Job Scheduling with Deadlines in DSA C - Execution Trace

Concept Flow - Job Scheduling with Deadlines

Start: List of Jobs with Deadlines and Profits

↓

Sort Jobs by Profit Descending

↓

Initialize Time Slots as Free

↓

For Each Job in Sorted List

↓

Find Latest Free Slot Before Deadline

↓

Assign Job to Slot

↓

Repeat for All Jobs

↓

Output Scheduled Jobs and Total Profit

↓

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.

Practice

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

easy

A. Maximize the number of jobs without considering 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 within their deadlines

Solution

1. Step 1: Understand the problem objective

   The problem asks to schedule jobs so that the total profit is maximized while respecting each job's deadline.

2. Step 2: Identify the goal

   The goal is to select jobs that fit within their deadlines and yield the highest total profit.

3. Final Answer:

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

4. Quick Check:

   Goal = Maximize profit within deadlines [OK]

Hint: Focus on maximizing profit while meeting deadlines [OK]

Common Mistakes:

• Ignoring deadlines and scheduling all jobs
• Trying to minimize jobs instead of maximizing profit
• Scheduling jobs without considering profit

2. Which of the following is the correct way to sort jobs by profit in descending order in C?

easy

A. sort(jobs, n, sizeof(Job), compareProfitDesc);

B. sort(jobs, jobs+n, compareProfitDesc);

C. qsort(jobs, n, sizeof(Job), compareProfitDesc);

D. qsort(jobs, n, sizeof(Job), compareProfitAsc);

Solution

1. Step 1: Identify the sorting function in C

   In C, qsort is used for sorting arrays with a comparator function.

2. Step 2: Check the correct parameters

   The correct call is qsort(array, number_of_elements, size_of_element, comparator_function). qsort(jobs, n, sizeof(Job), compareProfitDesc); matches this.

3. Final Answer:

   qsort(jobs, n, sizeof(Job), compareProfitDesc); -> Option C

4. Quick Check:

   Use qsort with correct parameters in C [OK]

Hint: Use qsort with array, count, size, comparator in C [OK]

Common Mistakes:

• Using C++ sort() in C code
• Passing wrong size or count parameters
• Using ascending comparator instead of descending

3. Given jobs with profits and deadlines: {Job1: profit=20, deadline=2}, {Job2: profit=15, deadline=2}, {Job3: profit=10, deadline=1}, {Job4: profit=5, deadline=3}, what is the maximum total profit after scheduling?

medium

A. 40

B. 45

C. 50

D. 35

Solution

1. Step 1: Sort jobs by profit descending

   Order: Job1(20,2), Job2(15,2), Job3(10,1), Job4(5,3)

2. Step 2: Schedule jobs greedily within deadlines

   Schedule Job1 at slot 2, Job2 at slot 1 (since slot 2 taken), Job4 at slot 3. Job3 cannot be scheduled (slot 1 taken). Total profit = 20+15+5=40.

3. Final Answer:

   40 -> Option A

4. Quick Check:

   Greedy scheduling = 40 profit [OK]

Hint: Schedule highest profit jobs first within deadlines [OK]

Common Mistakes:

• Scheduling jobs ignoring deadlines
• Overlapping jobs in same slot
• Counting all jobs without checking slot availability

4. Identify the error in this C code snippet for job scheduling:

for (int i = 0; i < n; i++) {
  int slot = jobs[i].deadline - 1;
  while (slot >= 0 && result[slot] != -1) {
    slot--;
  }
  if (slot >= 0) {
    result[slot] = i;
  }
}

medium

A. The loop should start from the last job, not the first

B. The array 'result' is not initialized to -1 before use

C. The condition 'slot >= 0' should be 'slot > 0'

D. The deadline should not be decremented by 1

Solution

1. Step 1: Check initialization of result array

   The array 'result' stores scheduled jobs. It must be initialized to -1 to mark free slots.

2. Step 2: Identify missing initialization

   The code snippet does not show initialization of 'result' to -1, which can cause incorrect scheduling.

3. Final Answer:

   The array 'result' is not initialized to -1 before use -> Option B

4. Quick Check:

   Initialize result array to -1 before scheduling [OK]

Hint: Always initialize scheduling array slots to -1 [OK]

Common Mistakes:

• Forgetting to initialize result array
• Wrong loop direction for scheduling
• Incorrect slot boundary conditions

5. You have 4 jobs: J1(profit=100, deadline=2), J2(profit=19, deadline=1), J3(profit=27, deadline=2), J4(profit=25, deadline=1). Using the job scheduling algorithm, what is the maximum profit and which jobs are scheduled?

hard

A. Profit=127; Jobs scheduled: J1 at slot 2, J3 at slot 1

B. Profit=144; Jobs scheduled: J1 at slot 2, J3 at slot 1, J2 at slot 1

C. Profit=125; Jobs scheduled: J1 at slot 1, J4 at slot 2

D. Profit=100; Jobs scheduled: J1 only

Solution

1. Step 1: Sort jobs by profit descending

   Order: J1(100,2), J3(27,2), J4(25,1), J2(19,1)

2. Step 2: Schedule jobs greedily within deadlines

   Schedule J1 at slot 2, J3 at slot 1 (slot 1 free). J4 and J2 cannot be scheduled as slot 1 is taken. Total profit = 100 + 27 = 127.

3. Final Answer:

   Profit=127; Jobs scheduled: J1 at slot 2, J3 at slot 1 -> Option A

4. Quick Check:

   Greedy scheduling = 127 profit [OK]

Hint: Schedule highest profit jobs first, fill latest slots [OK]

Common Mistakes:

• Scheduling multiple jobs in same slot
• Ignoring deadlines when scheduling
• Adding profits of unscheduled jobs