Computer sciencebubble sorting algorithm

SORTING
 Sorting is process of arranging the elements in a particular order. The
order may be ascending order or descending order. The advantage of
sorting is effective data accessing.
 Types of sorting: There are 2 types of sorting.
1. Internal sorting
2. External sorting
 Internal sorting: If all the elements (records) to be sorted are in the
main memory then such a sorting is called internal sorting.
 External sorting: If some of the elements (records) to be sorted are in
the secondary storage or disk such a sorting is called External
sorting.

Types of sorting techniques:
1. Bubble sort (Exchange sort or Sinking sort).
2. Selection sort.
3. Insertion sort.
4. Quick sort.
5. Merge sort.
6. Heap sort.
7. Shell sort
8. Radix sort.
9. Address calculation sort.

Efficiency of a sorting technique:
 How to select a sorting technique for a given set of elements?
 There are number of sorting techniques available to sort a given array
of data items. Each sorting technique has its own advantages and
disadvantages. Different techniques are useful in different applications.
 There are 3 most important factors are counted while selecting a
sorting technique, which are.
1. Coding time: The amount of time invested in writing full length
sorting program.
2. Execution time (Time complicity): The amounts of time required
execute the sorting program. This normally frequency of execution of
statements in a program i.e. number of times statements are
executed.
3. Memory requirement (Space complicity): The amount of memory
required to store the entire sorting program in main memory while
execution.

Analysis of a sorting technique:
 Analysis of a sorting technique depends of three factors, which are code
time, time complicity and space complicity. Among these 3 factors while
analyzing a sorting technique we mainly concentrate more on the time
complicity.
 The time complicity is amount of time required to execute the sorting
program. Which is analyzed in terms of 3 cases
1. Best case
2. Worst case
3. Average case

BUBBLE SORT
 It is most popular sorting technique among all other techniques
because is very simple to understand and implement. It is also called
exchange or sinking sort
 Working of Bubble Sort
 The algorithm begins by comparing the element at the bottom of the
array with next element. If the first element is grater the second
element, then are swapped or exchanged.
 This process in then repeated for next two elements i.e. for second and
third element. After n-1 comparisons the largest of all data items
bubbles up to the top of the array.
 The first n-1 comparisons constitute first pass. During second pass
number of comparison is one les than previous pass i.e. there are n-2
comparisons in the second pass. During second pass second largest
element bubbles up to the last but one position.

 Consider following array A of elements.
A
A[0] A[1] A[2] A[3] A[4]
Begin the sort by comparing first two elements
Compare A[0] and A[1]. Since 30>10, interchange
Compare A[1] and A[2]. Since 30>5, interchange Pass 1
Largest element 30 has bubble up to last position
30 10 5 20 15
30 10 5 20 15
10 30 5 20 15
10 5 30 20 15
10 5 20 30 15
10 5 20 15 30

Compare A[1] and A[2]. Since 10<20, no interchange Pass 2
Second largest element bubbles up to the position last but one.
Compare A[0] and A[1]. Since 5<10, no interchange
Pass 3
Compare A[1] and A[2]. Since 10<15, no interchange
Third largest element is in its right position.
Compare A[0] and A[2]. Since 5>10, no interchange Pass 4
Final sorted array after n-1 passes.
10 5 20 15 30
5 10 20 15 30
5 10 20 15 30
5 10 15 20 30
5 10 15 20 30
5 10 15 20 30
5 10 15 20 30
5 10 15 20 30
5 10 15 20 30

Algorithm:
Algorithm: BUBBLE_SORT(A, n) This algorithm sort a given array A[n] using bubble sort technique. Variables I and J are
used to index the array and temp is a temporary variable.
Step1: start
Step2: Input the array A[n]
Step3: [Compute the sorting]
Repeat For I0 to n-1
Step4: [Compare the adjacent elements]
Repeat For J0 to n-1-I
Step5: If (A[J]>A[J+1])
[Interchange A[J] and A[J+1]]
TempA[J]
A[J]A[J+1]
A[J+1]temp
[End If]
[End step3 for loop]
[End step4 for loop]
Step6: [Display output]
Repeat For I0 to n-1
Output A[I]
[End for]
Step9: stop

Analysis of bubble sort:
 Best case: If the given array of elements is in the ascending order, the
outer for loop will be executed n-1 times. The inner for loop and if
statement will be executed n-1 times for the first iteration of the outer
for loop, n-2 times for the second iteration of the outer for loop and so
on . Only one time during the n-1th iteration of the outer for loop. The
interchange part will not be executed even once.
 Worst case: : If the given array of elements is in reverse order, the outer
for loop will be executed n-1 times. The inner for loop, if statement and
interchange part will be executed n-1 times for the first iteration of the
outer for loop, n-2 times for the second iteration of the outer for loop
and so on. Only one time during the n-1th iteration of the outer for loop.
Hence maximum number of comparisons and interchange operations.

 Advantages:
1. Simple to understand and implement.
2. Very straight forward.
3. Better than selection sort.
 Disadvantages:
1. It runs slowly and hence it is not efficient, because more efficient sorting
techniques are available.
2. Even if array is sorted, n-1 comparisons are required.

Computer sciencebubble sorting algorithm

Computer sciencebubble sorting algorithm

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