Job Scheduling

Easy
0/40
1 upvote
Asked in company
Dell Technologies

Problem statement

You are given a list of ‘N’ jobs which are to be performed. Each job can be characterized by three parameters-

• Start Time, denoting the start time of the job.
• End Time, denoting the end time of the job.
• Profit associated with the job.

You are required to schedule the jobs in such a way that total profit will be maximized.

Note: 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’-
• Start time, End time and profit associated with job ‘A’ being 1, 1 and 30.
• Start time, End time and profit associated with job ‘B’ being 1, 2 and 40.
• Start time, End time and profit associated with job ‘C’ being 3, 4 and 30.

We will perform job ‘B’ at time t = 1 and job ‘C’ at time t = 3. 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 jobes

The next ‘N’ lines contain three space separated integers, start[i], end[i] and profit[i] denoting the start time, end time 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 <= start[i] <= 10^5
1 <= end[i] <=10^5
start[i] <= end[i] 
1 <= profit[i] <= 10^5

Time Limit: 1sec
Sample Input 1 :
2
3
1 2 10
2 3 50
3 4 30
3
1 2 20
3 4 30
5 6 40
Sample Output 1:
50
90

Explanation for Sample 1:

The optimal job scheduling for the first test case will be-
• Job 2 at time t = 2

The total profit in this case will be 50.

The optimal job scheduling for the second test case will be-
• Job 1 at time t = 1
• Job 2 at time t = 3
• Job 3 at time t = 5
The total profit in this case will be 20 + 40 + 30 = 90.
Sample Input 2 :
1
5
1 2 100
1 1 19
1 2 27
1 1 25
1 3 15
Sample Output 2 :
100
Hint

Can we use some recursive approach to solve this problem?

Approaches (3)
Recursive Approach

We can sort all the jobs according to their finish times. For each job, we will find the maximum profit both by including it in our answer and excluding it using recursion and return a maximum of the two.

 

The algorithm will be-

  • We will sort the jobs according to their finish times.
  • We call a recursion keeping current job ‘currJob’ as the parameter of our recursion. We start the recursion from the job which has the maximum finish time.
  • In each recursive call, we will-
    • We recur for maximum profit, excluding the current job ‘currJob’.
    • We now do the following:
      • We find the latest job which finishes in less time than the ‘currJob’. Let that job be ‘optJob’.
      • We include the profit of ‘currJob’ in our answer and recur for ‘optJob’.
    • We return the maximum of the two cases
Time Complexity

O(N*2^N), where N is the number of jobs.

 

The size of the recursion tree for each recursive call will be O(2^N). For each ‘currJob’ we are finding out the ‘optJob’ in O(N) time complexity. Hence, overall time complexity will be O(N*2^N).

Space Complexity

O(2^N), where N is the number of jobs.

 

The space complexity due to the recursion stack will be O(2^N).

Code Solution
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Job Scheduling
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