Supermarket

Time Limit: 2000MS Memory Limit: 65536K
Total Submissions: 21612 Accepted: 9563

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：有n见商品给出每件商品的利润和销售时间，没买一件商品消耗1单位的时间，问最大利润是多少？
思路：贪心，先对利润降序，每取一件商品对应天数的商品天数减一，这里用并查集维护天数的同步，用并查集的路径压缩把时间点串起来，询问时间复杂度常数时间。
代码：

#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
int n;
const int maxn=1e4+10;
typedef struct{
	int value,deadline;
}node;
node a[maxn];
int f[maxn];
bool cmp(node a,node b){
	return a.value>b.value;
}
int find_x(int x){//很关键，不仅起到很好的查询效果，而且路径压缩的时候把相同时间点连接起来了
	if(f[x]==-1)return x;
	return f[x]=find_x(f[x]);
}
int main(){
	while(cin>>n){
		memset(f,-1,sizeof(f));
		for(int i=1;i<=n;i++){
			cin>>a[i].value>>a[i].deadline;
		}
		int sum=0;
		sort(a+1,a+1+n,cmp);//按照利润降序
		for(int i=1;i<=n;i++){
			int t=find_x(a[i].deadline);//每次找到利润最大的商品
			if(t>0){//还有时间
				sum+=a[i].value;
				f[t]=t-1;//时间减一
			}
		}
		cout<<sum<<endl;
	}
}