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Data Structures G5029
Kingsley Sage
Room 5C16, Pevensey III
© University of Sussex 2006
Lecture 5
Lecture 5
Order
–Arrays vs binary search
Generic methods
–The Comparable interface
Binary search trees
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Efficiency of Ordered Data Structures: Binary Search and Binary Search Trees, Study notes of Computers and Information technologies
The importance of order in data structures and the efficiency gains of searching in ordered sets. It covers the concept of binary search and binary search trees, providing examples and code snippets in java. The text also touches upon generic methods and the comparable interface.
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2010/2011
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Data Structures G
Kingsley Sage
Room 5C16, Pevensey III
[email protected]
© University of Sussex 2006
Lecture 5
Lecture 5
Order
– Arrays vs binary search
Generic methods
– The Comparable interface
Binary search trees
Order
Many data structures provide sorting and searching
routines.
The idea of sorting pre-supposes that the data items are
ordered in some way.
Searching does not pre-suppose an order, but it is quicker
to search for an item if the items have been previously
sorted.
Many data types have an intrinsic ordering (like integers).
Other orderings can be created e.g. ASCII values for
characters, lexicographical values for strings.
Order affects searching efficiency …
Efficiency of search
Let’s say we have an un-ordered set of N
integers. What is the computational complexity
associated with finding the largest one?
– We need to examine each one, so order N , or O(N).
And if the set of integers is ordered?
– It will be at one end of the set, so for array,
computational complexity is constant time k , but we do
need to factor in sorting the integers in the first place.
– What about for a linked list?
Generic methods
public interface Comparable {
public int compareTo(Object o);
The wrapper classes for Java primitive types all implement this
interface.
compareTo returns a negative integer, zero, or a positive integer
according to whether this object is less than, equal to, or greater
than the specified object o.
See the on-line course notes for information on implementing
compareTo for you own particular class.
Generic binary search
public static final boolean contains(Comparable item, Comparable[] array,int n) { int low = 0; int high = n-1; while (low <= high) { int mid = (low+high) / 2; int compare = item.compareTo(array[mid]); if (compare < 0) { high = mid – 1; } else if (compare > 0) { low = mid + 1; } else { return true; } } return false; }
We can use this generic approach for binary search …
Binary search trees
A binary tree is an important linked data structure.
- A binary tree is either empty, or else consist of some data item together with a left and right descendant binary tree.
- A binary search tree is a binary tree in which the value stored at each node of the tree is greater than the values stored in the left sub tree, and less than the values stored in the right sub tree.
Binary search trees
Could organise using lexicographical values
coldplay busted pink madonna U macy gray shakira LHS: value is “smaller” RHS: value is “larger” The concepts of “smaller” and “larger” are defined according to the data you are processing …
Empty trees and node trees
We can now start to implement a Java class for binary trees …
public abstract class SearchTree {
public static SearchTree empty() {
return new EmptyTree();
public abstract boolean isEmpty();
…more methods
From this base abstract class, we can build EmptyTree and a
NodeTree …
Empty trees and node trees
class EmptyTree extends SearchTree { protected boolean isEmpty() {} public boolean isEmpty() { return true; } … more methods } class NodeTree extends SearchTree { private Comparable data; private SearchTree left; private SearchTree right; protected NodeTree(Comparable item) { data = item; left = empty(); right = empty(); } public boolean isEmpty() { return false; } … more methods }