Data Structure & Algorithms - Operations

21CSC201J
DATA STRUCTURES AND
ALGORITHMS
UNIT-1
DATA STRUCTURE
OPERATIONS

Data Structure Operations
• The data in the data structures are processed by certain operations.
o Traversing
o Searching
o Inserting
o Updating
o Deleting
o Sorting
o Merging

Data Structure Operations (Cont..)
• Traversing - Visiting each record so that items in the records can be accessed.
• Searching - Finding the location of the record with a given key or value or finding
all records which satisfy given conditions.
• Inserting - Adding a new record to the data structure.
• Updating – Change the content of some elements of the record.
• Deleting - Removing records from the data structure.
• Sorting - Arranging records in some logical or numerical order.
o (Eg: Alphabetic order)
• Merging - Combing records from two different sorted files into a single file.

Example
• An organization contains a membership file in which each record contains the
following data for a given member:
Name, Address, Telephone Number, Age, Sex
a. Suppose the organization wants to announce a meeting through a mailing.
Then one would traverse the file to obtain Name and Address of each
member.
b. Suppose one wants to find the names of all members living in a particular
area. Again traverse and search the file to obtain the data.
c. Suppose one wants to obtain Address of a specific Person. Then one would
search the file for the record containing Name.
d. Suppose a member dies. Then one would delete his or her record from the
file.

Example
e. Suppose a new person joins the organization. Then one would insert a
record into the file
f. Suppose a member has shifted to a new residence his/her address and
telephone number need to be changed. Given the name of the member, one
would first need to search for the record in the file. Then perform the
update operation, i.e. change some items in the record with the new data.
g. Suppose one wants to find the number of members whose age is 65 or above.
Again one would traverse the file, counting such members.

Abstract Data Types
• An Abstract Data type (ADT) is a type for objects whose behavior is defined by a
set of value and a set of operations.
• ADT refers to a set of data values and associated operations that are specified
accurately, independent of any particular implementation.
• The ADT consists of a set of definitions that allow us to use the functions while
hiding the implementation.
• Abstract in the context of data structures means everything except the detailed
specifications or implementation.
• Data type of a variable is the set of values that the variable can take.
• Examples: Stacks, Queues, Linked List
ADT = Type + Function Names + Behaviour of each function

ADT Operations
• While modeling the problems the necessary details are separated out from the
unnecessary details. This process of modeling the problem is called abstraction.
• The model defines an abstract view to the problem. It focuses only on problem
related stuff and that you try to define properties of the problem.
• These properties include
o The data which are affected.
o The operations which are identified.

ADT Operations ( Cont..)
• Abstract data type operations are
o Create - Create the data structure.
o Display - Displaying all the elements stored in the data structure.
o Insert - Elements can be inserted at any desired position.
o Delete - Desired element can be deleted from the data structure.
o Modify - Any desired element can be deleted/modified from the data structure.

Abstract Data Types Model
• The ADT model has two different parts
functions (public and private) and data
structures.
• Both are contained within the ADT model itself,
and do not come within the scope of the
application program.
• Data structures are available to all of the ADT’s
functions as required, and a function may call
any other function to accomplish its task.
• Data structures and functions are within the scope
of each other.

Abstract Data Types Model (Cont..)
• Data are entered, accessed, modified and
deleted through the external application
programming interface.
• For each ADT operation, there is an algorithm
that performs its specific task.
• The operation name and parameters are
available to the application, and they provide
only an interface to the application.
• When a list is controlled entirely by the
program, it is implemented using simple
structure.

Review Questions
• ______ are used to manipulate the data contained in various data structures.
• In ______, the elements of a data structure are stored sequentially.
• ______ of a variable specifies the set of values that the variable can take.
• Abstract means ______.
• If the elements of a data structure are stored sequentially, then it is a ______.

ALGORITHMS
SEARCHING TECHIQUES

Algorithms
• An algorithm is a well defined list of steps for solving a particular problem.
• The time and space are two major measures of the efficiency of an algorithm.
• The complexity of an algorithm is the function which gives the running time and /
or space in terms of input size.

