Download Fig1.f.Stack and queue visualized as linked structures

1.5 FUNDAMENTALS OF DATA STRUCTURES
Since most of the algorithms operate on the data , particular ways of arranging the data
play a critical role in the design & analysis of algorithms. A data structure can be defined as a
particular way of arrangement of data. The expression ``data structure'', however, is usually
used to refer to more complex ways of storing and manipulating data, such as arrays, stacks,
queues etc. We begin by discussing the simplest, but one of the most useful data structures,
namely the array.
ARRAY
Recall that an array is a named collection of homogeneous items An item’s place within
the collection is called an index. The index is an integer between 0 & 1.If there is no ordering on
the items in the container, we call the container unsorted, If there is an ordering, we call the
container sorted. The size of the array is given by max length. Every item in the array can be
accessed in the same constant amount of time.
Fig 1.b.
Linked list:
A linked list consists of head & node,A node consists of two fields.data & pointer.The
pointer points to the next data .The time to acces any data is variable & is dependent on the
position of the data in the list.
Fig 1.c.
Stacks:
Stacks are known as LIFO (Last In, First Out) lists. The last element inserted will be the
first to be retrieved, using Push and Pop
Push
–
Add an element to the top of the stack
Pop
–
Remove the element at the top of the stack
Fig 1.d
QUEUES: Accessing the elements of queues follows a FIFO (First In, First Out) order
The first element inserted will be the first to be retrieved, using Enqueue and Dequeue
•
Enqueue :Add an element after the rear of the queue
•
Dequeue Remove the element at the front of the queue
Fig 1.e.
Fig1.f.Stack and queue visualized as linked structures
Graphs
A data structure that consists of a set of nodes and a set of edges that relate the nodes to each
other.Undirected graph A graph in which the edges have no direction Directed graph (Digraph)
A graph in which each edg e is directed from one vertex to another (or the same) vertex. An
undirected graph G is a pair (V,E), where V is a finite set of points called vertices and E is a finite
set of edges.
An edge e ∈ E is an unordered pair (u,v), where u,v ∈ V.
In a directed graph, the edge e is an ordered pair (u,v). An edge (u,v) is incident from vertex u and
is incident to vertex v.
A path from a vertex v to a vertex u is a sequence <v0,v1,v2,…,vk> of vertices where v0
= v, vk = u, and (vi, vi+1) ∈ E for I = 0, 1,…, k-1.
The length of a path is defined as the number of edges in the path
Fig1.g. A directed undirected graph.
Graph Properties -- Acyclicity
Cycle
–
A simple path of a positive length that starts and ends a the same vertex.
Acyclic graph
•
–
A graph without cycles
–
DAG (Directed Acyclic Graph)
Paths and Connectivity Paths
– A path from vertex u to v of a graph G is defined as a sequence of adjacent (connected
by an edge) vertices that starts with u and ends with v.
Simple paths: All edges of a path are distinct.
Path lengths: the number of edges, or the number of vertices – 1.
Connected graphs
– A graph is said to be connected if for every pair of its vertices u and v there is a path
from u to v.
Connected component
-The maximum connected subgraph of a given graph
Graph Representation : A graph is represented by
•
Adjacency matrix
-- n x n boolean matrix if |V| is n.
–
The element on the ith row and jth column is 1 if there’s an edge from ith vertex
to the jth vertex; otherwise 0.
–
•
The adjacency matrix of an undirected graph is symmetric.
Adjacency linked lists
A collection of linked lists, one for each vertex, that contain all the vertices adjacent to the
list’s vertex
Fig1.h.Graph representation.