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