Searching Algorithms
• Searching Algorithms are designed to check for an element or retrieve an element
from any data structure where it is stored.
• Based on the type of search operation, these algorithms are generally classified
into two categories:
• Linear Search
• Binary Search

Linear Search
• Linear search is a very basic and simple search algorithm.
• In Linear search, we search an element or value in a given array by traversing the
array from the starting, till the desired element or value is found or we can
establish that the element is not present.
• It compares the element to be searched with all the elements present in the array
and when the element is matched successfully, it returns the index of the element
in the array, else it return -1.
• Linear search is applied on unsorted or unordered lists, when there are fewer
elements in a list.

Linear Search - Example
• Search each record of the file, one at a time, until finding the given value.

Algorithm for Linear Search
• In Steps 1 and 2 of the algorithm, we initialize the
value of POS and I.
• In Step 3, a while loop is executed that would be
executed till I is less than N.
• In Step 4, a check is made to see if a match is
found between the current array element and VAL.
• If a match is found, then the position of the array
element is printed, else the value of I is
incremented to match the next element with VAL.
• If all the array elements have been compared with
VAL and no match is found, then it means that
VAL is not present in the array.

Linear Search - Advantages
• When a key element matches the first element in the array, then linear search
algorithm is best case because executing time of linear search algorithm is O(n),
where n is the number of elements in an array.
• The list doesn’t have to sort. Contrary to a binary search, linear searching does not
demand a structured list.
• Not influenced by the order of insertions and deletions. Since the linear search
doesn’t call for the list to be sorted, added elements can be inserted and deleted.

Linear Search - Disadvantages
• The drawback of a linear search is the fact that it is time consuming if the size of
data is huge.
• Every time a vital element matches the last element from the array or an essential
element does not match any element Linear search algorithm is the worst case.

Binary Search
• Binary Search is used with sorted array or list. In binary search, we follow the
following steps:
1) We start by comparing the element to be searched with the element in the
middle of the list/array.
2) If we get a match, we return the index of the middle element and terminate
the process
3) If the element/number to be searched is greater than the middle element, we
pick the elements on the left/right side of the middle element, and move to
step 1.
4) If the element/number to be searched is lesser in value than the middle
number, then we pick the elements on the right/left side of the middle
element, and move to step 1.

Binary Search - Example
• Binary Search is useful when there are large number of elements in an array and
they are sorted.

Algorithm for Binary Search
• In Step 1, we initialize the value of variables, BEG,
END, and POS.
• In Step 2, a while loop is executed until BEG is less
than or equal to END.
• In Step 3, the value of MID is calculated.
• In Step 4, we check if the array value at MID is equal to
VAL. If a match is found, then the value of POS is
printed and the algorithm exits. If a match is not found,
and if the value of A[MID] is greater than VAL, the
value of END is modified, otherwise if A[MID] is
greater than VAL, then the value of BEG is altered.
• In Step 5, if the value of POS = –1, then VAL is not
present in the array and an appropriate message is
printed on the screen before the algorithm exits.

Binary Search (Cont..)
Advantages
• It eliminates half of the list from
further searching by using the result of
each comparison.
• It indicates whether the element being
searched is before or after the current
position in the list.
• This information is used to narrow the
search.
• For large lists of data, it works
significantly better than linear search.
Disadvantages
• It employs recursive approach which
requires more stack space.
• Programming binary search algorithm
is error prone and difficult.
• The interaction of binary search with
memory hierarchy i.e. caching is poor.

Difference between Linear & Binary Search
Linear Search
• Linear Search necessitates the input
information to be not sorted
• Linear Search needs equality
comparisons.
• Linear search has complexity C(n)=
n/2.
• Linear Search needs sequential access.
Binary Search
• Binary Search necessitates the input
information to be sorted.
• Binary Search necessitates an ordering
contrast.
• Binary Search has complexity C(n)=
log 2
n.
• Binary Search requires random access
to this information.

Data Structure & Algorithms - Operations

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