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1316 - Supermarket

Content

有N個商品分別有他們的價值和期限，每天只能賣一個商品，最多能獲利多少

A supermarket has a set Prod of products on sale. It earns a profit px for each product x ∈ P rod 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 ⊆ P rod 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 P rof it(Sell) = ∑x∈Sell px. An optimal selling schedule is a schedule with a maximum profit.

For example, consider the products P rod = {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

每筆測資的第一個數字N代表有幾個商品(0 ≤ n ≤ 10000)

之後有N個商品的價值pi和期限di(1 ≤ pi,di ≤ 10000)

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

輸出最大獲利

For each set of products, the program prints on the standard output the profit of an optimal selling chedule for the set. Each result is printed from the beginning of a separate line.

Note for the Sample:

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.

Sample Input
#1

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
#1

80 185

測資資訊：

記憶體限制：
512
MB

公開 測資點#0 (20%): 1.0s , <10M

公開 測資點#1 (20%): 1.0s , <10M

公開 測資點#2 (20%): 1.0s , <10M

公開 測資點#3 (20%): 1.0s , <10M

公開 測資點#4 (20%): 1.0s , <10M

公開 測資點#0 (20%): 1.0s , <10M

公開 測資點#1 (20%): 1.0s , <10M

公開 測資點#2 (20%): 1.0s , <10M

公開 測資點#3 (20%): 1.0s , <10M

公開 測資點#4 (20%): 1.0s , <10M

就算是O(N^2)也要試試看

2020 5月CPE第五題