G - Supermarket（贪心）

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本文介绍了一种解决商品销售调度问题的算法，旨在最大化利润。给定一组商品的价格和销售截止日期，算法通过贪心策略安排销售顺序，确保高价值商品优先售出。使用价格排序和时间标记策略，有效地解决了商品销售的最优化问题。

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A supermarket has a set Prod of products on sale. It earns a profit px for each product x∈Prod sold by a deadline dx that is measured as an integral number of time units starting from the moment the sale begins. Each product takes precisely one unit of time for being sold. A selling schedule is an ordered subset of products Sell ≤ Prod such that the selling of each product x∈Sell, according to the ordering of Sell, completes before the deadline dx or just when dx expires. The profit of the selling schedule is Profit(Sell)=Σ x∈Sellpx. An optimal selling schedule is a schedule with a maximum profit.
For example, consider the products Prod={a,b,c,d} with (pa,da)=(50,2), (pb,db)=(10,1), (pc,dc)=(20,2), and (pd,dd)=(30,1). The possible selling schedules are listed in table 1. For instance, the schedule Sell={d,a} shows that the selling of product d starts at time 0 and ends at time 1, while the selling of product a starts at time 1 and ends at time 2. Each of these products is sold by its deadline. Sell is the optimal schedule and its profit is 80.

Write a program that reads sets of products from an input text file and computes the profit of an optimal selling schedule for each set of products.

Input

A set of products starts with an integer 0 <= n <= 10000, which is the number of products in the set, and continues with n pairs pi di of integers, 1 <= pi <= 10000 and 1 <= di <= 10000, that designate the profit and the selling deadline of the i-th product. White spaces can occur freely in input. Input data terminate with an end of file and are guaranteed correct.

Output

For each set of products, the program prints on the standard output the profit of an optimal selling schedule for the set. Each result is printed from the beginning of a separate line.

Sample Input

4  50 2  10 1   20 2   30 1

7  20 1   2 1   10 3  100 2   8 2
   5 20  50 10

Sample Output

80
185

Hint

The sample input contains two product sets. The first set encodes the products from table 1. The second set is for 7 products. The profit of an optimal schedule for these products is 185.

题意：我们要卖东西了，作为一名ACMer，我们当然要靠着自己的聪明才智去赚更多的钱呀。有n个商品，分别给出他们的价格和截止日期（从第一天到这一天都可以卖这个东西），每一天只能卖出一样东西。这样的题见怪不怪了，我们当然要将最贵的先卖出去啊（贪心），所以我们要将价格从大到小排序，并且开个vis标记该天是否有卖东西，暴力即可了～～

#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn=10010;
struct node
{
    int p,d;//价格，截止日期
}q[maxn];
int vis[maxn];//标记第i天是否有卖商品
int cmp(node a,node b)//将价格从大到校排序，即保证在不冲突的前提下最贵的优先卖出
{
    return a.p>b.p;
}
int ans,n;
int main()
{
    while(cin>>n)
    {
        ans=0;
        memset(vis,0,sizeof(vis));
        for(int i=1;i<=n;i++)
            cin>>q[i].p>>q[i].d;
        sort(q+1,q+1+n,cmp);
        for(int i=1;i<=n;i++)//从最贵的开始卖～～
        {
            for(int j=q[i].d;j>=1;j--)//优先保证最贵的卖出去,注意这里一定是倒着遍历!
            {
                if(vis[j])
                    continue;
                vis[j]=1;       //标记当天已经有卖东西了
                ans+=q[i].p;
                break;
            }
        }
        cout<<ans<<endl;
    }
    return 0;
}