POJ 2063 Investment （完全背包）

A - Investment

Time Limit:1000MS     Memory Limit:30000KB     64bit IO Format:%I64d & %I64u

Submit Status Practice POJ 2063

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 3000	400 250

With
a capital of e10 000 one could buy two bonds of $4 000, giving a yearly
interest of $800. Buying two bonds of $3 000, and one of $4 000 is a
better idea, as it gives a yearly interest of $900. After two years the
capital has grown to $11 800, and it makes sense to sell a $3 000 one
and buy a $4 000 one, so the annual interest grows to $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 $12 850, which allows for
three times $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 $1 000 000), 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

1
10000 4
2
4000 400
3000 250

Sample Output

14050

算法思考：
    很有意思的一道完全背包问题，只要想到是背包问题，基本就能解决了！    

#include <stdio.h>
#include <string.h>

#define N 50006

int dp[N], w[N], p[N];

int max(int a, int b)
{
	return a > b ? a : b;
}

int main()
{
	int t;
	int aa, yy, d;
	int n, v, i, k;

	scanf("%d", &t);

	while(t--)
	{
		scanf("%d %d", &aa, &yy);
		scanf("%d", &d);

		for(i=1; i<=d; i++)
		{
			scanf("%d %d", &p[i], &w[i] );//花费 收入
			p[i] = p[i]/1000;
		}
        n = d;//种类

        while(yy--)
		{
			memset(dp, 0, sizeof(dp));
			v = aa/1000;
			for(i=1; i<=n; i++)
			{
				for(k=0; k<=v; k++)
				{
					if( k>=p[i] )
					dp[k] = max (dp[k], dp[k-p[i]]+w[i] );
				}
			}

			aa = aa+dp[v];

		}
		printf("%d\n", aa );
	}
}