worksheet 13: Sorted List Sets Name:
Worksheet 13: Sorted List Sets
An earlier lesson examined sorted vectors. Remember that there were two
important reasons to keep vectors in order. One is so we could use binary search
to perform a fast searching operation. But the second was that two sorted vectors
could be rapidly merged into a third.
There is no equivalent to binary search for a list. That is, even if a list is ordered,
searching still requires walking through the entire list. But the idea that two lists
can be rapidly merged into a third is still applicable. As with the vector, simply
walk down both collections in sequence, at each step copying the smallest
element into a new list:
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
We can use this insight to make a much faster Set abstraction. Recall from
Lesson 24 that the naive implementations of set union, intersection and
difference are each O(n2). In this lesson you will make a container that is much
faster. We will build on the list abstraction you created in Lessons 34 and 36.
The simplest operation to understand is intersection. To form an intersection
simply walk through the two lists, forming a new list that will contain the
intersection. If an element is found in both, add it the new intersection list.
Otherwise if an element is found in only one of the collections, ignore it.
An Active Learning Approach to Data Structures using C 1
