Investment （水题）完全背包加状态压缩--不然会TlE

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 10 00010 000 one could buy two bonds of 4 0004 000, giving a yearly interest of 800800. Buying two bonds of 3 0003 000, and one of 4 0004 000 is a better idea, as it gives a yearly interest of 900900. After two years the capital has grown to 11 80011 800 , and it makes sense to sell a 3 0003 000 one and buy a 4 0004 000 one, so the annual interest grows to 1 0501 050. This is where this story grows unlikely: the bank does not charge for buying and selling bonds. Next year the total sum is12 85012 850, which allows for three times 4 0004 000, giving a yearly interest of 1 2001 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 most1 000 0001 000 000), and the number of years the capital may grow (at most 40).

The following line contains a single number: the number d (1 <= d <= 10) of available bonds.

The next d lines each contain the description of a bond. The description of a bond consists of two positive integers: the value of the bond, and the yearly interest for that bond. The value of a bond is always a multiple of $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

110000 424000 4003000 250

Sample Output

14050

题意：

    john 现在有好多钱，他想把这些钱存在银行里，银行给出几种存钱福利，每种存钱的方式所需的资金不同，每年的利润也不同，现在给你N多money,让你求出在Y年之后的所能得到的最大值。

 看完题目后就发现是完全背包，但是没想到状态压缩，其实就是让循环的次数变少，减少复杂度。仔细看看题目其实有暗示。

The value of a bond is always a multiple of $1 000.

代码：

#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>#define maxn 1000000using namespace std;int money,y,p;int w[100],v[100];int f[maxn];int main(){    int T;    scanf("%d",&T);    while(T--)    {        scanf("%d%d",&money,&y);        scanf("%d",&p);        for(int i=0;i<p;i++)        {             scanf("%d%d",&w[i],&v[i]);             w[i]/=1000;  //状态压缩第一步        }        int sum=money;        for(int i=0;i<y;i++)        {            memset(f,0,sizeof f);        //注意memset 的使用，每年都得清零            sum=money;            sum/=1000;                              for(int i=0;i<p;i++)                for(int j=w[i];j<=sum;j++)                {                    f[j]=max(f[j],f[j-w[i]]+v[i]);                    }            money+=f[sum];        }        printf("%d\n",money);    }    return 0;}