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This is basically the weighted job scheduling problem.
This is the classic weighted interval scheduling problem. Sort jobs by end time, then use dynamic programming where dp[i] is the max profit considering jobs up to i. For each job, either skip it (dp[i-1]) or take it plus the best profit from jobs that end before its start (found via binary search).
Pro tip: Clarify the compatibility rule upfront: jobs that share an endpoint are compatible, so when finding the previous compatible job, use the largest end time <= current start time. Also, mention that sorting by end time is crucial for the DP to work correctly.
Restate the problem: given jobs with start, end, profit, find max profit from non-overlapping jobs. Confirm that sharing endpoints is allowed.
Sort the jobs in ascending order of their end times. This ordering ensures that when considering a job, all compatible jobs appear earlier in the list.
Let dp[i] be the maximum profit using jobs from 0 to i. For job i, find the latest job j < i such that end[j] <= start[i] (using binary search). Then dp[i] = max(dp[i-1], profit[i] + dp[j]).
Initialize dp[0] = profit[0]. Iterate i from 1 to n-1, compute dp[i] using the recurrence. Return dp[n-1] as the answer.
Time complexity: O(n log n) due to sorting and binary search. Space: O(n) for DP array. Discuss edge cases like empty input or single job.
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