How do you solve Maximum Profit in Job Scheduling on LeetCode?

Maximum Profit in Job Scheduling (LeetCode #1235) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Sorting jobs by end time allows us to efficiently find non-overlapping jobs.

What is the time complexity of Maximum Profit in Job Scheduling?

The optimal solution for Maximum Profit in Job Scheduling runs in O(n log n) time and uses O(n) space. The complexity is O(n log n) due to the sorting step, and O(n) for the DP array, making it efficient for larger inputs.

What is the brute force solution for Maximum Profit in Job Scheduling?

The brute force approach for Maximum Profit in Job Scheduling is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking all possible subsets of jobs to find the maximum profit without overlapping jobs. This is straightforward but inefficient, as it explores every combination. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Profit in Job Scheduling?

Maximum Profit in Job Scheduling uses the following concepts: Array, Binary Search, Dynamic Programming, Sorting. The recommended patterns to study are: Dynamic Programming, Binary Search, Sorting.

What are the interview tips for Maximum Profit in Job Scheduling?

Always clarify the problem constraints and edge cases before diving into coding. Explain your thought process clearly while coding to demonstrate your understanding. Practice similar problems to recognize patterns and improve your problem-solving speed.

What are common mistakes when solving Maximum Profit in Job Scheduling?

Not considering the case where jobs can start immediately after another ends. Failing to sort jobs before applying dynamic programming.

#1235

Maximum Profit in Job Scheduling

Hard

ArrayBinary SearchDynamic ProgrammingSortingDynamic ProgrammingBinary SearchSorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

💡

Intuition

Time O(n log n)Space O(n)

The optimal approach uses dynamic programming combined with binary search. By sorting jobs by their end times and using a DP array to store maximum profits, we can efficiently find the best non-overlapping job combinations.

⚙️

Algorithm

4 steps

1Step 1: Create a list of jobs and sort it by end time.
2Step 2: Initialize a DP array where dp[i] represents the maximum profit up to job i.
3Step 3: For each job, use binary search to find the last non-overlapping job and update dp[i] accordingly.
4Step 4: Return the maximum value in the DP array.

solution.py16 lines

1# Full working Python code
2from bisect import bisect_right
3
4def maxProfit(startTime, endTime, profit):
5    jobs = sorted(zip(startTime, endTime, profit), key=lambda x: x[1])
6    n = len(jobs)
7    dp = [0] * n
8    for i in range(n):
9        dp[i] = jobs[i][2]  # profit of current job
10        # Find the last non-overlapping job
11        j = bisect_right([jobs[k][1] for k in range(n)], jobs[i][0]) - 1
12        if j != -1:
13            dp[i] += dp[j]
14        if i > 0:
15            dp[i] = max(dp[i], dp[i - 1])  # max profit up to i
16    return dp[-1]

ℹ

Complexity note: The complexity is O(n log n) due to the sorting step, and O(n) for the DP array, making it efficient for larger inputs.

1Sorting jobs by end time allows us to efficiently find non-overlapping jobs.
2Dynamic programming helps in building solutions incrementally by storing results of subproblems.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.