What is the time complexity of Most Profit Assigning Work?

The optimal solution has a time complexity of O(nlogn + mlogm).

What data structures are used to solve Most Profit Assigning Work?

This problem uses Array, Two Pointers, Binary Search, Greedy, Sorting. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Most Profit Assigning Work?

Insight 1: Sorting the jobs by difficulty and the workers by ability allows for an efficient, greedy approach. Insight 2: Maintaining a running maximum profit of jobs that a worker *can* do is crucial to maximizing profit.

Which companies ask LeetCode 826. Most Profit Assigning Work in interviews?

This problem is frequently asked at DoorDash, NetEase.

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Most Profit Assigning Work - LeetCode 826 Solution

Most Profit Assigning Work - Complete Solution Guide

Most Profit Assigning Work is LeetCode problem 826, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You have n jobs and m workers. You are given three arrays: difficulty , profit , and worker where: difficulty[i] and profit[i] are the difficulty and the profit of the i th job, and worker[j] is the ability of j th worker (i.e., the j th worker can only complete a job with difficulty at most worker[j] ). Every worker can be assigned at most one job , but one job can be completed multiple times . For example, if three workers attempt the same job that pays $1 , then the total profit will be $3 .

Detailed Explanation

The problem asks us to assign jobs to workers to maximize the total profit. Each job has a difficulty and a profit associated with it. Each worker has an ability, meaning they can only perform jobs with a difficulty level less than or equal to their ability. A worker can only be assigned at most one job, but a job can be completed multiple times by different workers. The goal is to find the maximum possible total profit by optimally assigning jobs to workers.

Solution Approach

The solution sorts the jobs by difficulty and the workers by ability. It then iterates through the sorted workers. For each worker, it finds the most profitable job that the worker can do (i.e., the job's difficulty is less than or equal to the worker's ability). This is done by keeping track of the maximum profit seen so far from the jobs that the current worker can do. Once the most profitable job is found, its profit is added to the total profit. This greedy approach works because sorting allows us to efficiently find the best job for each worker without having to check all possible jobs for each worker.

Step-by-Step Algorithm

Step 1: Create an array of job pairs (difficulty, profit).
Step 2: Sort the job array by difficulty in ascending order.
Step 3: Sort the worker array in ascending order.
Step 4: Initialize total profit to 0.
Step 5: Initialize maximum profit to 0 (to track the max profit available for current worker).
Step 6: Initialize job index to 0.
Step 7: Iterate through the sorted worker array.
Step 8: For each worker, iterate through the sorted job array (starting from the last checked job index) to find the maximum profit job that worker can do.
Step 9: Update maximum profit with the maximum profit among jobs worker can do.
Step 10: Add the maximum profit to total profit for that worker's assignment.
Step 11: Return total profit.

Key Insights

Insight 1: Sorting the jobs by difficulty and the workers by ability allows for an efficient, greedy approach.
Insight 2: Maintaining a running maximum profit of jobs that a worker *can* do is crucial to maximizing profit.
Insight 3: The problem can be solved by iterating through the sorted workers and, for each worker, finding the most profitable job they are capable of doing.

Complexity Analysis

Time Complexity: O(nlogn + mlogm)

Space Complexity: O(n)

Topics

This problem involves: Array, Two Pointers, Binary Search, Greedy, Sorting.

Companies

Asked at: DoorDash, NetEase.

Most Profit Assigning Work | LeetCode 826

Medium

Array Two Pointers Binary Search Greedy Sorting

Time: O(nlogn + mlogm)Space: O(n)

Solution Code

Available in:

import java.util.Arrays;
import java.util.Comparator;

class Solution {
    public int maxProfitAssignment(int[] difficulty, int[] profit, int[] worker) {
        int n = difficulty.length;
        int[][] jobs = new int[n][2];
        for (int i = 0; i < n; i++) {
            jobs[i][0] = difficulty[i];
            jobs[i][1] = profit[i];
        }

        Arrays.sort(jobs, Comparator.comparingInt(a -> a[0]));
        Arrays.sort(worker);

        int total_profit = 0;
        int max_p = 0;
        int job_i = 0;

        for (int w : worker) {
            while (job_i < n && jobs[job_i][0] <= w) {
                max_p = Math.max(max_p, jobs[job_i][1]);
                job_i++;
            }

            total_profit += max_p;
        }

        return total_profit;
    }
}

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Problem Info

Description

Problem 826: Most Profit Assigning Work - Detailed explanation and solution approaches.

