Leetcode #826: Most Profit Assigning Work
In this guide, we solve Leetcode #826 Most Profit Assigning Work in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
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 ith job, and worker[j] is the ability of jth worker (i.e., the jth worker can only complete a job with difficulty at most worker[j]).
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Two Pointers, Binary Search, Sorting
Intuition
The constraints hint that we can reason about two ends of the data at once, which is perfect for a two-pointer scan.
Moving one pointer at a time keeps the invariant intact and avoids nested loops.
Approach
Place pointers at the left and right ends and move them based on the comparison or target condition.
This yields a clean linear pass after any required sorting.
Steps:
- Set left and right pointers.
- Move a pointer based on the condition.
- Update the best answer while scanning.
Example
Input: difficulty = [2,4,6,8,10], profit = [10,20,30,40,50], worker = [4,5,6,7]
Output: 100
Explanation: Workers are assigned jobs of difficulty [4,4,6,6] and they get a profit of [20,20,30,30] separately.
Python Solution
class Solution:
def maxProfitAssignment(
self, difficulty: List[int], profit: List[int], worker: List[int]
) -> int:
worker.sort()
jobs = sorted(zip(difficulty, profit))
ans = mx = i = 0
for w in worker:
while i < len(jobs) and jobs[i][0] <= w:
mx = max(mx, jobs[i][1])
i += 1
ans += mx
return ans
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.