Job Scheduling with Deadlines in DSA Typescript - Execution Trace

Concept Flow - Job Scheduling with Deadlines

Start with list of jobs

↓

Sort jobs by profit descending

↓

Initialize schedule slots as empty

↓

For each job in sorted list

↓

Find latest free slot before job deadline

↓

If slot found, assign job to slot

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Repeat for all jobs

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Output scheduled jobs and total profit

Sort jobs by profit, then assign each to the latest free slot before its deadline to maximize total profit.

Execution Sample

DSA Typescript

interface Job {
  id: string;
  deadline: number;
  profit: number;
}

// 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	Current Job	Sorted Jobs	Slot Checked	Slot Assigned	Schedule State	Total Profit
1	Start	[J1(2,100), J2(1,19), J3(2,27), J4(1,25), J5(3,15)]	-	-	[null, null, null]	0
2	Pick J1(2,100)	[J1(2,100), J3(2,27), J4(1,25), J2(1,19), J5(3,15)]	Slot 2	Slot 2	[null, J1, null]	100
3	Pick J3(2,27)	[J3(2,27), J4(1,25), J2(1,19), J5(3,15)]	Slot 2 (occupied), Slot 1	Slot 1	[J3, J1, null]	127
4	Pick J4(1,25)	[J4(1,25), J2(1,19), J5(3,15)]	Slot 1 (occupied)	No slot	[J3, J1, null]	127
5	Pick J2(1,19)	[J2(1,19), J5(3,15)]	Slot 1 (occupied)	No slot	[J3, J1, null]	127
6	Pick J5(3,15)	[J5(3,15)]	Slot 3	Slot 3	[J3, J1, J5]	142
7	End	-	-	-	[J3, J1, J5]	142

💡 All jobs processed or no free slots available for remaining jobs.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
schedule	[null, null, null]	[null, J1, null]	[J3, J1, null]	[J3, J1, null]	[J3, J1, null]	[J3, J1, J5]	[J3, J1, J5]
totalProfit	0	100	127	127	127	142	142

Key Moments - 2 Insights

Why do we check slots from the job's deadline backwards?

Checking slots backward ensures we place the job as late as possible before its deadline, leaving earlier slots free for other jobs, as shown in steps 3 and 6.

Why can't some jobs be scheduled even if there are empty slots?

If all slots before a job's deadline are occupied, the job cannot be scheduled, like in steps 4 and 5 where slot 1 is already taken.

Visual Quiz - 3 Questions

Look at the execution table at Step 3. Which slot was finally assigned to job J3?

A Slot 3

B Slot 2

C Slot 1

D No slot assigned

💡 Hint

Check the 'Slot Assigned' column at Step 3 in the execution table.

At which step does the total profit first reach 127?

A Step 3

B Step 4

C Step 2

D Step 6

💡 Hint

Look at the 'Total Profit' column in the execution table for the value 127.

If job J5 had a deadline of 1 instead of 3, what would happen to the schedule at Step 6?

A J5 would be assigned to Slot 1

B J5 would not be assigned any slot

C J5 would be assigned to Slot 3

D J5 would replace J3 in Slot 1

💡 Hint

Refer to how slots are assigned before deadlines in the execution table and variable tracker.

Concept Snapshot

Job Scheduling with Deadlines:
- Sort jobs by profit descending.
- For each job, find latest free slot before deadline.
- Assign job to that slot if available.
- Maximize total profit by greedy placement.
- Slots represent time units; no overlaps allowed.

Full Transcript

Job Scheduling with Deadlines is a method to maximize profit by scheduling jobs within their deadlines. We start with a list of jobs, each having 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 available slot before its deadline. If the slot is free, we assign the job there; if not, we check earlier slots. This process continues until all jobs are checked. The schedule shows which jobs fit in which slots, and the total profit sums the profits of scheduled jobs. Some jobs may not fit if all slots before their deadlines are taken. This greedy approach ensures maximum profit by prioritizing high-profit jobs and placing them as late as possible to leave room for others.