Job Scheduling with Deadlines in DSA Java - 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 deadline

↓

If slot found, assign job to slot

↓

Repeat for all jobs

↓

Output scheduled jobs and total profit

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

Execution Sample

DSA Java

Job[] jobs = {
  new Job('A', 2, 100),
  new Job('B', 1, 19),
  new Job('C', 2, 27),
  new Job('D', 1, 25),
  new Job('E', 3, 15)
};

Defines jobs with id, deadline, and profit to schedule for maximum profit.

Execution Table

Step	Job Considered	Sorted Order	Slot Checked	Slot Status	Action	Scheduled Slots	Total Profit
1	A	A(100), C(27), D(25), B(19), E(15)	Slot 2	Free	Assign A to slot 2	[_, A, _]	100
2	C	A(100), C(27), D(25), B(19), E(15)	Slot 2	Occupied	Check slot 1 Free, Assign C to slot 1	[C, A, _]	127
3	D	A(100), C(27), D(25), B(19), E(15)	Slot 1	Occupied	No free slot before deadline 1	[C, A, _]	127
4	B	A(100), C(27), D(25), B(19), E(15)	Slot 1	Occupied	No free slot before deadline 1	[C, A, _]	127
5	E	A(100), C(27), D(25), B(19), E(15)	Slot 3	Free	Assign E to slot 3	[C, A, E]	142

💡 All jobs considered, scheduling complete.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	Final
Scheduled Slots	[_, _, _]	[_, A, _]	[C, A, _]	[C, A, _]	[C, A, _]	[C, A, E]	[C, A, E]
Total Profit	0	100	127	127	127	142	142

Key Moments - 3 Insights

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

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

Why are jobs D and B not scheduled even though they have deadlines?

At their deadline slots (slot 1), the slot is already occupied (rows 3 and 4), and no earlier slot is free, so they cannot be scheduled without losing profit.

How does sorting jobs by profit affect the schedule?

Sorting by profit descending (row 1) ensures we try to schedule the most profitable jobs first, increasing the chance to maximize total profit.

Visual Quiz - 3 Questions

Look at the execution_table at step 2, which slot is assigned to job C?

A Slot 2

B Slot 1

C Slot 3

D No slot assigned

💡 Hint

Check the 'Slot Checked' and 'Action' columns at step 2 in execution_table.

At which step does the total profit first reach 127?

A Step 1

B Step 3

C Step 2

D Step 5

💡 Hint

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

If job E had a deadline of 1 instead of 3, what would happen to the final scheduled slots?

A Job E would not be scheduled because slot 1 is occupied

B Job E would be assigned to slot 1, replacing job C

C Job E would be assigned to slot 2

D Job E would be assigned to slot 3 anyway

💡 Hint

Refer to variable_tracker and execution_table rows 2 and 5 about slot availability.

Concept Snapshot

Job Scheduling with Deadlines:
- Sort jobs by profit descending.
- For each job, assign to latest free slot before deadline.
- If no slot free, skip job.
- Result: maximize total profit.
- Slots represent time units; one job per slot.

Full Transcript

Job Scheduling with Deadlines is a method to maximize profit by scheduling jobs within their deadlines. We start by sorting jobs from highest to lowest profit. Then, for each job, we try to place it in the latest available time slot before its deadline. If that slot is taken, we check earlier slots. If no slot is free, we skip that job. This way, we fill slots with the most profitable jobs first, ensuring maximum total profit. The example shows jobs A, C, and E scheduled successfully, while D and B are skipped due to no free slots. The total profit sums the profits of scheduled jobs.

Practice

1. What is the main goal of the Job Scheduling with Deadlines problem?

easy

A. Maximize the number of jobs scheduled regardless of profit

B. Minimize the number of jobs scheduled

C. Schedule jobs in the order they appear without considering deadlines

D. Maximize the total profit by scheduling jobs before their deadlines

Solution

1. Step 1: Understand the problem objective

   The problem aims to schedule jobs so that each job finishes before its deadline to earn profit.

2. Step 2: Identify the optimization goal

   We want to maximize total profit, not just count or order jobs.

3. Final Answer:

   Maximize the total profit by scheduling jobs before their deadlines -> Option D

4. Quick Check:

   Goal = Maximize profit [OK]

Hint: Focus on maximizing profit within deadlines [OK]

Common Mistakes:

• Thinking it's about scheduling all jobs
• Ignoring profit values
• Scheduling jobs without deadline checks

2. Which of the following Java code snippets correctly sorts an array of jobs by their profit in descending order?

easy

A. Arrays.sort(jobs, (a, b) -> a.profit - b.profit);

B. Arrays.sort(jobs, Comparator.comparingInt(j -> j.deadline));

C. Arrays.sort(jobs, (a, b) -> b.profit - a.profit);

D. Arrays.sort(jobs);

Solution

1. Step 1: Identify sorting by profit descending

   To sort descending by profit, compare b.profit - a.profit.

