Bubble

BUBBLE SORT :

Bubble sort is a simple sorting algorithm also called Sinking

algorithm which just goes through a set of data ( list of numbers or characters)

and compares each member with its right neighbour . The pass through the list

is repeated until no more swaps are needed , which indicates that the list is

sorted . Although the algorithm is simple , It is too slow and impractical for a

large set of data.

PSEUDOCODE :

bubble(A,n)

while n>0 // n is the no of elements

k=0

for i=1 to n-1

if (A[i-1] > A[i])

swap A[i-1],A[i]

k=i

n=k;

WORKING :

The bubble sort working with an example :

A[] = {9,3,6,1,8,4,2}

The length of the array is 7 i.e. let n=7.

9 3 6 1 8 4 2

For references : http://comsciguide.blogspot.com/

For 1st iteration :

9 3 6 1 8 4 2

3 9 6 1 8 4 2

3 6 9 1 8 4 2

3 6 1 9 8 4 2

3 6 1 8 9 4 2

3 6 1 8 4 9 2

3 6 1 8 4 2 9

After 1st iteration we will get a largest element (9) at the last index

of the array . So for the 2nd iteration we need not to include it , because as in

the sorted list , the last element will be the largest one.

For 2nd iteration :

3 6 1 8 4 2

3 6 1 8 4 2


3 1 6 8 4 2

3 1 6 8 4 2

3 1 6 4 8 2

3 1 6 4 2 8

Here u can observe the second largest element (8) in the array is in it's

place (at n-2 index).

For 3rd iteration :

3 1 6 4 2

1 3 6 4 2

1 3 6 4 2

1 3 4 6 2

1 3 4 2 6

For 4th iteration :


1 3 4 2

1 3 4 2

1 3 4 2

1 3 2 4

For 5th iteration

1 3 2

1 3 2

1 2 3

For 6th iteration :

1 2

As here , there is no swaps , IF condition won't execute . So n=k i.e.

(n=1) and the program will stop. Finally the sorted array is

1 2 3 4 6 8 9

PERFORMANCE :

Bubble sort has worst-case and average complexity both (n2),


where n is the number of items being sorted. There exist many sorting

algorithms with substantially better worst-case or average complexity of

O(nlogn) . Therefore, bubble sort is not a practical sorting algorithm when n is

large.

The positions of the elements in bubble sort will play a large part in

determining its performance . Large elements at the beginning of the list do not

pose a problem , as they are quickly swapped . Small elements towards the end

however, move to the beginning extremely slowly. This has led to these types of

elements being named rabbits and turtles respectively.

It has a special feature , that the largest element( at last index ) gets

sorted first, with smaller elements taking longer to move to their correct

positions.

The only significant advantage that bubble sort has over most other

implementations, even quicksort, but not insertion sort, is that the ability to

detect that the list is sorted in efficient way .When the list is already sorted

(best-case), the complexity of bubble sort is only O(n). By contrast, most other

algorithms, even those with better average-case complexity, perform their

entire sorting process on the set and thus are more complex.

ANALYSIS :

U will be knowing that we do sort for a set of numbers.

Suppose if u have given array of elements which is already sorted and

one element is added to this..U will be having doubt where we have to


add this element(at the begining or ending of array)..What is that

complexity for this sorting, if we add new element at the last..?

Takealookwithanexample:

Let's take this array which is already sorted.

1 2 3 4 6 8 9

Considerthecaseofaddingthenewnumber(assume5)at

thebeginingofthearray.

The new array becomes

5 1 2 3 4 6 8 9

For 1st iteration :

5 1 2 3 4 6 8 9

1 5 2 3 4 6 8 9

1 2 5 3 4 6 8 9

1 2 3 5 4 6 8 9


1 2 3 4 5 6 8 9

// the array is sorted and k=5 ..so n=5

1 2 3 4 5 6 8 9

1 2 3 4 5 6 8 9

1 2 3 4 5 6 8 9

FOR 2ND ITERATION :

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

As for 2nd iteration , no swaping occurs i.e. k=n=1. So there is no chance

of 3rd iteration and the program exits.

Nowconsiderthecaseofaddingthenewnumber(assume5)

attheendingofthearray.

The new array becomes


1 2 3 4 6 8 9 5

For 1st iteration :

1 2 3 4 6 8 9 5

1 2 3 4 6 8 9 5

1 2 3 4 6 8 9 5

1 2 3 4 6 8 9 5

1 2 3 4 6 8 9 5

1 2 3 4 6 8 9 5

1 2 3 4 6 8 9 5

1 2 3 4 6 8 5 9

For 2nd iteration :

1 2 3 4 6 8 5 9

1 2 3 4 6 8 5 9


1 2 3 4 6 8 5 9

1 2 3 4 6 8 5 9

1 2 3 4 6 8 5 9

1 2 3 4 6 8 5 9

1 2 3 4 6 5 8 9

1 2 3 4 6 5 8 9

For 3rd iteration :

1 2 3 4 6 5 8 9

1 2 3 4 6 5 8 9

1 2 3 4 6 5 8 9

1 2 3 4 6 5 8 9

1 2 3 4 5 6 8 9


1 2 3 4 5 6 8 9

1 2 3 4 5 6 8 9

1 2 3 4 5 6 8 9// the array is sorted

and k=7 ..so n=7

For 4th iteration :

1 2 3 4 5 6 8 9

1 2 3 4 5 6 8 9

1 2 3 4 5 6 8 9

1 2 3 4 5 6 8 9

1 2 3 4 5 6 8 9

1 2 3 4 5 6 8 9


1 2 3 4 5 6 8 9

1 2 3 4 5 6 8 9

As for 4th iteration , no swaping occurs i.e. k=n=1. So there no

chance of 5th iteration and the program exits.

Fromtheanalysis,weobservethatbyaddinganelement

atthefrontofindex,thecostofrunningtimeislessascomparedto

thecostofrunningtimeforthecaseofaddingelementatthelast.

IN PRACTICE :

Bubble sort is one of the simplest sorting algorithm to implement

and easy to understand . Due to its simplicity, bubble sort is often used to

introduce the concept of an algorithm, or a sorting algorithm, to introductory

students.

But due its O(n2) complexity , It will not be efficient for the case of

large lists .Its O(n2) complexity means that its efficiency decreases dramatically

on lists of large number of elements . Even among simple O(n2) sorting

algorithms like insertion sort are usually considerably more efficient.


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Bubble