Download data structuer Lecture 1

DATA STRUCURES II
CSC 2302
QUIZ
1. What is Data Structure ?
2 . Mention the classifications of data structure
giving example of each .
3 . Briefly explain the following : Stack , Queue ,
and an array .
4 . Mention the operations that can be
performed on any linear data structure.
DATA STRUCTURE
• A data structure is an arrangement of data in a
computer’s memory .
• Arrays , Linked lists , queues , stacks , binary
trees are examples of common data
structures.
• Different data structures works well for a
diffferent purpose .
• Algorithms are used to manipulate data
contained in a given data structure.
Classification of data structures
• Data structure can be classified as either
Linear data structure or Non-linear data
structures
• A data stucture is said to be linear if all its
elements form a sequence or linear list e.g
array , queue , stack and Linked list
• A data structure is non-linear if its element
does not form a linear list e.g Tree and Graph
Data structures operations
• The following operations can be perform on
any linear data structure.
• Traversal : Processing each element in the list
• Search : Finding the location of the element
with a given value
• Insertion : Adding new element to the list
• Deletion : Removing an element from the list
Cont.
• Sorting : Arranging the element in some type
of order
• Merging : Combining two lists into a single
lists
Array
• An array is a list of finite number n of similar
data elements referenced respectively by a set
of n consecutive numbers .
• Arrays can have n dimensions
• One-dimentional arrays are arrays in which
each element is referenced by one subscript.
• A two- dimentional array is a collection of
similar data elements where each element is
referenced by two subscript.
STACK
• Some data structures allow insertion and
deletion at any place in the list(beginning ,
middle and end)
• Stack and Queue allow only insertion and
deletion at the beginning or the end of the list
, not in the middle.
• Stack is a linear data structure in which item
may be added or remove at only one end
called TOP.
Cont.
• A handy mnemonic for stack is called LIFO
• Other names of stack are ‘’piles’’ or ‘’push
down list”
Cont.
•
•
•
•
•
•
Push()
: Insert element in to stack
POP()
: Delete element from stack
isEmpty() : returns true if stack has no element
isFull()
: Check to see if there is enough space
makeEmpty () : Set stack empty
Count () : returns amount of element in
stack
Application of stack
• Used to perform efficient arithmetic operation
• Use for basic designing of an OS for interrupt
handling
• Use to implement function call in nested
procedure (eg if A is main program and B and
C are sub-programs)
• Use in recursion
QUEUE
• Is a linear list of elements
• Deletion can only take place at one end called
front
• Insertion can take place at rear
• Also called FIFO (First one enter first to go out)
• In computer science example of QUEUE is in
timesharing , in which program with the same
priority form a QUEUE.
DEQUE
• A DEQUE is a linear list in which element can be
added or removed at both end , but not in the
middle
• DEQUE refers to double ended QUEUE
• Two variation of DEQUE
1. Output restricted DEQUE : allow deletion at only
one end , but allow insertion at both end
2. Input restricted DEQUE : allow insertion only at
one end of the list , but allow deletion at both
end
PRIORITY QUEUE
• Is a collection of element such that each element has
been asssign a priority
• The following rules are applied when element are
deleted and process
1) An element of higher priority is processed before any
element of lower order
2) Two element with same priority are procced according
to the order in which they were added to the QUEUE
Cont.
• Priority Queue are used in timesharing system
progaram with high priority are proccesed first
and progarm with same priority form a
standard queue .
NON-LINEAR DATA STRUCTURE
?
TREES
• We have disscussed only linear data structure
e.g Arrays , Stack and Queue , Lists
• Some other Linear data Structures not
disscused are Strings and Lists
• Tree is a non-linear data structure
• Use mainly to represent hierachical
relationship between elements e.g records ,
family tree and table of contents
Application of tree
• Organizational Chart
• File System
• Unix / windows File Structure
Cont.
• Definition : A tree is a finite set of one or
more nodes .
• There are diferent kinds of tree : Binary
tree , 2-Tree or extended binary tree and
complete binary tree
Binary Tree
• A binary tree T is defined as a finite set of
elements , called nodes , such that :
(a) T is empty (Called the null tree or empty
tree).
(b) T contains a distinguish node R , called Root
and the remaining nodes form an ordered
pair of disjoint binary trees T1 and T2 .
Terminologies in Tree
• Internal node : node that contains atleast one
child
• External node ( Leaf) : Sometimes called
terminal node and does not contain any child
(node)
• Degree of node is the number of subtree
• Edge : Is the line from node to successor
Cont.
• Path : Sequence od edges (Connection of two
or more edges)
• Level number : Each node is assign a level
number , Root of tree starts with 0 always
• Generation : Node with the same level
number are said to be of the same generation
• Depth of tree : Maximum number of node in a
branch , depth can also be express as
maximum number of level + 1
Cont.
• Similar Trees : Binary trees are similar if they
have the same structure or shape .
• Tree are said to be copy if they are similar and
if they have the same contents at
corresponding nodes
Application of Binary Tree
• Some of the application of binary trees are
(1) Arithmetic Expression or Expression Tree
(2) Decision Tree
Arithmetic Expression
• Binary Trees are used to represent arithemetic
expressions
• Internal node : Operators
• External Node : Operands
Example
• Consider algebraic expression E below ;
E = (a-b)/((c*d)+e)
This expression can be represented in binary
Tree and each every algebraic expression will
correspond to a unique tree and vice versa .
Cont.
• Each Variabe or constant in E appears as an
‘’ Internal ’’ node in T whose left and right
subtrees correspond to the operands of the
operation.
• Below is the Corresponding Tree
Complete Binary Tree
A tree is said to be complete if all its
level , except possibly the last , have
the maximum number of possible
nodes , and if all nodes at the last level
appear as far left as possible .
Extended Binary Trees : 2-Trees
• A binary Tree T is said to be a 2-Tree or an
extended binary tree if each node N has either
0 or 2 childern.
• Node with 0 Childern are called external node
and are represented by square
• Node with 2 childern are called internal node
and are represented with circle
• Any binary tree can be change to extended
binary tree
Full Binary Tree
• A full binary tree is a binary tree in which
every node in the tree has 2 children except
the leaves of the tree . Or
• A full binary tree is a binary tree in which
every node in the tree has exactly zero or 2
childern.
Tree traversal
• Three ways to traverse a tree
(1) Preorder
(2) Inorder
(3) Postorder
Conti
(a) PreOrder : Node-Left-Right (NLF)
1 . Procces the root R
2 . Traverse the left subtree of R in preorder
3 . Traverse the right subtree of R in preorder
Cont.
(a) InOrder : Left-Node-Righ(LNR)
1 . Traverse the left subtree of R in preorder
2 . Procces the root R
3 . Traverse the right subtree of R in preorder
Cont.
(a) Post-order : Left-Node-Righ(LNR)
1 . Traverse the left subtree of R in preorder
2 . Traverse the right subtree of R in preorder
3 . Procces the root R
Example