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Think about correctness (20 points) in class we discussed the interval scheduling problem: given a set i of jobs [s, e], where s is the start time and e > s is the end time, select a subset s of i containing a maximal number of non-overlapping jobs. (if you missed class that day, you can find examples and more discussion of this problem in section 1.2 of the text by skeina, available online through the isu library.) here is a proposed algorithm to solve this problem: start with an empty set s while i is nonempty find the job j such that the midpoint (s e) / 2 is earliest remove j from i remove all jobs from i that overlap j add j to the solution s decide whether the algorithm is correct. if you believe it is correct, give an informal explanation for why it works. if you believe it is incorrect, provide a test case on which it fails (counterexample).

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