A Comparative Study of Sorting and Searching Algorithms

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 05 Issue: 01 | Jan-2018 www.irjet.net p-ISSN: 2395-0072
© 2018, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 1412
A Comparative Study of Sorting and Searching Algorithms
Ms ROOPA K1 , Ms RESHMA J2
1 IV sem M.Tech, Department of Computer Science and Engineering, BNM Institute of Technology, Bengaluru, India
2Assistant Professor, Department of Computer Science and Engineering, BNM Institute of Technology,
Bengaluru, India
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ABSTRACT - The modern era is the age of expertise and
focuses on new development along with the comparing of
existing technologies. Here, a comparative study aims to
come up with the most efficient sorting algorithms or the
techniques used. Sorting is an important data structure
operation for managing data. Sorting algorithms and
searching techniques are both distinct. Searching is based
on searching the element for the given list, where in Sorting
is to arrange the given list in a particular order which can
be in ascending or descending order.
Most of these data are being compared, sorted only
for a portion and the piece of data which is actually used for
determining sorted order is known as the Key. The
methodology used is to evaluate the performance using CPU
time and memory space. Sorting algorithms and searching
technique can operate both on sorted and unsorted list of
elements. The items may be stored individually as records in
a database or may be elements of a search space defined by
a procedure.
There are different types of algorithms and
techniques for performing different tasks and as well as
same tasks, with each having its own advantages and
disadvantages depending on the type of data structure. An
analysis is being carried out on various sorting algorithms
and searching techniques on parameters like space and time
complexity. Based on the analysis, a comparative study is
being made so that the user can choose the type of
technique used based on the requirement.
Key Words: Quick sort, Selection sort, Bubble sort,
Binary search, Comparisons.
1. INTRODUCTION
In the latest technology, the system can store large
and complex amounts of item or data from which the user
can access this item or data either individually or in bulk.
Consider for an example, if a contact number provided in
the telephone directory has to be searched. Then, the data
has to be sorted and searched.
Searching is a process of identifying a specific item or
data and helps in recovery of a particular item or a data
from the given set of items in a list. Where in based upon
this, the answer is obtained like the item which is to be
recovered is present or not in the given list. As a result, it
requires determined sorting techniques and searching
algorithm to perform the process of searching and fetching
the key from the given list within less time.
A comparative study of sorting techniques and
searching algorithm based upon time and space
complexity is discussed. Different sorting techniques and
searching algorithms along with the implementation are
dependent upon situation. Usually, sorting techniques
depends mainly with two parameters, in which, first
parameter tells the time taken for execution the data and
second parameter tells about the speed or space taken for
execution of the data. Some of the different sorting
techniques are as follows:
 Quick sort
 Selection sort
 Bubble sort
 Insertion sort
 Merge sort
 Heap sort
1.1 Quick Sort
Quick sort as the name suggests helps in sorting list of
items very quickly with less space and is based upon the
Divide and Conquer principle also known as a Partition
Exchange sort[6]. This type of sorting is known as one of
the best sorting algorithms as it has efficiency and can
handle complex and vast lists of item without using extra
storage in it. It takes the following steps for processing of
an item or data for the given list:
o Step 1: Pick the element from the given list and
use as a pivot.
o Step 2: Partition these elements into two sub-lists.
o Elements less than pivot.
o Elements greater than pivot.
o Step 3: Quick sort two sub-lists.
o Step 4: Repeat the process until the entire lists of
item are sorted.
o Step 5: Return result.
Below figure 1 shows a simple representation of Quick
sort [7] technique considering the pivot elements.

