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

Recall & Review

beginner

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

To schedule jobs in such a way 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 gained 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 profitable jobs first to maximize total profit.

intermediate

What data structure is commonly used to keep track of free time slots in Job Scheduling with Deadlines?

An array or list representing time slots is used to mark which slots are free or occupied.

intermediate

Explain the greedy step to assign a job to a time slot.

For each job, starting from its deadline slot, check backward to find the latest free slot to schedule it.

What is the first step in the greedy algorithm for Job Scheduling with Deadlines?

A Schedule jobs with earliest deadline first

B Sort jobs by ascending deadline

C Assign jobs randomly

D Sort jobs by descending profit

Sorting jobs by descending profit helps prioritize scheduling the most valuable jobs first.

If a job's deadline is 3, which time slots do we check to schedule it?

A Slots 1 to 3, starting from 3 backwards

B Only slot 3

C Slots after 3

D Slots before 1

We check from the job's deadline backward to find the latest free slot before or on the deadline.

What happens if no free slot is found for a job before its deadline?

A The job is skipped

B The job is scheduled after deadline

C The job is scheduled anyway

D The job's deadline is extended

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

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

A O(n)

B O(n log n)

C O(log n)

D O(n^2)

Sorting n jobs by profit uses comparison-based sorting, which takes O(n log n) time.

Which of these is NOT a typical property of a job in Job Scheduling with Deadlines?

A Deadline

B Profit

C Duration longer than 1 unit

D Unique job ID

Typically, each job takes exactly 1 unit of time; longer durations require different scheduling approaches.

Describe the greedy approach to solve Job Scheduling with Deadlines.

Think about scheduling the most profitable jobs first and checking slots backward from deadline.

Explain why sorting jobs by profit helps maximize total profit in scheduling.

Consider what happens if you schedule low profit jobs first.

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 before their deadlines

Solution

1. Step 1: Understand the problem goal

   The problem asks to schedule jobs so that total profit is maximized while respecting deadlines.

2. Step 2: Identify the objective

   Scheduling jobs before their deadlines to get maximum profit is the main goal.

3. Final Answer:

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

4. Quick Check:

   Goal = Maximize profit with deadlines [OK]

Hint: Focus on maximizing profit within deadlines [OK]

Common Mistakes:

• Ignoring deadlines and scheduling all jobs
• Trying to minimize jobs instead of maximizing profit
• Scheduling jobs in input order without sorting

2. Which of the following TypeScript code snippets correctly declares a job interface with id, deadline, and profit properties?

easy

A. type Job = { id: string; deadline: string; profit: string }

B. class Job { id; deadline; profit; }

C. interface Job { id: number; deadline: number; profit: number; }

D. interface Job { id; deadline; profit; }

Solution

1. Step 1: Check correct TypeScript interface syntax

   interface Job { id: number; deadline: number; profit: number; } correctly declares an interface with typed properties.

2. Step 2: Identify incorrect options

   type Job = { id: string; deadline: string; profit: string } uses strings instead of numbers, class Job { id; deadline; profit; } is a class without types, interface Job { id; deadline; profit; } misses types.

3. Final Answer:

   interface Job { id: number; deadline: number; profit: number; } -> Option C

4. Quick Check:

   Correct interface syntax = interface Job { id: number; deadline: number; profit: number; } [OK]

Hint: Use interface with typed properties for job data [OK]

Common Mistakes:

• Using class without types for data structure
• Omitting types in interface properties
• Using wrong types like string for numeric fields

3. What will be the output of the following TypeScript code that schedules jobs to maximize profit?

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

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

function scheduleJobs(jobs: Job[]): string[] {
  jobs.sort((a, b) => b.profit - a.profit);
  const result: (string | null)[] = Array(jobs.length).fill(null);
  for (const job of jobs) {
    for (let j = Math.min(jobs.length, job.deadline) - 1; j >= 0; j--) {
      if (result[j] === null) {
        result[j] = job.id;
        break;
      }
    }
  }
  return result.filter(id => id !== null) as string[];
}

console.log(scheduleJobs(jobs));

medium

A. ['a', 'd', 'e']

B. ['a', 'c', 'e']

C. ['b', 'd', 'e']

D. ['a', 'b', 'c']

Solution

1. Step 1: Sort jobs by profit descending

   Sorted jobs: a(100), c(27), d(25), b(19), e(15).

