Leetcode #1235: Maximum Profit in Job Scheduling
In this guide, we solve Leetcode #1235 Maximum Profit in Job Scheduling 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
We have n jobs, where every job is scheduled to be done from startTime[i] to endTime[i], obtaining a profit of profit[i]. You're given the startTime, endTime and profit arrays, return the maximum profit you can take such that there are no two jobs in the subset with overlapping time range.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Array, Binary Search, Dynamic Programming, Sorting
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: startTime = [1,2,3,3], endTime = [3,4,5,6], profit = [50,10,40,70]
Output: 120
Explanation: The subset chosen is the first and fourth job.
Time range [1-3]+[3-6] , we get profit of 120 = 50 + 70.
Python Solution
class Solution:
def jobScheduling(
self, startTime: List[int], endTime: List[int], profit: List[int]
) -> int:
def dfs(i):
if i >= n:
return 0
_, e, p = jobs[i]
j = bisect_left(jobs, e, lo=i + 1, key=lambda x: x[0])
return max(dfs(i + 1), p + dfs(j))
jobs = sorted(zip(startTime, endTime, profit))
n = len(profit)
return dfs(0)
Complexity
The time complexity is , where is the number of jobs. The space complexity is O(1).
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.