(i) Consider the greedy algorithm for interval scheduling which picks the compatible interval that finishes as soon as possible. This gives an optimal solution for the problem of finding the maximum number of intervals. Does the corresponding algorithm using latest start time find an optimal solution? (That is, consecutively schedules compatible jobs in descending order of latest start time.) If YES, provide an informal argument, and discuss if it constructs the same schedule? If NO, provide a counterexample to show where the heuristics breaks down.

(ii) Is the optimal job schedule obtained for Interval Partitioning problem always unique? If YES, provide an informal argument. If NO, provide a counterexample.