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
lxy2000: 2022-04-27 10:38:12

This problem is so easy!

4444: 2021-05-15 13:15:10

Solved using LIS pattern in DP.
O(N^2) complexity got AC.

it_uchi: 2021-01-06 19:54:05

AC. Easy. Even though my approach was correct. I got WA i overlook a part of input.

distructo: 2020-12-29 10:38:59

Remember the end and start of two events can be same

abhishen99: 2020-12-16 17:31:38

easy peasy ....

soranaimanas: 2020-08-19 09:30:42

Thanks @csals I did the same mistake.

sarodesparsh: 2020-07-13 14:30:06

Nice problem.. AC in one go

Last edit: 2020-07-13 14:30:50
csals: 2020-07-07 21:45:25

The 2nd column is duration not end time. Wasted 1 hr !!

aditya2020: 2020-06-17 20:22:47

If anyone doesn't get on geeksofgeeks. Really good explanation is given and good understanding of this problem's category gets formed.

Last edit: 2020-06-17 20:23:07
vineetjai: 2019-10-24 12:04:59

nice problem..

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