Data Structures and Algorithm Analysis in C - SVS

Structures, Algorithm Analysis: CHAPTER 3: LISTS, STACKS, AND QUEUES
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Figure 3.24 Buckets after first step of radix sort
8 729
1 216 27
0 512 125 343 64
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Figure 3.25 Buckets after the second pass of radix sort
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27
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0 125 216 343 512 729
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Figure 3.26 Buckets after the last pass of radix sort
As an example, we could sort all integers that are representable on a computer
(32 bits) by radix sort, if we did three passes over a bucket size of 2 11 . This
algorithm would always be O(n) on this computer, but probably still not as
efficient as some of the algorithms we shall see in Chapter 7, because of the
high constant involved (remember that a factor of log n is not all that high, and
this algorithm would have the overhead of maintaining linked lists).
Multilists
Our last example shows a more complicated use of linked lists. A university with
40,000 students and 2,500 courses needs to be able to generate two types of
reports. The first report lists the class registration for each class, and the
second report lists, by student, the classes that each student is registered for.
The obvious implementation might be to use a two-dimensional array. Such an array
would have 100 million entries. The average student registers for about three
courses, so only 120,000 of these entries, or roughly 0.1 percent, would actually
have meaningful data.
What is needed is a list for each class, which contains the students in the
class. We also need a list for each student, which contains the classes the
student is registered for. Figure 3.27 shows our implementation.
mk:@MSITStore:K:\Data.Structures.and.Algorithm.Analysis.in.C.chm::/...
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2006-1-27