Job Scheduling with Deadlines in DSA Rust - 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

↓

Repeat for all jobs

↓

Output scheduled jobs and total profit

Jobs are sorted by profit, then each job is placed in the latest free slot before its deadline to maximize total profit.

Execution Sample

DSA Rust

struct Job { id: char, deadline: usize, profit: usize }

let mut jobs = vec![
  Job {id: 'a', deadline: 2, profit: 100},
  Job {id: 'b', deadline: 1, profit: 19},
  Job {id: 'c', deadline: 2, profit: 27},
  Job {id: 'd', deadline: 1, profit: 25},
  Job {id: 'e', deadline: 3, profit: 15},
];

This code defines jobs with deadlines and profits to be scheduled for maximum profit.

Execution Table

Step	Job Considered	Sorted Order	Slot Checked	Slot Assigned	Schedule State	Total Profit
1	a	a	Slot 2 (free)	Yes	[_, a, _]	100
2	c	a, c	Slot 2 (occupied), Slot 1 (free)	Yes	[c, a, _]	127
3	d	a, c, d	Slot 1 (occupied)	No	[c, a, _]	127
4	b	a, c, d, b	Slot 1 (occupied)	No	[c, a, _]	127
5	e	a, c, d, b, e	Slot 3 (free)	Yes	[c, a, e]	142
6	End	-	-	-	[c, a, e]	142

💡 All jobs considered; no more jobs to schedule.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	Final
jobs_sorted	[]	[a]	[a, c]	[a, c, d]	[a, c, d, b]	[a, c, d, b, e]	[a, c, d, b, e]
schedule_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 - 2 Insights

Why do we try to place a job in the latest free slot before its deadline instead of the earliest?

Placing a job in the latest free slot before its deadline leaves earlier slots free for other jobs with earlier deadlines, maximizing total scheduled jobs and profit. See execution_table steps 1 and 2 where jobs are placed in latest slots.

Why are some jobs skipped even though they have profit?

If all slots before a job's deadline are occupied, the job cannot be scheduled. For example, jobs 'd' and 'b' in steps 3 and 4 find no free slot and are skipped.

Visual Quiz - 3 Questions

Look at the execution_table at step 2, which slot was assigned to job 'c'?

A Slot 3

B Slot 1

C Slot 2

D No slot assigned

💡 Hint

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

At which step does the total profit reach 142?

A Step 3

B Step 4

C Step 5

D Step 6

💡 Hint

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

If job 'e' had a deadline of 1 instead of 3, what would happen in the schedule?

A Job 'e' would be skipped due to no free slot

B Job 'e' would be scheduled in slot 1

C Job 'e' would be scheduled in slot 3 anyway

D Total profit would increase

💡 Hint

Refer to variable_tracker and execution_table steps where slot availability is checked before deadlines.

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 available.
- Maximizes total profit by scheduling highest profit jobs first.
- Schedule represented as array of slots with assigned jobs.

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 no slot is free, we skip that job. This approach ensures we use time slots efficiently to get the most profit. The example shows jobs with different deadlines and profits. We assign jobs step-by-step, updating the schedule and total profit. Some jobs are skipped if no slot is free. The final schedule and profit are shown after all jobs are considered.

Practice

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

easy

A. Schedule jobs in the order they arrive without considering deadlines

B. Minimize the number of jobs scheduled

C. Maximize total profit by scheduling jobs before their deadlines

D. Maximize the number of jobs scheduled regardless of profit

Solution

1. Step 1: Understand the problem goal

   The problem asks to schedule jobs so that each job finishes before its deadline and the total profit is maximized.

2. Step 2: Identify the objective

   Maximizing total profit means choosing jobs with higher profit and fitting them before their deadlines.

3. Final Answer:

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

4. Quick Check:

   Goal = Maximize profit before deadlines [OK]

Hint: Focus on profit maximization within deadlines [OK]

Common Mistakes:

• Thinking the goal is to schedule all jobs
• Ignoring deadlines when scheduling
• Trying to minimize jobs instead of maximizing profit

2. Which Rust data structure is best suited to keep track of free time slots when implementing job scheduling with deadlines?

easy

A. Vec (vector) with boolean flags for slots

B. HashMap with job IDs as keys

C. LinkedList of jobs sorted by profit

D. BinaryHeap for storing jobs by deadline

Solution

1. Step 1: Identify the need for tracking free slots

   We need to know which time slots are free to schedule jobs before their deadlines.

2. Step 2: Choose a data structure for slot tracking

   A vector of booleans can mark each slot as free or occupied efficiently.

