FUNDAMENTALS: DATA STRUCTURES & ALGORITHMS
(GLOSSARY OF TERMS)
DATA:
values (quantification) to record properties, attributes and states of the real world,
using some representation which reflects systematic quantification.
INFORMATION: facts, properties, relationships etc. used as the basis for reasoning, interpretation
and/or calculation of multiple Data.
KNOWLEDGE: principles, rules, understanding, intelligence used to make deductions and identify
relationships between multiple data and/o ADTs.
DATA TYPE: a set of data values (instances) and a set of operations permitted on the values. All
data values in the set therefore has the same properties
STRUCTURED DATA TYPE: each instance has several components. The components are
related by some rules/framework e.g. sets, sequences, trees, graphical or
combination of these definitions
ABSTRACTION: facility to choose only those features required (levels of abstraction) to fulfil the
stated objectives (controls/reduces complexity of the description).
COMPONENT (ELEMENT): one of several instances (of any Data Type or ADT) that makes up
the set constituting an instance of the ADT in which they are members. Where there
are several components of the same ADT, then they are organised in a structure
such as a SET or LIST.
ABSTRACT DATA TYPE: permits the definition of the components i.e. the other ADTs used and
the operations required by the ADT; it separates what (specification) from the how
(implementation).
OBJECT:
can be used to refer to an instance of any ADT or any CLASS. Any OBJECT
implementation has the following attributes –
NAME
TYPE NAME
REFERENCE
VALUE(S)
(Identifier) (ADT or CLASS name) (address in memory) (from the domain set)
REFERENCE VALUE: of object names in Java are object references only, with storage for the
object data values being created when required through the new operator
SET:
A collection of instances of ADTs or ADTs themselves that have no relationship
with each other except that they are members of the set. A set therefore has no
structure. A set data type in invariably used initially as the data type for the
several components of the same type when the internal structure of the ADT
has yet to be decided
SEQUENCE: (A sequence of length 0 is empty. A sequence of length N  1 of elements from a
set T is the ordered pair (Sn-1, t) where Sn-1 is a sequence of length n-1 of elements
from T and t is an element of T.
LIST:
is a sequence with properties of first/last and predecessor/successor and each
element has a on-to-one relationship with elements of an ordinal data type reflecting
positional information; implemented using static/dynamic arrays(consecutively
stored components) or linked lists using object references.
INDEX LIST: a LIST ordered by position, by keyvalue, by time etc. but with the following
important differences Elements (components) must all be of the same ADT. Each ADT element
(component) can contain a component for positional information - index value i.e.
of type int or an object reference. This relates it to an instance of some other ADT
located elsewhere (usually stored as a List ADT).
45
STACK:
An ADT to which you can add (PUSH) any ADT instance but the last instance
added is recovered with a retrieve (POP) operation; LAST IN FIRST OUT.
QUEUE:
An ADT to which you can add (ENQUEUE) any ADT instance but the instance that
is retrieved by a get operation (SERVE) is that element that had been there the
longest: FIRST IN FIRST OUT
HASH LIST: Where the elements are mapped onto the address space of a list by generating an
address (index) derived from applying a Hash Function to the element(s)
identifying key. It simulates the properties of a SET ADT. Methods needed to
handle the COLLISIONS – where the Hash Function generates the same index from
two different component identifying keys.
GRAPH:
an ordered pair G = <V,E> where V is a finite non-empty set of vertices or nodes
and E is a set of edges (each being an unordered pair of vertices). Other properties
include – Digraph, Path, Cycle – starting and finishing node in a path is the same
node.
TREE:
finite connected graph
BINARY TREE: a finite set of nodes that is either empty or consists of a root and two binary
subtrees which are disjoint and are called the left band right subtrees. Traversals of
the tree include – depth first, breadth first, pre-order, in-order (symmetric) and
post-order.
BINARY SEARCH TREE: as for a binary tree except that for any node ni having a key ki all the
nodes in the left subtree to the node ni have a key value “less than” ki and all nodes
in the right subtree have a key value “greater than” ki
AVL TREE: A height balanced tree where the height difference between the left and right
subtrees to any node does not differ by more than 1.
HIGHER ORDER TREES: where there can be more than two subtrees to any one or more nodes
in the tree. Various representations including conversion to/from a Binary Tree and
generating Sequential Enumerated Lists
MULTI-WAY TREES (B-TREES): a method of organising large trees by grouping nodes
(subtrees) into blocks of consecutively stored keys and links to lower level blocks.
The Order of the B-tree determines the minimum number of consecutive keys that
a block must contain; and no more than twice the Order. This optimised the search
efficiency and storage utilisation. Insertion/Deletion are complex operations.
DIGRAPH: As for a graph except that the edges are ordered pairs of vertices (reflecting the
directionality of the edge). Matrices are a convenient way to represent the
properties of graphs/digraphs. Properties include – Adjacency, Precedence,
Succedence and Paths. Deriving the path matrix from the Adjacency matrix is an
important process. Traversals include – Depth-First, Breadth-First and Shortest
Path generating algorithms. Adjacency and Generaised Lists are other ways of
representing Graphs/Digraphs.
46