Maximum Profit in Job Scheduling

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.

If you choose a job that ends at time X you will be able to start another job that starts at time X.

Example 1:

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.

Example 2:

Input: startTime = [1,2,3,4,6], endTime = [3,5,10,6,9], profit = [20,20,100,70,60]
Output: 150
Explanation: The subset chosen is the first, fourth and fifth job.
Profit obtained 150 = 20 + 70 + 60.

Example 3:

Input: startTime = [1,1,1], endTime = [2,3,4], profit = [5,6,4]
Output: 6

Constraints:

• 1 <= startTime.length == endTime.length == profit.length <= 5 * 104
• 1 <= startTime[i] < endTime[i] <= 109
• 1 <= profit[i] <= 104

Approach

• We create a class for better handling

• Create list with job sorted by end time

• Use Tree Map dp to use methods like floorKey which returns greatest key less than equal to key and lastEntry which is mapping associated with greatest key

• Time Complexity: O(n log n)

  Sorting jobs: O(n log n)

  For each job: TreeMap.floorKey and put operations → O(log n)

  Total: O(n log n)

• Space Complexity: O(n)

  jobs list: O(n)

  TreeMap to store at most n entries: O(n)

class Solution {
    private class Job {
        int start, end, profit;
        Job(int s, int e, int p) {
            start = s;
            end = e;
            profit = p;
        }
    }
 
    public int jobScheduling(int[] startTime, int[] endTime, int[] profit) {
        List<Job> jobs = new ArrayList<>();
        for (int i = 0; i < startTime.length; i++) {
            jobs.add(new Job(startTime[i], endTime[i], profit[i]));
        }
 
        jobs.sort(Comparator.comparingInt(j -> j.end)); // sort by end time asc
        TreeMap<Integer, Integer> dp = new TreeMap<>();
        dp.put(0,0);
 
        for (Job job: jobs) {
            int prevTime = dp.floorKey(job.start);
            int currProfit = dp.get(prevTime) + job.profit;
 
            if (currProfit > dp.lastEntry().getValue()) {
                dp.put(job.end, currProfit);
            }
        }
 
        return dp.lastEntry().getValue();
    }
}