Worksheet 7: Sorted Vector Bag Name:
An Active Learning Approach to Data Structures using C
1
Worksheet 7: Sorted Vector Bag
Why would it make sense to store the elements of a Vector in sorted order? To
understand, ask yourself the following question. Suppose you were given a
telephone book and asked to find the number for an individual named Chris
Smith. Now suppose you were asked to find the name of the person who has
telephone number 543-7352. Which task is easier?
In an earlier class you encountered the
binary search
algorithm. The version
shown below takes as argument the value being tested, and returns in O(log n)
steps either the location at which the value is found,
or if it is not in the collection
the location the value can be inserted and still preserve order.
int binarySearch (EleType *data, int size, EleType testValue) {
int low = 0;
int high = size;
while (low < high) {
int mid = (low + high) / 2;
if (LT(data[mid], testValue))
low = mid + 1;
else
high = mid;
}
return low;
}
To get a feel for the binary search algorithm, try searching for the element 6 in
the following array. How many steps does it take? Then try searching for 7. What
position is returned? What happens if you perform an insert at that position?
Finally, try searching for the values 1 and 16. Again, ask what happens if you
perform a search for those elements.
2
4
5
6
8
9
11
15
Using the binary search algorithm, implement a Bag that maintains values in a
sorted vector. A Bag, you will remember, implements the three operations add,
contains, and remove. Describe
the asymptotic execution time for
each of the operations.
Notice that the VectorBag and the
SortedVectorBag implement exactly the same API. Under what circumstances
would you want to use a SortedVectorBag instead of a simple VectorBag?
VectorBag
SortedVectorBag
add
O(n)
contains
O(n)
remove
O(n)
