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Volume 2, Issue 1, January – February 2013
ISSN 2278-6856
Study of Sorting Algorithm to Optimize Search
Results
Savina1, Surmeet Kaur2
1,2
Departmaent of Computer Science and Engineering Lovely professional university, Jalandhar, India
ABSTRACT: Sorting involves rearranging information into
almost any choice algorithm. Illustration of insertion sort
for input list [5, 2, 4, 6, 1, 3]:
either ascending or descending order. There are many sorting
algorithms; Sorting has been an area of interest for all those
who have been involved into the mining field of data. Sorting
data is important to search the data appropriately. For
different types of works different types of sorting algorithm
has been proposed by different scientist. There are several
issues with sorting to taken into account but In this paper, we
will compare the bubble sort with binary sort then merge
them to take the better performance of be focusing on the
time factor of the sorting. This research is about comparing
and merging such an algorithm which fits into each and
every account of sorting and searches the data appropriately.
For the same we will have to look into the previous done
algorithms also and then we would have to compare the
previous work with our latest done work.
1.2 Selection Sort:-Selection sort is also a simple a
comparison sorting algorithm. The algorithm works as
follows:
1. Find the minimum value in the list
2. Swap it with the value in the first position
3. Repeat the steps above for the remainder of the list
(starting at the second position and advancing each time)
Figure 1.2: Example of straight selection sort list
[1,3,4,5,7]:
Keywords: Sorting, algorithms, comparison, bubble sort,
binary sort, merge sort.
1. INTRODUCTION
In this paper we have seen that there are different types of
sorting and their internal structure. Now let’s get to know
what exactly are the problems in sorting .The first
problem is selecting the best suited algorithm for sorting.
The Selection Sort is used for selecting the algorithm.
There are many sorting algorithms. All sorting algorithm
are for different kind of problem .To choose an algorithm
depends upon what kind of structure we do have.
Accordingly the architecture and complexity is different.
Hence we need to design a kind of binary algorithm for
sorting which can fit in most of the cases. If we would
like to compare the bubble algorithms, it does have
different scenario. We can merge them according to the
complexity which they possess. It is also necessary that
we choose the best category, i.e. whether internal or
external sorting algorithm. Now whatever we choose as
an algorithm, our aim is to emphasis on the timing factor.
By timing factor I mean that how much time it takes to
execute the structure of the searching. Hence our aim is to
compare the best suited generated algorithm for searching
in terms of time compatibility.
1.1 Insertion Sort:-Insertion sort is a simple a
comparison sorting algorithm. Every iteration of insertion
sort removes an element from the input data, inserting it
into the correct position in the already-sorted list, until no
input elements remain. The choice of which element to
remove from the input is arbitrary, and can be made using
Volume 2, Issue 1 January - February 2013
2. RELATED WORK
A sorting algorithm is an algorithm that puts elements of
a list in a certain order. The most-used orders are
numerical order and lexicographical order. Efficient
sorting is important for optimizing the use of other
algorithms such as search and merge algorithms which
require input data to be in sorted lists; it is also often
useful for data and for producing human-readable Output.
More formally, the output must satisfy two conditions.
The output is in non decreasing order each element is no
smaller than the previous element according to the
desired total order. The output is a permutation
reordering of the input.
2.1 BUBBLE SORT Although the shell sort algorithm is
significantly better than insertion sort, there is still room
for improvement. One of the most popular sorting
algorithms is quick sort. Quick sort executes in O (n log
n) on average and O (n2) in the worst-case. However,
with proper precautions, worst-case behavior is very
unlikely. Quick sort is a non-stable sort. It is not an inplace sort as stack space is required. The quick sort
algorithm works by partitioning the array to be sorted,
then recursively sorting each partition. In Partition, one
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Volume 2, Issue 1, January – February 2013
ISSN 2278-6856
of the array elements is selected as a pivot value. Bubble
Sort is not known to be a good algorithm because it is a
quadratic-time sorting algorithm. However, efforts have
been made to improve the performance of the algorithm.
