[Solved] You are given a list of jobs where each job has a start time, an end time, and a profit.... Which algorithmic approach guarantees an optimal solution for this problem? | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Maximum Profit in Job Scheduling

You are given a list of jobs where each job has a start time, an end time, and a profit. You want to schedule jobs to maximize total profit such that no two jobs overlap. Which algorithmic approach guarantees an optimal solution for this problem?

ADynamic programming with jobs sorted by end time and binary search to find compatible jobs

BPure brute force recursion checking all subsets of jobs

CGreedy algorithm that always picks the job with the earliest end time

DDynamic programming based on sorting jobs by start time and using prefix sums

Step-by-Step Solution

Step 1: Understand job scheduling constraints
The problem requires selecting non-overlapping jobs to maximize profit, which is a classic weighted interval scheduling problem.
Step 2: Identify the optimal approach
Sorting jobs by end time allows binary searching for the last compatible job, enabling a DP solution that builds optimal profit incrementally.
Final Answer:
Option A -> Option A
Quick Check:
Greedy fails on overlapping jobs with higher profit; DP with binary search handles all cases optimally [OK]

Quick Trick: Sort by end time and use DP with binary search [OK]

Common Mistakes:

MISTAKES

Assuming greedy by earliest end time always works
Sorting by start time only
Trying brute force without pruning

Trap Explanation:

PITFALL

Greedy by earliest end time looks plausible but fails when a later job yields more profit without overlap.

Interviewer Note:

CONTEXT

Tests if candidate recognizes the weighted interval scheduling pattern and the need for binary search in DP.

Master "Maximum Profit in Job Scheduling" in Dynamic Programming: Knapsack

3 interactive learning modes - each teaches the same concept differently

Try It Solution Trace

More Dynamic Programming: Knapsack Quizzes

Which algorithmic approach guarantees an optimal solution for this problem?

Step 1: Understand job scheduling constraints

Step 2: Identify the optimal approach

Final Answer:

Quick Check:

Want More Practice?