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

   Job 'a' scheduled at slot 1 (deadline 2), 'c' at slot 0 (deadline 2), 'd' cannot fit before deadline 1 (slot 0 taken), 'b' cannot fit, 'e' scheduled at slot 2 (deadline 3).

3. Final Answer:

   ['a', 'c', 'e'] -> Option B

4. Quick Check:

   Scheduled jobs = ['a', 'c', 'e'] [OK]

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

Common Mistakes:

• Scheduling jobs in input order without sorting
• Assigning earliest slot instead of latest
• Ignoring deadline constraints

4. Identify the bug in the following TypeScript function for job scheduling and select the correct fix.

function scheduleJobs(jobs: Job[]): string[] {
  jobs.sort((a, b) => a.profit - b.profit);
  const result: (string | null)[] = Array(jobs.length).fill(null);
  for (const job of jobs) {
    for (let j = job.deadline - 1; j >= 0; j--) {
      if (result[j] === null) {
        result[j] = job.id;
        break;
      }
    }
  }
  return result.filter(id => id !== null) as string[];
}

medium

A. Sort jobs by profit descending instead of ascending

B. Initialize result array with zeros instead of null

C. Loop j from 0 to job.deadline - 1 instead of reverse

D. Remove the inner loop and assign jobs directly

Solution

1. Step 1: Analyze sorting order

   Jobs are sorted by profit ascending, which schedules low profit jobs first, reducing total profit.

2. Step 2: Correct sorting order

   Sorting by profit descending ensures high profit jobs are scheduled first for maximum profit.

3. Final Answer:

   Sort jobs by profit descending instead of ascending -> Option A

4. Quick Check:

   Profit descending sort fixes scheduling [OK]

Hint: Sort jobs by descending profit to fix scheduling [OK]

Common Mistakes:

• Sorting by ascending profit reduces total profit
• Changing loop direction incorrectly
• Using zero instead of null for empty slots

5. Given the following jobs with deadlines and profits, what is the maximum total profit achievable by scheduling jobs before their deadlines? Jobs: - Job1: deadline = 4, profit = 70 - Job2: deadline = 1, profit = 80 - Job3: deadline = 1, profit = 30 - Job4: deadline = 2, profit = 100 - Job5: deadline = 3, profit = 40 Select the correct maximum profit.

hard

A. 290

B. 210

C. 240

D. 230

Solution

1. Step 1: Sort jobs by profit descending

   Order: Job4(100), Job2(80), Job1(70), Job5(40), Job3(30).

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

   Job4 at slot 1 (deadline 2), Job2 at slot 0 (deadline 1), Job1 at slot 3 (deadline 4), Job5 at slot 2 (deadline 3), Job3 cannot fit (slot 0 taken).

3. Step 3: Calculate total profit

   100 + 80 + 70 + 40 = 290, but slots are 0-based: slots 0,1,2,3 used. Actually, Job2 (deadline 1) at slot 0, Job4 (deadline 2) at slot 1, Job5 (deadline 3) at slot 2, Job1 (deadline 4) at slot 3. Total profit = 100 + 80 + 40 + 70 = 290.

4. Step 4: Re-check options

   Confirm scheduling: slots 0:Job2, 1:Job4, 2:Job5, 3:Job1. All fit, total 290.

5. Final Answer:

   290 -> Option A

6. Quick Check:

   Max profit = 290 [OK]

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

Common Mistakes:

• Assuming all jobs fit without checking slots
• Adding profits of unscheduled jobs
• Misinterpreting deadlines as exact time slots