Sinking sort - Better than quick sort (in some cases)

BUBBLE SORT :             

                       

                  Bubble sort is a simple sorting algorithm also called Sinking sort 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 :

  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.

For 1^st iteration :

 

                               

                       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 :

  

                  

                
                Here u can observe the second largest element (8) in the array is in it's place (at n-2 index).

For 3^rd iteration :        

     

For 4^th iteration:  

For 5^th iteration :    

 For 6^th iteration :

                                                                                               
                     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

 

PERFORMANCE :

                   Bubble sort has worst-case and average complexity both О(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..?

Take a look with an example :

 

For 1^st iteration :

 

FOR 2ND ITERATION :

                  As for 2^nd iteration , no swaping occurs i.e. k=n=1. 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 .

For 1^st iteration :

For 2^nd iteration :

 

For 3^rd iteration :

For 4^th iteration :

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

 Code :

 CLICK HERE