RENT - Rent your airplane and make money

"ABEAS Corp." is a very small company that owns a single airplane. The customers of ABEAS Corp are large airline companies which rent the airplane to accommodate occasional overcapacity.

Customers send renting orders that consist of a time interval and a price that the customer is ready to pay for renting the airplane during the given time period. Orders of all the customers are known in advance. Of course, not all orders can be accommodated and some orders have to be declined. Eugene LAWLER, the Chief Scientific Officer of ABEAS Corp would like to maximize the profit of the company.

You are requested to compute an optimal solution.

Small Example

Consider for instance the case where the company has 4 orders:

  • Order 1 (start time 0, duration 5, price 10)
  • Order 2 (start time 3, duration 7, price 8)
  • Order 3 (start time 5, duration 9, price 7)
  • Order 4 (start time 6, duration 9, price 8)

The optimal solution consists in declining Order 2 and 3 and the gain is 10+8 = 18.
Note that the solution made of Order 1 and 3 is feasible (the airplane is rented with no interruption from time 0 to time 14) but non-optimal.


The first line of the input contains a number T ≤ 30 that indicates the number of test cases to follow. The first line of each test case contains the number of orders n (n ≤ 10000). In the following n lines the orders are given. Each order is described by 3 integer values: The start time of the order st (0 ≤ st < 1000000), the duration d of the order (0 < d < 1000000), and the price p (0 < p < 100000) the customer is ready to pay for this order.


You are required to compute an optimal solution. For each test case your program has to write the total price paid by the airlines.


0 5 10
3 7 14
5 9 7
6 9 8

Warning: large Input/Output data, be careful with certain languages

hide comments
Adrian Kuegel: 2012-10-11 15:08:38

No, they can be in any order. But sorting them yourself should be easy, right?

Soumajyoti: 2012-09-28 19:08:25

Are the inputs given in sorted order of their start times??

Last edit: 2012-10-09 21:45:56
Adrian Kuegel: 2011-08-02 10:40:39

No, there are no blank lines between different test cases (if there would be blank lines, this would be written in the problem description).
Edit: your runtime errors in the case you assumed there are blank lines are because of this assumption. In the other two submissions you have in fact TLE (SPOJ unfortunately displays a runtime error instead).

Last edit: 2011-08-02 10:43:21
Balasubramanian: 2011-07-30 17:24:26

Well, can someone tell me if there will be a blank line between every set of test cases?

.::Manish Kumar::.: 2011-06-30 07:13:29

similar to ACTIV

Adrian Kuegel: 2011-06-24 07:24:10

@Eclipse: I am not an admin, but as the one who added the problem I can see your submission. The only thing I will tell you is that your submission fails on many test cases. You may try to develop a brute force solution and check it locally against your solution which got WA.

Last edit: 2011-06-24 07:24:37
hemezh: 2011-06-22 12:30:11

@ADMIN: Can u please give me a test case in which my submission is wrong? Please check 5277912.

Adrian Kuegel: 2011-06-22 07:50:53

See my comment on 2010-02-24 16:00:08

Archit Goel: 2011-06-18 21:19:23

i have the same question as seshadri.
Can it be assumed that the orders are given in ascending start time?

Adrian Kuegel: 2010-04-16 08:35:49

That looks quite funny. Of course you posted it earlier than me :-)

Added by:Adrian Kuegel
Time limit:3s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM Southwestern European Regional Contest, Paris 2003