Fig -1: A Simple Representation of a Quick Sort
The advantages and disadvantages of Quick Sort are as
follows[8]:
Advantages:
o This is one of the best sorting algorithms.
o It can handle large items for the given lists.
o Does not require extra storage.
Disadvantages:
o The worst-case performance is same as to bubble,
selection and insertion sort.
o In case the given lists are already sorted, then
bubble sort is more efficient compared to quick
sort.
o For sorting the integers of given items, radix sort
plays an important role as compared to quick sort.
1.2 Selection Sort
One of the simplest techniques used is the
selection sort which works for the given lists of item or
data each time by selecting one item at a time and orders
along with placing it in a correct position in sequence. This
does not require extra storage space to hold the lists[11].
For selecting the item randomly this technique is helpful.
The following steps are used for processing the
elements in given lists of items.
 Step 1: First finds the smallest element for the
given lists of item or data.
 Step 2: Replaces that item or data in the first
position.
 Step 3: Next, again finds the smallest element
among the lists.
 Step 4: Get replaced in second position.
 Step 5: Same procedure is followed unless the
elements are sorted.
 Step 6: Returns result.
Fig -2: Selection Sort for Different Passes
Above figure 2 shows the number of passes taken for the
given inputs[7]. The advantages and disadvantages of
Selection Sort are as follows[8]:
Advantages:
o Before sorting the given lists, the ordering of
items or datas can be initialized.
o This works even for the smaller lists of items or
datas.
o Need no extra storage for the original lists of
items.
Disadvantages:
o For the large set of items or datas this sorting
results in poor efficiency.
o Requires an N-squared number steps for sorting
items for the given lists.
o Compared to selection sort, the quick sort is most
efficient.
1.3 Bubble Sort
The bubble sort works on the basis for given lists by
swapping adjacent item or data in order, until the entire
lists of item or data are obtained in a sequence based upon
their key values. This technique is popular and easy for
execution of data in which it does not require extra
storage space. This takes the following steps as shown
below:
 Step 1: Consider the set of elements which can be
of any item or data for the given lists.
 Step 2: Swap the first two items or data for the
given lists adjacently using one by one pairs.
 Step 3: Repeat the process for all the items or data
in the given list.
 Step 4: Return result for the same.
And figure 3 represents the simple step by step
swapping of numbers for the given inputs[7].

Fig -3: Bubble Sort Technique
The advantages and disadvantages of Bubble Sort are as
follows[8]:
Advantages:
o It is one of the popular and easily implemented
algorithms.
o Without using the extra storage, the items can be
swapped easily.
o Requires minimum space for given lists.
Disadvantages:
o Requirement of N-squared number steps for
sorting items.
o This type of sorting does not deal with large
number of items for the given lists.
o Appropriate for academic teaching and cannot be
used for real time applications.
As discussed earlier, searching algorithms becomes
the most important part of the any programs[9]. Searching
can be involved in many ways either to search an entry for
the given database for the lists of items or datas, available
virtual space, which can be the suitable searching
algorithm, based upon time and space density and so on.
Entire array lists are sorted in order faster as compared to
other algorithms. Some of the algorithms are as follows:
1. Linear Search
2. Binary Search
3. Tree Search
4. Jump Search
5. Interpolation Search
6. Exponential Search
7. Fibonacci Search
Here, the main concentration is on Binary Search
algorithm which is the most popular algorithm used for a
complex and large database along with records ordered in
an associated statistical key format[10]. This uses a
recursive technique for searching a specific item from the
given lists, resulting in reducing the searching space. The
prerequisite for binary search is that the list should be in
sorted order. Steps to be followed while performing
Binary search are as follows:
• Firstly, it works by dividing the given lists of an
array into halves and looks at the middle element
of the list.
• In case the key element is smaller than the middle
element, then the second half of the given list is
ignored and the first half of the list is considered.
• Otherwise, if the key element considered is
greater than the middle value, then the first half of
the given list gets ignored and only the second
half of the list is considered.
• Repeat with the left over half until the key
element is found.
• In case the key element is found, it is returned
else it returns -1 if the key element is not found.
The advantages and disadvantages of Binary Search are as
follows[8]:
Advantages:
• This is one of the simplest algorithms.
• Checking of each item or data for the given list of
array is faster.
• Takes log2(N) log2(N) evaluations for average
and worst-case.
Disadvantages:
• The binary search is most complex search when
compared to other searches.
• In a given array list, if the items is in sorted
sequence only then this searching mechanism
works.
• If the searching technique does not support
random access of items for the given lists then it
leads to a lot of efficiency.
2. RELATED WORKS
An era of technical knowledge is being increasing
rapidly for the analysis and comparative of different types
algorithms used for searching any type of complex or large
data’s given for the lists of items or data’s. Focuses on
expansion of different searching techniques such as binary
or linear searches related to analysis and comparisons
that are made for the given lists of items or data’s so as to
find out which searching technique is more efficient in
resulting determination of time[3].
Searching refers to a process of inspecting whether
the required item or data for the given lists is present or
not which can be done using the key value. Some of the
different types of techniques are sequential search, binary
search, linear search, tree search and so on. Based upon
these searching techniques, a single record one at a time
can be fetched and also recovered from the storages that
are available either internally or externally within a minor
amount of time for the user.

