1
CS261–DataStructures
Sorting Vectors
Vector: Variations
• There are some useful variations on the basic Vector data
structure
• Sorting vectors Æsort the vector elements (and keep it
sorted as elements are added,changed, and removed)
• Applications of sorting vectors
Search
• An unsorted vector requires a linear search
• Sorted vector can use the “Divide and Conquer” concept
Ant
0
Bird
1
Cat
2
Fox
4
Goat
5
Horse
6
Lion
7
Newt
8
Rat
9
Dog
3
Snake
10
Sorted Vectors
• Data abstraction:
– Store elements in anindexed data structure
– Uses binary searchto maintain order for insert and delete
public class SortedVector implements Sorted, Bag,
FindMin, FindNth,
SortAlgorithm {
protected Indexed data;
protected Comparator test;
public SortedVector() { test = new DefaultComparator();
data = new Vector(); }
public SortedVector(Comparator c)
{ test = c; data = new Vector(); }
public SortedVector(Indexed v, Comparator c)
{ test = c; sort(v); data = v; }
.
.
.
protected int binarySearch(Object key) { … }
}
Why use composition rather
than inheritance?
Binary Search
• Divide and conquer
• Easy to understand – difficult to program perfectly:
protected int binarySearch(Object key) {
int low = 0;
int high = data.size();
while (low < high) {
int mid = (low + high) / 2;
if (test.compare(data.elementAt(mid), key) < 0)
low=mid+1;
else
high = mid;
}
return low;
}
Sorted Vectors: Sorted Interface
public interface Sorted extends Collection {
// NO NEW METHODS.
}
• Sorted interface guarantees:
1. Implementation of the Collection methods – by calling t he
corresponding methods for data
2. When enumerated, elements will beordered from “smallest” to
“largest”
3. Traverse and count duplicates to determine frequency
• How do we know we’ll get an enumeration in order?
– Underlying vectoris maintained in sequence – i.e., elements are
put in their correct place
– An indexed enumeration produces elementsin the index order
