one, so the annual interest grows to 1050.Thisiswherethisstorygrowsunlikely:thebankdoesnotchargeforbuyingandsellingbonds.Nextyearthetotalsumis12 850, which allows for three times 4000,givingayearlyinterestof1 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.Thevalueofabondisalwaysamultipleof1 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

多次完全背包：用每一年的本息作为最大背包容量，股票的价格作为体积，利息作为价值
因为这句话→_→The value of a bond is always a multiple of $1 000.所以可以把本息与股票价格同时除以1000（背包体积与物品体积同时缩小），这样可以缩短时间。

#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>using namespace std;#define maxn 100050int dp[maxn];int main(){    int t, amount,year, d, value[11], bond[11], i, j, k, money, ans, temp;    scanf("%d",&t);    while(t--){        scanf("%d %d %d",&amount,&year, &d);        for(i = 0; i < d; ++i){            scanf("%d %d", &value[i], &bond[i]);            value[i] /= 1000;        }        ans = 0;        temp = 0;           for(k = 1; k <= year; ++k){            memset(dp, 0, sizeof(dp));            money = amount/1000;            for(i = 0; i < d; ++i){                for(j = value[i]; j <= money; ++j){                    dp[j] = max(dp[j], dp[j-(value[i])] + bond[i]);                    if(temp < dp[j]) temp = dp[j];                }               }            amount += temp;        }        printf("%d\n",amount);    }}