2. Step 2: Check lambda syntax correctness

   Arrays.sort(jobs, (a, b) -> b.profit - a.profit); uses (a, b) -> b.profit - a.profit which sorts descending.

3. Final Answer:

   Arrays.sort(jobs, (a, b) -> b.profit - a.profit); -> Option C

4. Quick Check:

   Descending profit sort = Arrays.sort(jobs, (a, b) -> b.profit - a.profit); [OK]

Hint: Use (b.profit - a.profit) for descending sort [OK]

Common Mistakes:

• Using a.profit - b.profit for descending order
• Sorting by deadline instead of profit
• Using default sort without comparator

3. Given the following jobs with (id, deadline, profit):
Job[] jobs = { new Job('a', 2, 100), new Job('b', 1, 19), new Job('c', 2, 27), new Job('d', 1, 25), new Job('e', 3, 15) };
What is the maximum profit achievable by scheduling these jobs before their deadlines?

medium

A. 142

B. 185

C. 100

D. 115

Solution

1. Step 1: Sort jobs by profit descending

   Sorted: a(100,2), d(25,1), c(27,2), b(19,1), e(15,3)

2. Step 2: Schedule jobs greedily before deadlines

   Schedule 'a' at slot 2, 'c' at slot 1 (slot 2 taken), 'e' at slot 3. Total profit = 100 + 27 + 15 = 142.

3. Final Answer:

   142 -> Option A

4. Quick Check:

   Profit sum = 142 [OK]

Hint: Schedule highest profit jobs first in latest free slot [OK]

Common Mistakes:

• Scheduling jobs without sorting by profit
• Overlapping jobs in same slot
• Ignoring deadlines

4. Identify the error in the following Java code snippet for job scheduling:

Arrays.sort(jobs, (a, b) -> a.profit - b.profit);
boolean[] slot = new boolean[maxDeadline + 1];
for (Job job : jobs) {
  for (int j = job.deadline; j > 0; j--) {
    if (!slot[j]) {
      slot[j] = true;
      totalProfit += job.profit;
      break;
    }
  }
}

medium

A. Sorting should be in descending order of profit

B. Slot array size should be maxDeadline, not maxDeadline + 1

C. Inner loop should run from 1 to job.deadline, not backward

D. No error, code is correct

Solution

1. Step 1: Check sorting order

   Sorting by a.profit - b.profit sorts ascending, but we need descending to maximize profit.

2. Step 2: Verify scheduling logic

   The slot array and inner loop correctly find latest free slot before deadline.

3. Final Answer:

   Sorting should be in descending order of profit -> Option A

4. Quick Check:

   Profit descending sort needed [OK]

Hint: Sort jobs by profit descending to maximize total profit [OK]

Common Mistakes:

• Sorting ascending by profit
• Incorrect slot array size off by one
• Loop direction confusion

5. You have jobs with deadlines and profits:
Job[] jobs = { new Job('x', 4, 70), new Job('y', 1, 80), new Job('z', 1, 30), new Job('w', 2, 100), new Job('v', 3, 40) };
Using the job scheduling algorithm, which jobs will be scheduled to maximize profit and what is the total profit?

hard

A. Jobs w, y, x scheduled; Total profit = 250

B. Jobs y, w, v, x scheduled; Total profit = 290

C. Jobs y, w, x scheduled; Total profit = 250

D. Jobs y, w, v scheduled; Total profit = 220

Solution

1. Step 1: Sort jobs by profit descending

   Sorted: w(100,2), y(80,1), x(70,4), v(40,3), z(30,1)

2. Step 2: Schedule jobs greedily in latest free slot before deadline

   Schedule y at slot 1, w at slot 2, v at slot 3, x at slot 4. z cannot be scheduled (slot 1 taken). Total profit = 80+100+40+70=290.

3. Final Answer:

   Jobs y, w, v, x scheduled; Total profit = 290 -> Option B

4. Quick Check:

   Profit sum = 290 [OK]

Hint: Schedule highest profit jobs in latest free slots first [OK]

Common Mistakes:

• Scheduling jobs ignoring deadlines
• Not choosing latest free slot
• Missing highest profit jobs