Supermarket
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.
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.
并查集优化：首先了解p值越大，更应该卖出，所以我们可以考虑在最后时期 d值 时卖出，该时期如若已被其他物品占有，就往前搜索，找到空余的时间卖出。然后用并查集优化搜索过程，如若确定该时间被卖物品，构造树pre[x] = x - 1;这样通过find()就阔以快速地寻找到空余时间了。
#include<cstdio> #include<cstring> #include<algorithm> using namespace std; int pre[10005]; struct node{ int p,d; bool operator<(const node &x)const{ return p > x.p; } }a[10005]; void init(){ for(int i = 1; i <= 10000; i++) pre[i] = i; } int find(int x){ return pre[x] == x ? pre[x] : pre[x] = find(pre[x]); } int main(){ int n; while(~scanf("%d",&n)){ int ans = 0; init(); for(int i = 0; i < n; i++){ scanf("%d%d",&a[i].p,&a[i].d); } sort(a,a+n); for(int i = 0; i < n; i++){ int fi = find(a[i].d); if(fi > 0){ ans += a[i].p; pre[fi] = fi-1; } } printf("%d\n",ans); } return 0; }