The binary and linear searches are the two
techniques considered in a given lists of items or data’s for
searching essentials[3]. In case of binary search instead of
checking each and every item one by one can be sorted in
order and saves time. Whereas in case of linear search
increases the time for searching a particular item or data.
A comparison table between binary and linear searches
can be illustrated as follows[12]:
Basis of
Comparison
Binary Search Linear Search
Time
Complexity
O(log 2 N) O(N)
Best case
time
Center Element O(1) First Element
O(1)
Prerequisite
for an array
Array must be in
sorted order
Not required
Worst case
for N
number of
elements
Can conclude after
only log2N
comparisons
N comparisons
are required
Can be
implemented
on
Cannot be directly
implemented on
linked list
Array and
Linked list
Insert
operation
Require processing to
insert at its proper
place to maintain a
sorted list.
Easily inserted
at the end of
list
Algorithm
type
Divide and conquer in
nature
Iterative in
nature
Usefulness Somehow tricky
algorithm and
elements must be
arranged in order
Easy to use and
no need for any
ordered
elements
Lines of
Code
More Less
Table 1: Comparison table of Binary Search and
Linear Search
This results that when both the searches such as
binary and linear searches are used for comparisons of the
given set of lists of items or data’s. Binary search can be
used or designed for the larger and complex lists of items
or data’s and arranged either in ascending or descending
order by taking minor amount of time than linear search
which can be used for less significant data’s.
Sorting algorithm assists in depth knowing about
the definitions of each and every algorithm, work
procedures, time and space complexities and so on. In
general, is used to compare the difference between the
swapping of records, requirement of memory space and
estimation made between worst, average and best
positions[2].
Here, examines mainly about the bubble, selection
and gnome sorts along with some of the most important
algorithms such as Divide and Conquer and Dynamic
Programming etc. Hence, whenever an inputs are given for
these three algorithms estimations of time for each and
every algorithm are calculated and results that none of
these algorithm can provide an accurate solution. Also,
gives information about the algorithm which can be
defined as the line by line procedure for explaining exact
problem. It holds a set of protocols while processing each
and every lines of algorithm.
This specifies that different types of sorting
algorithms enclose its own method for solving the worst,
average and best positions based upon the inputs along
with the space used and gives an idea that more than one
algorithms can be used for solving numerous problems[4].
Finally, concludes that when used the similar set of inputs
which are been sorted for these algorithms, study shows
that the gnome sort calculates the time very rapidly for
the given set of inputs when compared along with
selection and bubble sorts. Whenever for the given inputs
in case if necessary the exchange of inputs can be done
using bubble and gnome sorts.
Modern technology has evolved advanced facts
for the expansion of required information relating to
different types of techniques and algorithms. These
techniques and algorithms when used and selected
together without making a proper option leads to various
problems while processing the data’s. Hence, in this
survey endeavours[1] in opting for proper techniques and
algorithms based upon their time and space complexity.
By using different techniques such as bubble sort,
selection sort and insertion sort the time and space
complexity are carried out and analysis is performed to
check for knowing which among these three techniques
provides the majority efficiency used, while sorting the
data’s for the given lists of elements.
The method for dealing with these quantities of
items or data’s processes sorting of elements that are
present in the lists then the searching mechanism takes
place for execution of datas. Sorting here refers in filtering
of elements for the given lists such as sorting of contact
numbers given in telephone directory, sorting of aadhar
card numbers in the given data set and so on. For
performing a lengthy sorting for the given sequence, a
variety of functioning process are required and can come
to know which is the suitable algorithm essential for

