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3b). If Bobby is deleted from the list, however, we need to move up all the elements that follow to fill in the space—or do we? 3(c). 3d). In an array-based implementation, we do not actually remove the element; instead, we cover it up with the element that previously followed it (if the list is sorted) or the element in the last position (if the list is unsorted). Finally, we decrement length. Because the preconditions for DeleteItem state that an item with the same key is definitely present in the list, we do not need to test for the end of the list.
7(a) shows the values of first, last, and midPoint during the first iteration. In this iteration, “bat” is compared with “dog,” the value in info[midpoint]. Because “bat” is less than (comes before) “dog,” last becomes midPoint – 1 and first stays the same. 7(b) shows the situation during the second iteration. This time, “bat” is compared with “chicken,” the value in info[midpoint]. Because “bat” is less than (comes before) “chicken,” last becomes midPoint – 1 and first again stays the same. 7c), midPoint and first are both 0.
3 Abstract Data Type Sorted List info[middle]. Because “bat” is less than “cat,” last becomes midPoint – 1. Now that last is less than first, the process stops; found is false. The binary search is the most complex algorithm that we have examined so far. 1 shows first, last, midPoint, and info[midpoint] for searches of the items “fish,” “snake,” and “zebra,” using the same data as in the previous example. 1 carefully. 1 Iteration Trace of the Binary Search Algorithm Iteration first item: fish First Second Third item: snake First Second Third Fourth item: zebra First Second Third Fourth Fifth last midPoint info[midPoint] Terminating Condition 0 6 6 10 10 7 5 8 6 dog horse fish found is true 0 6 9 10 10 10 10 10 5 8 9 10 dog horse rat snake found is true 0 6 9 10 11 10 10 10 10 10 5 8 9 10 dog horse rat snake last < first Notice that the loop never executes more than four times.