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Maximum Profit in Job Scheduling
Certification: Advanced Level
Accuracy: 0%
Submissions: 0
Points: 20
Write a C++ program to find the maximum profit from non-overlapping job schedules, given start and end times and corresponding profits.
Example 1
- Input: startTime = [1,2,3,3] endTime = [3,4,5,6] profit = [50,10,40,70]
- Output: 120
- Explanation:
- Jobs at index 0 and 3 yield maximum profit without overlap.
- Job 0: Start at time 1, end at time 3, profit = 50
- Job 3: Start at time 3, end at time 6, profit = 70
- Total profit = 50 + 70 = 120
Example 2
- Input: startTime = [1,2,3,4,6] endTime = [3,5,10,6,9] profit = [20,20,100,70,60]
- Output: 150
- Explanation:
- Jobs at index 0, 3, and 4 yield maximum profit:
- Job 0: Start at time 1, end at time 3, profit = 20
- Job 3: Start at time 4, end at time 6, profit = 70
- Job 4: Start at time 6, end at time 9, profit = 60
- Total profit = 20 + 70 + 60 = 150
Constraints
- 1 ≤ startTime.length ≤ 5×10⁴
- startTime[i] < endTime[i] ≤ 10⁹
- 1 ≤ profit[i] ≤ 10⁴
- All jobs have distinct start times
- Time Complexity: O(n log n)
- Space Complexity: O(n)
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Solution Hints
- Sort jobs by start time to process them in chronological order
- Use dynamic programming to keep track of the maximum profit up to each job
- Implement binary search to find the latest non-overlapping job
- Consider using memoization to avoid redundant calculations
- The solution requires combining sorting, binary search, and dynamic programming techniques