What is the optimal time complexity of solving Job Sequencing?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Job Sequencing?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Job Sequencing?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Job Sequencing?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingEasy

Job Sequencing

Learn how to solve the 'Job Sequencing' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function job_scheduling(jobs) that takes a list of tuples jobs where each tuple is (job_id, deadline, profit). Each job takes 1 unit of time to complete. Find the maximum profit and the number of jobs completed, and return them as a tuple (job_count, max_profit).

Constraints

•1 <= len(jobs) <= 10^4
•1 <= deadline <= 100
•1 <= profit <= 1000

Examples

Example 1

Input

job_scheduling([(1, 4, 20), (2, 1, 10), (3, 1, 40), (4, 1, 30)])

Output

(2, 60)

Explanation

We can do job 3 at time 1 and job 1 at time 2. Total profit is 40 + 20 = 60.

Example 2

Input

job_scheduling([(1, 2, 100), (2, 1, 19), (3, 2, 27), (4, 1, 25), (5, 3, 15)])

Output

(3, 142)

Explanation

We can do job 1, 3, and 5 for a total profit of 100 + 27 + 15 = 142.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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