With Bidirectional Bubble Sort, the average number of
comparisons is slightly reduced and Batcher’s Sort
similar to Shell sort also performs significantly better
than Bidirectional Bubble Sort by carrying out
comparisons in a novel way so that no propagation of
exchange is necessary. Bubble sort is a simple sorting
algorithm. It works by repeatedly stepping through the
list to be sorted, comparing each pair of adjacent items
and swapping them if they are in the wrong order. First
pass bubble out the largest element and places in the last
position and second pass place the second largest in the
second last position and so on. Thus, in the last pass
smallest items is placed in the first position. Because, it
only uses comparisons to operate on elements, it is a
comparison sort.
For I = 1: n,
Swapped = false
For j = n: i+1,
If a[j] < a [j-1],
Swap a [j,j-1]
Swapped = true
Break if not swapped
End
Example: - Bubble sort (sorted elements are shaded)
23 78 45 8 32 56
Original List
Unsorted
8
23 78 45 32 56
after Pass 1
Unsorted
8
23 32 78 45 56
after Pass 2
Sorted
Unsorted
8
23 32 45 78 56
after Pass 3
Sorted
Unsorted
8
23 32 45 56 78
after Pass 4
Sorted
Sorted
2.2 BINARY SORT:-In computer science, a binary sort
algorithm finds the position of a specified value within a
sorted array. In each step, the algorithm compares the
input key value with the key value of the middle element
of the array. If the keys match then a matching element
has been found so its index, or position, is returned.
Otherwise, if the sought key is less than the middle
element's key, then the algorithm repeats its action on the
sub-array to the left of the middle element or, if the input
key is greater, on the sub-array to the right. If the
remaining array to be searched is reduced to zero, then
the key cannot be found in the array and a special "Not
found" indication is returned. However, if we place our
items in an array and sort them in either ascending or
descending order on the key first, then we can obtain
much better performance with an algorithm called Binary
Sort. These are following functions in this paper which
can be implemented in Binary Sort Order:
Volume 2, Issue 1 January - February 2013
1. Bin sort is recursive: it determines whether the search
key lies in the lower or upper half of the array, then calls
itself on the appropriate half.
2. There is a termination condition two of them in fact!
If low>high then the partition to be searched has
no elements in it and
If there is a match with the element in the middle
of the current partition, then we can return
immediately.
3. AddToCollection will need to be modified to ensure
that each item added is placed in its correct place in the
array. The
procedure is simple:
Search the array until the correct spot to insert the
new item is found,
Move all the following items up one position and
Insert the new item into the empty position thus
created.
4. Bin search is declared static. It is a local function and
is not used outside this class and if it were not declared
static, it would be exported and be available to all parts of
the program. The static declaration also allows other
classes to use the same name internally.
Each step of the algorithm divides the block of items
being searched in half. We can divide a set of n items in
half at most log2 n times. Thus the running time of a
binary search is proportional to log n and we say this is
an O (log n) algorithm. Binary search requires a more
complex program than our original search and thus for
small n it may run slower than the simple linear search.
However, for large n, lim log n \ n = 0. Thus at large n,
log n is much smaller than n, consequently an O (log n)
algorithm is much faster than an O (n) one. In worst
case, insertion may require n operation to insert into a
sorted list. We can find the place in the list where the new
item belongs using binary search in O (log n) operations.
However, we have to shuffle all the following items up
one place to make way for the new one. In the worst case,
the new item is the first in the list, requiring n move
operations for the shuffle. A similar analysis will show
that deletion is also an O (n) operation. If our collection is
static it doesn't change very often - if at all - then we may
not be concerned with the time required to change its
contents: we may be prepared for the initial build of the
collection and the occasional insertion and deletion to
take some time. In return, we will be able to use a simple
data structure which has little memory overhead.
However, if our collection is large and dynamic, i.e. items
are being added and deleted continually, and then we can
obtain considerably better performance using a data
structure called a tree.
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Volume 2, Issue 1, January – February 2013
ISSN 2278-6856
the pre sorted of the input affects the running time. Let
get to know about two sorting techniques and analyze
their performance. The two techniques are: 1. Internal
Sorting, 2. External Sorting.
