Job Scheduling with Deadlines in DSA Rust - Cheat Sheet & Quick Revision

Recall & Review

beginner

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

To schedule jobs so that the maximum number of jobs are completed before their deadlines, maximizing total profit or count.

beginner

In Job Scheduling with Deadlines, what does each job typically have?

Each job has a deadline by which it must be completed and a profit or value earned if completed on time.

intermediate

Why do we sort jobs by profit in descending order in the greedy approach?

Sorting by profit ensures we try to schedule the most valuable jobs first to maximize total profit.

intermediate

How do we find a time slot for a job in the greedy algorithm?

We try to assign the job to the latest available slot before its deadline to keep earlier slots free for other jobs.

advanced

What data structure can help efficiently find free time slots for jobs?

A disjoint set (union-find) or an array to track free slots can be used to quickly find available time slots.

What is the first step in the greedy job scheduling algorithm?

A Assign all jobs to the first slot

B Sort jobs by deadline in ascending order

C Sort jobs by profit in descending order

D Schedule jobs randomly

Sorting jobs by profit ensures we consider the most valuable jobs first.

If a job's deadline is 3, which time slots can it be assigned to?

A Any slot from 1 to 3

B Any slot after 3

C Only slot 3

D Only slot 1

Jobs must be completed before or on their deadline, so slots 1, 2, or 3 are valid.

What happens if no free slot is available before a job's deadline?

A The job is scheduled anyway

B The job is skipped

C The deadline is extended

D The job is split into smaller jobs

If no slot is free before the deadline, the job cannot be scheduled.

Which algorithmic approach is commonly used for Job Scheduling with Deadlines?

A Greedy algorithm

B Dynamic programming

C Divide and conquer

D Backtracking

Greedy approach is efficient and effective for this problem.

What is the time complexity of sorting jobs by profit if there are n jobs?

A O(n^2)

B O(n)

C O(log n)

D O(n log n)

Sorting typically takes O(n log n) time.

Explain the greedy approach to solve Job Scheduling with Deadlines.

Think about scheduling the most valuable jobs first and placing them as late as possible.

Describe how to find a free time slot for a job with a given deadline.

Start from the deadline and move backward to find a free slot.

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