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Three months later, the companion project, Mars Polar Lander, crashed when the jolt from the deployment of its parachute made the software respond as if the probe had touched the surface of the planet, and the software turned off the retro rockets Without the braking rockets, the craft fell from about 130 feet and was destroyed These two mission failures were due to problems with software, and wasted about $180 million (http://newsbbccouk/2/hi/science/nature/4522291stm) One can argue that the problems were not with the software but with the humans who created the software That way of looking at the problem focuses attention on the responsibility of the engineers That is why these failures are properly reviewed in a chapter on the ethics and the social issues of computing.

The quick sort is best for sorting large arrays of primitive types. The selection sort can be seen as a sort-on-output process: Insert the elements into an array as they are given, and then repeatedly select out the next largest element. The insertion sort can be seen as a sorton-input process: Repeatedly insert each element into its correct ordered position in an array, and then remove them in their array order. So the selection sort inserts the elements into the array in O(n) time and removes them in O(n 2 ), while the insertion sort inserts the elements into the array in O(n2) time and removes them in O(n). Both result in an O(n2) algorithm. The heap sort can be seen as a partial-sort-on-input-and-partial-sort-on-output process: Insert the elements into an array maintaining the (partially sorted) heap property, and then repeatedly select the first (which is the smallest) element and restore the heap property. Both the insertion process and the removal process have the same O(n lgn) running time, resulting in a total O(n lgn) running time. The Java API uses the merge sort to implement its Arrays.sort() methods for arrays of objects, and it uses the quick sort to implement its Arrays.sort() methods for arrays of primitive types. The shell sort, quick sort, and heap sort are unstable. The merge sort, radix sort, and bucket sort require extra array storage. The bubble sort, selection sort, insertion sort, merge sort, and quick sort work as well on external files of records. The shell sort, merge sort, quick sort, and bucket sort all would run significantly faster on a parallel computer. Matching the algorithms with their graphical output is shown in Figure 14.8.

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14.1 The O(n2) algorithm should take: a. 12.4 milliseconds (4 times as long) to run on the 400-element array. b. 124 seconds (40,000 times as long) to run on the 40,000-element array. That s about 2 minutes. This answer can be computed algebraically as follows. The running time t is proportional to n2, so there is some constant c for which t = c n2. If it takes t = 3.1 milliseconds to sort n = 200 elements, then (3.1 milliseconds) = c (200 elements)2, so c = (3.1 milliseconds)/(200 elements)2 = 0.0000775 milliseconds/element2. Then, for n = 40,000, t = c n2 = (0.0000775 milliseconds/ element2) (40,000 elements)2 = 124,000 milliseconds = 124 seconds. The O(n lg n) algorithm should take 1.24 seconds (400 times as long) to run on the 40,000-element array. This answer can be computed algebraically. The running time t is proportional to nlgn, so there

With software controlling pacemakers, automobile engine controls, antilock brake systems, missile targeting, medical equipment, driverless transports, elevators, robotic equipment, and industrial processes, when software fails, the results can be fatal One example is the overexposure to radiation suffered by cancer patients in Panama during 2000 During November of 2000, 28 people being treated for cancer at the National Cancer Institute in Panama were accidentally exposed to much more radiation than prescribed At least five died of the experience, and many of the others risked serious radiation-related complications from excessive exposure to radiation, according the the US FDA (http://wwwfdagov/cdrh/ocd/panamaradexphtml, July 6, 2001) When investigated, the cause turned out to be an erroneous software algorithm in the Multidata software controlling the Theratronics Cobalt-60 machine.

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