Comparison of algorithms
Best
Nam
Avera
Worst
Memory
ge
Stabl
Method
e
e
Bubb
2.3 MERGE SORT: - Merge sort takes advantage of the
ease of merging already sorted lists into a new sorted list.
Merge sort is good for data that's too big to have in
memory at once because its pattern of storage access is
very regular. It also uses even fewer comparisons with
binary sort and heap sort. It is especially suited for data
stored as linked lists. Merge Sort is a O (nlogn) sorting
algorithm. It starts by comparing every two elements i.e.,
1 with 2, then 3 with 4... And swapping them if the first
should come after the second. It then merges each of the
resulting lists of two into lists of four, then merges those
lists of four, and so on; until at last two lists are merged
into the final sorted list. Of the algorithms described here,
this is the first that scales well to very large lists, because
its worst-case running time is O (n log n). Merge sort has
seen a relatively recent surge in popularity for practical
implementations, being used for the standard sort routine
in the programming languages Perl, Java and among
others. Merge sort is an O (n log n) comparison-based
divide and conquer sorting algorithm. Conceptually, a
merge sort works as follows:
1. If the list is of length 0 or 1, then it is already sorted.
Otherwise:
2. Divide the unsorted list into two sub lists of about half
the size.
3. Sort each sub list recursively by re-applying merge sort
algorithm.
4. Merge the two sub lists back into one sorted list.
3. RESULT & DISCUSSION
Sorting algorithms used in computer science are often
classified by: Computational complexity worst, average
and best behavior of element comparisons in terms of the
size of the list. For typical sorting algorithms good
behavior is O (nlogn) and bad behavior is O (n2).Memory
usage and use of other computer resources. In particular,
some sorting algorithms are "in place". This means that
they need only O (1) memory beyond the items being
sorted and they don't need to create auxiliary locations for
data to be temporarily stored, as in other sorting
algorithms.
Recursion some algorithms are either
recursive or non-recursive, while others may be both e.g.,
merge sort. Stability stable sorting algorithms maintain
the relative order of records with equal keys i.e., values.
Whether or not they are a comparison sort. A comparison
sort examines the data only by comparing two elements
with a comparison operator. Adaptability Whether or not
Volume 2, Issue 1 January - February 2013
n
n2
n2
1
Yes
Exchanging
n
nlogn
nlogn
n
Yes
Insertion
nlogn
nlogn
Depends:
Yes
Merging
le
Sort
Binar
y
Sort
Merg
nlogn
e
Worst
Sort
case is n
At the result of this paper is in the sorting algorithm is
that the binary sort is merge with bubble sort to obtain
better performance of the time complexity. In this
comparison of bubble sort and binary sort there should be
check the complexity of best case, average case and worst
case. Then merge the bubble sort with binary sort and
insertion method is used for binary sort and selection
method is used for bubble sort. These algorithms are used
to depend on need.
4. CONCLUSION
In this paper, we can use sorting algorithms. We present
different sorting algorithms models. This research is
about finding or creating such an algorithm which fits
into each and every account of sorting and searches the
data appropriately, such as Bubble Sort, B Sort and
Merge Sort. However, we study sorts because general
sorts do not work in all situations and because sorting is a
simple illustration of algorithmic techniques. This paper
started by giving an overview over selected algorithms for
time factor of the sorting, which uncovered both
weaknesses and strengths of existing approaches.
Algorithms should give a time complexity for the selected
set of quality characteristics and explain the relationships
between concepts. This paper has introduced two sorting
algorithms than the merge sorting algorithms. The first is
based upon sorting by the insertion technique, whereas
the second is based upon sorting by the exchange
technique. The analysis of Merge algorithms shows that
they score the best performance when binary sort and
heap sort can be merged. This paper is best compare to
privies this is compare based on the time, complexity if
the current is time is less then thus is the best algorithm.
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Web Site: www.ijettcs.org Email: [email protected], [email protected]
Volume 2, Issue 1, January – February 2013
ISSN 2278-6856
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Savina received the MCA degree from Punjab
Technical University and pursuing M.tech in
Lovely professional university, Jalandhar, India
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