【POJ - 1456】Supermarket (贪心,优先队列 或并查集)
題干:
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 25 20 50 10Sample Output
80 185Hint
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.
題目大意:
超市里有N個商品. 第i個商品必須在保質期(第di天)之前賣掉, 若賣掉可讓超市獲得pi的利潤.?
每天只能賣一個商品.
現在你要讓超市獲得最大的利潤。
解題報告:
? ?優先隊列就行了,考慮成每一個cur天的決策,如果這一天還不到截止日期,那就直接push,并且把cur++。如果到了截止日期,那就只能看看需不需要更新pq中的元素,最后元素的個數一定就是答案。這題還有并查集做法:【51Nod - 1163】最高的獎勵,按權值排序,遍歷來找到可以最早安放的日期。
AC代碼:
#include<cstdio> #include<iostream> #include<algorithm> #include<queue> #include<map> #include<vector> #include<set> #include<string> #include<cmath> #include<cstring> #include<bitset> #define ll long long #define pb push_back #define pm make_pair using namespace std; typedef pair<int,int> pii; const int MAX = 2e5 + 5; int n; pii p[MAX]; int main() {while(~scanf("%d",&n)) {for(int i = 1; i<=n; i++) cin>>p[i].second>>p[i].first;sort(p+1,p+n+1);priority_queue<int,vector<int>,greater<int> > pq;int cur = 1;for(int i = 1; i<=n; i++) {if(cur <= p[i].first) {pq.push(p[i].second);cur++;}else {if(p[i].second > pq.top()) pq.pop(),pq.push(p[i].second);}} int ans = 0;while(!pq.empty()) ans += pq.top(),pq.pop();printf("%d\n",ans);}return 0 ; }?
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