Supermarket | 贪心 + 优先队列
from poj 1456
from acwing 145
时间限制 ：2s
内存限制：65M
Description:
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)=Σx∈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.
题目大意：
一个超市有 一些即将过期商品，且每天只能卖出一件商品，给定你这些过期商品的利润和过期日期，问你这家超市能获得的最多收益是多少。
这个题目一看肯定第一时间就是想到贪心吧！？
这个题目可以将所有的商品按照过期时间排序，从最后一天开始遍历，对于每一天，只要有过期日期超过这一天的商品，那么就在所有过期日期在该天之后的商品中挑出利润最大的商品在该天出售。
AC代码：
#include<iostream>
#include<queue>
#include<algorithm>
using namespace std;
#define pii pair<int,int>
pii w[10005]; //每件商品的利润和价格都用一个pair存储
bool cmp(pii a,pii b){
return a.second > b.second; //按照商品的过期时间从大到小排序
}
int n,max_day,note,sum; //商品数，所有商品过期时间最晚的时间，记录某件商品，最大利益
priority_queue<int> q; //存储目前能卖的商品
int main(){
while(cin>>n){
note = 1,sum = 0;
for(int i = 1;i <= n;++i) cin>>w[i].first>>w[i].second;
sort(w + 1,w + 1 + n,cmp);
max_day = w[1].second;
while(!q.empty()) q.pop();
while(max_day--){
//从最后一天往前遍历
while(note <= n && w[note].second > max_day) //如果某件商品的过期日期大于max_day说明它在该天是能卖的，存入到优先队列
q.push(w[note++].first);
if(!q.empty()) //每一天都从优先队列中取出可卖的利润最大的商品售卖
sum += q.top(),q.pop();
}
cout<<sum<<endl;
}
return 0;
}