3. Final Answer:

   Vec (vector) with boolean flags for slots -> Option A

4. Quick Check:

   Use Vec<bool> to track free slots [OK]

Hint: Use a boolean vector to mark free/occupied slots [OK]

Common Mistakes:

• Using HashMap which is unnecessary for fixed slots
• Using LinkedList which is inefficient for slot checking
• Using BinaryHeap which is for priority, not slot tracking

3. What is the output of the following Rust code snippet that schedules jobs with deadlines and profits?

struct Job { id: char, deadline: usize, profit: usize }

fn job_scheduling(jobs: &mut Vec<Job>) -> Vec<char> {
    jobs.sort_by(|a, b| b.profit.cmp(&a.profit));
    let max_deadline = jobs.iter().map(|j| j.deadline).max().unwrap_or(0);
    let mut slots = vec![false; max_deadline];
    let mut result = Vec::new();

    for job in jobs.iter() {
        for slot in (0..job.deadline).rev() {
            if !slots[slot] {
                slots[slot] = true;
                result.push(job.id);
                break;
            }
        }
    }
    result
}

fn main() {
    let mut jobs = vec![
        Job { id: 'A', deadline: 2, profit: 100 },
        Job { id: 'B', deadline: 1, profit: 19 },
        Job { id: 'C', deadline: 2, profit: 27 },
        Job { id: 'D', deadline: 1, profit: 25 },
        Job { id: 'E', deadline: 3, profit: 15 },
    ];
    let scheduled = job_scheduling(&mut jobs);
    println!("{:?}", scheduled);
}

medium

A. ['A', 'B', 'E']

B. ['A', 'D', 'E']

C. ['B', 'D', 'E']

D. ['A', 'C', 'E']

Solution

1. Step 1: Sort jobs by profit descending

   Sorted jobs: A(100,2), C(27,2), D(25,1), B(19,1), E(15,3)

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

   Schedule A at slot 1 (0-based), C at slot 0, E at slot 2. D and B cannot be scheduled as slots 0 and 1 are taken.

3. Final Answer:

   ['A', 'C', 'E'] -> Option D

4. Quick Check:

   Jobs scheduled = ['A', 'C', 'E'] [OK]

Hint: Sort by profit, assign latest free slot before deadline [OK]

Common Mistakes:

• Scheduling jobs in arrival order instead of profit order
• Assigning earliest slot instead of latest free slot
• Ignoring slot availability and deadlines

4. Identify the bug in this Rust code snippet for job scheduling with deadlines:

fn schedule_jobs(jobs: &mut Vec<(char, usize, usize)>) -> Vec<char> {
    jobs.sort_by(|a, b| b.2.cmp(&a.2));
    let max_deadline = jobs.iter().map(|j| j.1).max().unwrap_or(0);
    let mut slots = vec![false; max_deadline];
    let mut result = Vec::new();

    for job in jobs.iter() {
        for slot in 0..job.1 {
            if !slots[slot] {
                slots[slot] = true;
                result.push(job.0);
                break;
            }
        }
    }
    result
}

medium

A. Jobs are sorted by profit ascending instead of descending

B. Inner loop should iterate slots in reverse order to assign latest slot

C. Result vector should store job profits instead of IDs

D. Slots vector size is incorrect, should be max_deadline + 1

Solution

1. Step 1: Check sorting order

   Jobs are sorted by profit descending (b.2.cmp(&a.2)), which is correct to prioritize high-profit jobs.

2. Step 2: Check slot assignment loop

   The loop iterates from 0 to deadline-1, assigning the earliest available slot. The correct approach assigns the latest free slot before the deadline to leave earlier slots for future jobs with tighter deadlines, so the loop should be reversed using (0..job.1).rev().

3. Final Answer:

   Inner loop should iterate slots in reverse order to assign latest slot -> Option B

4. Quick Check:

   Assign latest free slot by looping backwards [OK]

Hint: Loop slots backward to assign latest free slot [OK]

Common Mistakes:

• Assigning earliest slot instead of latest free slot
• Using wrong slot vector size (off-by-one)
• Storing wrong data in result vector

5. Given jobs with deadlines and profits: A(4, 70), B(1, 80), C(1, 30), D(2, 100), E(3, 40), how many jobs can be scheduled to maximize profit and what is the total profit? Use the job scheduling with deadlines approach.

hard

A. 4 jobs, total profit 290

B. 3 jobs, total profit 250

C. 3 jobs, total profit 220

D. 4 jobs, total profit 240

Solution

1. Step 1: Sort jobs by profit descending

   Sorted: D(100,2), B(80,1), A(70,4), E(40,3), C(30,1)

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

   Schedule B at slot 0 (deadline 1), D at slot 1 (deadline 2), E at slot 2 (deadline 3), A at slot 3 (deadline 4). C cannot be scheduled as slot 0 is taken.

3. Step 3: Calculate total profit

   Profits: B(80) + D(100) + E(40) + A(70) = 290

4. Final Answer:

   4 jobs, total profit 290 -> Option A

5. Quick Check:

   4 jobs scheduled, profit = 290 [OK]

Hint: Sort by profit, assign latest free slot before deadline [OK]

Common Mistakes:

• Scheduling fewer jobs than possible
• Ignoring slot availability and deadlines
• Adding profits of unscheduled jobs