ImprovedBreakpointReversalsort (? 1 while b( > 0 2 f has a decreasing strip Among all possible reversals, choose reversal ? that minimizes b(r) else Choose a reversal ? that flips an increasing strip in ? 7output 8 return 2. The if-test in line 2 of the ImprovedBreakpointReversalSort algorithm ensures that the algorithm never gets stuck in a situation were there is no way to eventually decrease the number of breakpoints. Again using ?-3 4 6 5 8 1 7 2, construct a permutation ? where this if-test is needed. (Find a step that ImprovedBreakpointReversalSort might have ended up with where there are no decreasing strips, and no reversal that reduces the number of breakpoints). If you found such a step in (1), you can use that one. You do not need to solve it from this step on, just give an example of such a permutation. ImprovedBreakpointReversalsort (? 1 while b( > 0 2 f has a decreasing strip Among all possible reversals, choose reversal ? that minimizes b(r) else Choose a reversal ? that flips an increasing strip in ? 7output 8 return 2. The if-test in line 2 of the ImprovedBreakpointReversalSort algorithm ensures that the algorithm never gets stuck in a situation were there is no way to eventually decrease the number of breakpoints. Again using ?-3 4 6 5 8 1 7 2, construct a permutation ? where this if-test is needed. (Find a step that ImprovedBreakpointReversalSort might have ended up with where there are no decreasing strips, and no reversal that reduces the number of breakpoints). If you found such a step in (1), you can use that one. You do not need to solve it from this step on, just give an example of such a permutation