Job Scheduling Problem

Moderate

0/80

Average time to solve is 15m

Contributed by

2 upvotes

Asked in companies

Problem statement

You are given a list of ‘N’ jobs which has to be performed. Each job is associated with a deadline and a profit if the job is completed before the deadline. Each job takes one unit of time to complete.

You are required to schedule the jobs in such a way that total profit will be maximized. Only one job can be scheduled at a time, and jobs can be scheduled at only integer moments of time greater than or equal to one.

For example-

Let there be three jobs ‘A’, ‘B’, and ‘C’-
•Profit and deadline associated with job ‘A’ being 20 and 1.
•Profit and deadline associated with job ‘B’ being 30 and 2.
•Profit and deadline associated with job ‘C’ being 40 and 2.

We will perform job ‘C’ at time t = 1 and job ‘B’ at time t = 2. The total profit will be 70. There is no other sequence of jobs which can fetch us a better overall profit.

Detailed explanation ( Input/output format, Notes, Images )

Input Format

The first line of input contains an integer ‘T’ denoting the number of test cases to run. Then the test case follows.

The first line of each test case contains a single space-separated integers ‘N’, denoting the total number of jobs.

The next ‘N’ lines contain two space-separated integers, 'deadline[i]' and 'profit[i]' denoting the deadline and the profit associated with the 'i-th' job.

Output Format :

For each test case, print the maximum profit after scheduling all the jobs in an optimal manner.

Output for each test case will be printed in a new line.

Note

You do not need to print anything; it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 5
1 <= N <= 10 ^ 3
1 <= deadline[i] <= N
1 <= profit[i] <= 10 ^ 9

Time Limit: 1 sec

Sample Input 1 :

Sample Output 1:

80
70

Explanation for Sample 1:

The optimal job scheduling for the first test case will be-

•Job 2 at time t = 1
•Job 3 at time t = 2

The total profit, in this case, will be 50 + 30 = 80.

The optimal job scheduling for the second test case will be-

•Job 2 at time t = 1
•Job 3 at time t = 2

The total profit, in this case, will be 40 + 30 = 70.

Sample Input 2 :

Sample Output 2 :

Console