Topics

Array Two Pointers Binary Search Greedy Sorting

Companies

DoorDashNetEase

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:826

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

11 steps

1
Step 1: Create an array of job pairs (difficulty, profit).
2
Step 2: Sort the job array by difficulty in ascending order.
3
Step 3: Sort the worker array in ascending order.
4
Step 4: Initialize total profit to 0.
5
Step 5: Initialize maximum profit to 0 (to track the max profit available for current worker).
6
Step 6: Initialize job index to 0.
7
Step 7: Iterate through the sorted worker array.
8
Step 8: For each worker, iterate through the sorted job array (starting from the last checked job index) to find the maximum profit job that worker can do.
9
Step 9: Update maximum profit with the maximum profit among jobs worker can do.
10
Step 10: Add the maximum profit to total profit for that worker's assignment.
11
Step 11: Return total profit.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(nlogn + mlogm)

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is dominated by the sorting of the jobs and workers. The space complexity comes from the extra space used to create the `jobs` array, storing the difficulties and profits together as pairs. While the additional looping of the worker array is O(m) and inside that loop there is the potential to iterate over the jobs again O(n), because the index `job_i` of the jobs array is kept, overall this only visits each job once on average so the cost is amortized O(m+n) time. Therefore the most computationally expensive steps are the sorts.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Binary Search

After sorting jobs by difficulty, for each worker, perform a binary search to find the most difficult job they can do, then find the maximum profit among the jobs with difficulty up to that level.

Time: O(n log n + m log n), where n is the number of jobs and m is the number of workers.Space: O(n), same as the main approach.

Trade-offs: Binary search might be slightly slower than the two-pointer approach in the given constraints but becomes more efficient if the jobs are sorted more frequently than the workers.

✨

Key Insights

1Insight 1: Sorting the jobs by difficulty and the workers by ability allows for an efficient, greedy approach.
2Insight 2: Maintaining a running maximum profit of jobs that a worker *can* do is crucial to maximizing profit.
3Insight 3: The problem can be solved by iterating through the sorted workers and, for each worker, finding the most profitable job they are capable of doing.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Two Pointers

Using two indices to traverse data from different positions simultaneously.

Binary Search

Halving the search space each step. Like finding a word in a dictionary!

Greedy Algorithm

Making the best choice at each step without looking ahead.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: Empty `difficulty` or `profit` array. The code implicitly handles this case because the loops will not execute if the arrays are empty, and the initial profit will be 0, which is the correct behavior.
Edge case 2: Empty `worker` array. Similarly, the code will correctly return 0 profit.
Edge case 3: All workers can do all jobs. The algorithm correctly finds the job with the highest profit and assigns it to all workers, resulting in the maximum possible profit.
Edge case 4: No worker can do any job. The `max_p` will remain 0, and the total profit will also be 0.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not sorting the jobs and workers. Without sorting, the greedy approach will not work correctly, and the result will be incorrect.

✗Common mistake 2: Not keeping track of the maximum profit seen so far. For each worker, it's important to find the *most* profitable job they can do, not just any job.

✗Common mistake 3: Assigning the same job to multiple workers when it's more profitable to assign different jobs to workers. The algorithm addresses this by assigning the maximum available profit for each worker, not forcing all workers to take the exact same job.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Task assignment. Matching tasks (with varying difficulties and rewards) to workers (with varying skills) to maximize total reward.

🏦Real-world scenario 2: Resource allocation. Allocating resources (with varying costs and benefits) to projects (with varying requirements) to maximize overall benefit.

🎮Real-world scenario 3: Online advertising. Matching ads (with different bids and target audiences) to users (with different demographics and interests) to maximize advertising revenue.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: September 15, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 14

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 7

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

When is the two-pointer technique most effective?

Two pointers work best on sorted arrays or when searching for pairs/triplets that satisfy a condition. Common patterns include: moving pointers inward from both ends (like in two-sum variants), fast/slow pointers for cycle detection, or left/right pointers for partitioning.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Most Profit Assigning Work"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether two pointers techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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