Job Scheduling with Deadlines in DSA C - Execution Trace

Concept Flow - Job Scheduling with Deadlines

Start: List of Jobs with Deadlines and Profits

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Sort Jobs by Profit Descending

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Initialize Time Slots as Free

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For Each Job in Sorted List

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Find Latest Free Slot Before Deadline

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Assign Job to Slot

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Repeat for All Jobs

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Output Scheduled Jobs and Total Profit

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End

The flow sorts jobs by profit, then tries to schedule each job in the latest free slot before its deadline, skipping if no slot is free.

Execution Sample

DSA C

struct Job { int id; int deadline; int profit; };
// Jobs: {id:1, d:2, p:100}, {id:2, d:1, p:19}, {id:3, d:2, p:27}
// Schedule jobs to maximize profit within deadlines

This code schedules jobs by sorting them by profit and placing each in the latest available slot before its deadline.

Execution Table

Step	Job Considered (id, deadline, profit)	Action	Slot Status (index: job_id)	Profit Accumulated
1	Job 1 (d=2, p=100)	Check slot 2 (free), assign job 1	1: -, 2: 1	100
2	Job 3 (d=2, p=27)	Check slot 2 (occupied), check slot 1 (free), assign job 3	1: 3, 2: 1	127
3	Job 2 (d=1, p=19)	Check slot 1 (occupied), no free slot, skip job 2	1: 3, 2: 1	127
4	All jobs considered	Scheduling complete	1: 3, 2: 1	127

💡 All jobs processed or no free slots before deadlines

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
slots	[-, -]	[-, 1]	[3, 1]	[3, 1]	[3, 1]
profit	0	100	127	127	127

Key Moments - 2 Insights

Why do we check the latest slot before the deadline instead of the earliest?

Checking the latest slot (see Step 1 and 2 in execution_table) allows earlier slots to remain free for other jobs with earlier deadlines, maximizing total profit.

Why is Job 2 skipped even though it has a deadline of 1?

At Step 3, slot 1 is already occupied by Job 3, so no free slot is available before Job 2's deadline, so it is skipped.

Visual Quiz - 3 Questions

Look at the execution_table at Step 2, which slot does Job 3 get assigned to?

A Slot 2

B Slot 1

C No slot assigned

D Both slots 1 and 2

💡 Hint

Check the 'Action' and 'Slot Status' columns at Step 2 in execution_table

At which step does the total profit reach 127?

A Step 2

B Step 1

C Step 3

D Step 4

💡 Hint

Look at the 'Profit Accumulated' column in execution_table

If Job 2 had a deadline of 3 instead of 1, what would happen at Step 3?

A Job 2 would replace Job 3 in slot 1

B Job 2 would still be skipped

C Job 2 would be assigned to slot 3

D Job 2 would be assigned to slot 1

💡 Hint

Consider slot availability and deadline when assigning jobs as shown in execution_table

Concept Snapshot

Job Scheduling with Deadlines:
- Sort jobs by descending profit
- For each job, assign it to the latest free slot before its deadline
- Skip if no slot is free
- Maximizes total profit within deadlines
- Uses a simple array to track slot assignments

Full Transcript

Job Scheduling with Deadlines is about choosing jobs to maximize profit without missing deadlines. We start with a list of jobs, each with a deadline and profit. First, we sort jobs by profit from highest to lowest. Then, for each job, we try to place it in the latest free time slot before its deadline. If no slot is free, we skip that job. We keep track of which slots are occupied and the total profit earned. This method ensures the best profit by filling slots starting from the latest possible time, leaving earlier slots for other jobs. The example shows three jobs: Job 1 with deadline 2 and profit 100, Job 3 with deadline 2 and profit 27, and Job 2 with deadline 1 and profit 19. Job 1 is assigned to slot 2, Job 3 to slot 1, and Job 2 is skipped because slot 1 is taken. The total profit is 127. This approach uses simple arrays and loops, making it easy to implement and understand.