Consider the following "minimize gaps" interval scheduling problem: Given is a global start time S and finish time F. Given also is a set of n intervals where the i-th interval starts at time si and ends at time fi, s 0 is the smallest possible. Select both intervals and discard overlapping intervals. Recursively do the same selection process with intervals that finish at or before si: the recursive call will have Snew = S and Fnew = si. Similarly, recursively do the same selection process with intervals that start at or after fj: now Snew = f; and Fnew = F. If there is no such pair of intervals, select a single interval that minimizes the gap between S and F (do not make any further recursive calls). None of these strategies works all the time. Find a counterexample for each strategy. In other words, for each strategy, find a set of intervals and S and F so that the strategy does not produce an optimal solution, highlight intervals selected by the strategy and state the corresponding gap time, and highlight intervals in an optimal solution (one that minimizes the overall gap time) and state the corresponding gap time. Consider the following "minimize gaps" interval scheduling problem: Given is a global start time S and finish time F. Given also is a set of n intervals where the i-th interval starts at time si and ends at time fi, s 0 is the smallest possible. Select both intervals and discard overlapping intervals. Recursively do the same selection process with intervals that finish at or before si: the recursive call will have Snew = S and Fnew = si. Similarly, recursively do the same selection process with intervals that start at or after fj: now Snew = f; and Fnew = F. If there is no such pair of intervals, select a single interval that minimizes the gap between S and F (do not make any further recursive calls). None of these strategies works all the time. Find a counterexample for each strategy. In other words, for each strategy, find a set of intervals and S and F so that the strategy does not produce an optimal solution, highlight intervals selected by the strategy and state the corresponding gap time, and highlight intervals in an optimal solution (one that minimizes the overall gap time) and state the corresponding gap time