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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 : bubbleAn while n0 // n is the no of elements k0 for i1 to n-1 if Ai-1 Ai swap Ai-1Ai ki nk WORKING : The bubble sort working with an example : A 9361842 The length of the array is 7 i.e. let n7. 9 3 6 1 8 4 2 For references : http://comsciguide.blogspot.com/

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For 1 st 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 1 st iteration we will get a largest element 9 at the last index of the array . So for the 2 nd iteration we need not to include it because as in the sorted list the last element will be the largest one. For 2 nd iteration : 3 6 1 8 4 2 3 6 1 8 4 2 For references : http://comsciguide.blogspot.com/

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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 its place at n-2 index. For 3 rd 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 4 th iteration : For references : http://comsciguide.blogspot.com/

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1 3 4 2 1 3 4 2 1 3 4 2 1 3 2 4 For 5 th iteration 1 3 2 1 3 2 1 2 3 For 6 th iteration : 1 2 As here there is no swaps IF condition wont execute . So nk i.e. n1 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 Оn 2 For references : http://comsciguide.blogspot.com/

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where n is the number of items being sorted. There exist many sorting algorithms with substantially better worst-case or average complexity of Onlogn . 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 On. 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 For references : http://comsciguide.blogspot.com/

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add this elementat the begining or ending of array..What is that complexity for this sorting if we add new element at the last.. Take a look with an example : Lets take this array which is already sorted. 1 2 3 4 6 8 9 Consider the case of adding the new number assume 5 at the begining of the array . The new array becomes 5 1 2 3 4 6 8 9 For 1 st 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 For references : http://comsciguide.blogspot.com/

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1 2 3 4 5 6 8 9 // the array is sorted and k5 ..so n5 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 2 nd iteration no swaping occurs i.e. kn1. So there is no chance of 3 rd iteration and the program exits.    Now consider the case of adding the new number assume 5  at the ending of the array . The new array becomes For references : http://comsciguide.blogspot.com/

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1 2 3 4 6 8 9 5 For 1 st 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 2 nd iteration : 1 2 3 4 6 8 5 9 1 2 3 4 6 8 5 9 For references : http://comsciguide.blogspot.com/

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

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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 k7 ..so n7 For 4 th 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 For references : http://comsciguide.blogspot.com/

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1 2 3 4 5 6 8 9 1 2 3 4 5 6 8 9 As for 4 th iteration no swaping occurs i.e. kn1. So there no chance of 5 th iteration and the program exits. From the analysis  we observe that by adding an element  at the front of index  the cost of running time is less as compared to  the cost of running time for the case of adding element at the last. 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 On 2 complexity It will not be efficient for the case of large lists .Its On 2 complexity means that its efficiency decreases dramatically on lists of large number of elements . Even among simple On 2 sorting algorithms like insertion sort are usually considerably more efficient. For references : http://comsciguide.blogspot.com/