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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.

CHAP. 9]

For the ampli er of Fig. 3-10, show that if the source internal impedance Ri is not negligible, but Ri ( RB R1 kR2 , then the low-frequency cuto point is given by !L hie Ri hfe 1 RE RE CE hie Ri

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

Show that, for the ampli er of Fig 3-10 as described in Problem 85, if RB ) RE hie , then the current-gain ratio becomes independent of frequency In the ampli er of Fig 3-10, let CC ! 1; CE 100 F; RE 20 k ; hie 100 ; hfe 75, RC RL 2 k , R1 2 k , and R2 20 k Determine (a) the low-frequency current gain, (b) the midfrequency current gain, and (c) the low-frequency cuto point Ans: a 3:11; b 35:54; c 5:71 rad/s In the ampli er of Problem 86, let Ri 500 and all else remain unchanged Determine the value of the emitter bypass capacitor required to ensure that fL 200 Hz Compare your result with that of Problem 86 to see that consideration of the source internal impedance allows the use of a smaller bypass capacitor.

CHAP. 14]

In any case, the US law provides serious penalities for both harmless hacking and computer fraud. The Computer Fraud and Abuse Act was first passed in 1986, and it was amended in 1994, 1996, and 2001. Accessing a government computer without authorization, and communicating any information with respect to national defense or foreign relations to anyone not otherwise authorized, carries a penalty of a large fine and imprisonment for up to 20 years. Accessing the computer of any financial institution when one is not authorized to do so can be punished with up to 10 years in prison, and a large fine. Simply obtaining the information is a crime, whether one does anything with that information or not. Trafficking in password information can also draw a 10-year prison term. Simply damaging a computer, for instance by releasing a computer virus, can be punished with 5 years in prison. Even causing damage by accident while improperly accessing another computer can be punished with a year in prison! Many sections of the ACM Code of Ethics appropriately warn against unauthorized access of another s computer. These include sections 1.2, 1.3, 1.7, and 2.8, as well as: 1.8 Honor confidentiality. 2.3 Know and respect existing laws pertaining to professional work. 3.3 Acknowledge and support proper and authorized uses of computing resources.