Description
In Pearlania everybody is fond of pearls. One company, called The Royal Pearl, produces a lot of jewelry with pearls in it. The Royal
Pearl has its name because it delivers to the royal family of Pearlania. But it also produces bracelets and necklaces for ordinary people. Of course the quality of the pearls for these people is much lower then the quality of pearls for the royal family.In
Pearlania pearls are separated into 100 different quality classes. A quality class is identified by the price for one single pearl in that quality class. This price is unique for that quality class and the price is always higher then the price for a pearl
in a lower quality class.
Every month the stock manager of The Royal Pearl prepares a list with the number of pearls needed in each quality class. The pearls are bought on the local pearl market. Each quality class has its own price per pearl, but for every complete deal in a certain quality class one has to pay an extra amount of money equal to ten pearls in that class. This is to prevent tourists from buying just one pearl.
Also The Royal Pearl is suffering from the slow-down of the global economy. Therefore the company needs to be more efficient. The CFO (chief financial officer) has discovered that he can sometimes save money by buying pearls in a higher quality class than is actually needed.No customer will blame The Royal Pearl for putting better pearls in the bracelets, as long as the
prices remain the same.
For example 5 pearls are needed in the 10 Euro category and 100 pearls are needed in the 20 Euro category. That will normally cost: (5+10)*10+(100+10)*20 = 2350 Euro.Buying all 105 pearls in the 20 Euro category only costs: (5+100+10)*20 = 2300 Euro.
The problem is that it requires a lot of computing work before the CFO knows how many pearls can best be bought in a higher quality class. You are asked to help The Royal Pearl with a computer program.
Given a list with the number of pearls and the price per pearl in different quality classes, give the lowest possible price needed to buy everything on the list. Pearls can be bought in the requested,or in a higher quality class, but not in a lower one.
Every month the stock manager of The Royal Pearl prepares a list with the number of pearls needed in each quality class. The pearls are bought on the local pearl market. Each quality class has its own price per pearl, but for every complete deal in a certain quality class one has to pay an extra amount of money equal to ten pearls in that class. This is to prevent tourists from buying just one pearl.
Also The Royal Pearl is suffering from the slow-down of the global economy. Therefore the company needs to be more efficient. The CFO (chief financial officer) has discovered that he can sometimes save money by buying pearls in a higher quality class than is actually needed.No customer will blame The Royal Pearl for putting better pearls in the bracelets, as long as the
prices remain the same.
For example 5 pearls are needed in the 10 Euro category and 100 pearls are needed in the 20 Euro category. That will normally cost: (5+10)*10+(100+10)*20 = 2350 Euro.Buying all 105 pearls in the 20 Euro category only costs: (5+100+10)*20 = 2300 Euro.
The problem is that it requires a lot of computing work before the CFO knows how many pearls can best be bought in a higher quality class. You are asked to help The Royal Pearl with a computer program.
Given a list with the number of pearls and the price per pearl in different quality classes, give the lowest possible price needed to buy everything on the list. Pearls can be bought in the requested,or in a higher quality class, but not in a lower one.
Input
The first line of the input contains the number of test cases. Each test case starts with a line containing the number of categories
c (1<=c<=100). Then, c lines follow, each with two numbers ai and pi. The first of these numbers is the number of pearls ai needed in a class (1 <= ai <= 1000).
The second number is the price per pearl pi in that class (1 <= pi <= 1000). The qualities of the classes (and so the prices) are given in ascending order. All numbers in the input are integers.
The second number is the price per pearl pi in that class (1 <= pi <= 1000). The qualities of the classes (and so the prices) are given in ascending order. All numbers in the input are integers.
Output
For each test case a single line containing a single number: the lowest possible price needed to buy everything on the list.
题意:多组数据。每组数据输入一个n表示有n种珍珠,接下来n行分别输入该种珍珠的需求量和价格,按照行数的递增珍珠的等级依次递增,低等级的珍珠可以按高等级的珍珠价格购买,为了防止游客只买一个珍珠购买珍珠的价格必须另外多付10个当前珍珠等级的价格,求购买所需珍珠的最低价格。
思路:数组dp[i]表示购买所有前i种珍珠的最低价格。购买所有前i种珍珠的方式可能是所有所需价格都按珍珠最高等级价格购买,也可能是之前所有j种珍珠按其最低价格购买方式加上剩下的所需珍珠数量按珍珠最高等级价格的购买方式,按其中最少花费的购买方式购买珍珠。
Sample Input
2 2 100 1 100 2 3 1 10 1 11 100 12
Sample Output
330 1344
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <queue>
#define INF 0x3f3f3f3f
#define esp 1e-9
using namespace std;
int sum[1000],price[1000],dp[1000];
int main()
{
//freopen("lalala.text","r",stdin);
int n,t;
scanf("%d",&t);
while(t--)
{
memset(sum,0,sizeof(sum));
memset(price,0,sizeof(price));
memset(dp,INF,sizeof(dp));
scanf("%d",&n);
scanf("%d %d",&sum[1],&price[1]);
dp[1]=(sum[1]+10)*price[1];
for(int i=2; i<=n; i++)
{
scanf("%d %d",&sum[i],&price[i]);
sum[i]+=sum[i-1]; //到当前等级总共所需的珍珠数量
for(int j=1; j<i; j++) //枚举当前等级之前的购买方式
{
dp[i]=min(dp[i],min(dp[j]+(sum[i]-sum[j]+10)*price[i],(sum[i]+10)*price[i]));
} //取最小时也要比较自身已更新的数据
}
printf("%d\n",dp[n]);
}
return 0;
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