calculating time and space firmness for the given bubble,
insertion and selection sorts[1].
With the help of structural design and then put
into practice calculating the estimation of these techniques
results in identifying the estimation of time and space
taken by these three sorting techniques such as bubble,
insertion and selection sorts.
The purpose here is to measure the time estimated for the
given linear and binary searching techniques as and when
the inputs are selected[5]. Searching generally refers in
resulting the required item which has been identified for
the provided list of elements. Searching are of two types
namely: 1) Internal Searching and 2) External Searching.
1) Internal Searching: Is the method of searching an
data or item for the given set of inputs in Random
Access Memory (RAM) is known as Internal
Searching.
2) External Searching: Is the method of searching an
data or item for the given set of inputs by not
using RAM but externally stored devices is known
as External Searching.
Here, gives in depth details of the linear and binary
searches and which one among the two searching
techniques provides a faster access for the inputs and
provides the best time estimation [5]. Some of the
advantages and disadvantages of linear and binary
searches are also examined. Ultimately, wraps the
concepts of searching techniques such as linear and binary
searches along with the working procedures and examines
the differences between these searching techniques.
3. CONCLUSION
This paper covers some of the popular sorting
techniques like quick sort, selection sort and bubble sort.
It highlights the advantages and disadvantages of the
above sorting algorithms. Binary and linearly search is
also explained and compared. It helps in finding out which
sorting techniques takes less time and space for the given
inputs.
REFERENCES
1. Makinde O.E. et.al, “Performance Evaluation of
Sorting Techniques” ,ARPN Journal of Systems
and Software, VOL. 3, NO. 5, August 2013.
2. D.R. Aremu et.al, “A Comparative Study of Sorting
Algorithms”, African Journal of Computing & ICT,
Vol 6. No. 5, December 2013 .
3. Ayush Pathak, “Analysis and Comparative Study
of Searching Techniques”, International Journal of
Engineering Sciences & Research Technology,
March, 2015.
4. Jehad Hammad, “A Comparative Study between
Various Sorting Algorithms”, International Journal
of Computer Science and Network Security,
VOL.15 No.3, March 2015.
5. Yuvraj Singh Chandrawat et.al, “Analysis and
Comparative Study of Searching Techniques”,
International Journal of Engineering Sciences &
Research Technology, October, 2015.
6. http://faculty.simpson.edu
7. https://www.studytonight.com
8. http://z-sword.blogspot.in
9. https://www.techwalla.com
10. https://www.quora.com
11. https://www.geeksforgeeks.org
12. https://techdifferences.com
BIOGRAPHIES:
Ms Roopa K is a student from IV sem,
M.Tech in Computer Science &
Engineering at B N M Institute of
Technology, Bengaluru.
Ms. Reshma J is working as
Assistant Professor in Department
of Computer Science and
Engineering at B N M Institute of
Technology, Bengaluru. She has
over twelve years of teaching
experience. She is pursuing her
research in the area of Wireless
Sensor Networks. She has published articles in
International Journals and Conferences.

A Comparative Study of Sorting and Searching Algorithms

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