【POJ】1456 - Supermarket（并查集，好题）

Supermarket

Time Limit: 2000MS Memory Limit: 65536KTotal Submissions: 11154 Accepted: 4910

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)=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 17  20 1   2 1   10 3  100 2   8 2   5 20  50 10

Sample Output

80185

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.

Source

Southeastern Europe 2003

很好的一个并查集的题，先用sort快排，把最值钱的商品放在第一个，然后先从当前最值钱的开始算，如果当天可以卖的话，就拿一天卖掉，如果有商品占了那一天，就往前一天寻找，并查集在这里就作为最靠近其保质期当天的那一天，如果其根为0，则表示该商品没有空闲的天卖出。

代码如下：

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;int f[11111];//表示当前时间点上一个空闲时间，通过find函数可找到根节点，即空闲时间struct node{int p,d;}a[11111];int find(int x){if (f[x]==-1)return x;//当前时间空闲else{f[x]=find(f[x]);return f[x];}}bool cmp(node a,node b){return a.p>b.p;}int main(){int u;int ans;while (~scanf ("%d",&u)){for (int i=0;i<u;i++)scanf ("%d %d",&a[i].p,&a[i].d);memset (f,-1,sizeof(f));sort(a,a+u,cmp);//按价值从大到小排序ans=0;for (int i=0;i<u;i++){int t;t=find(a[i].d);//寻找其空闲时间点if (t>0){ans+=a[i].p;//若时间点合法，就卖出！f[t]=t-1;//把该时间的合法时间往前推移1 }}printf ("%d\n",ans);}return 0;}