Sorting And Its Types

SORTINGSorting refers to operations of

arranging a set of data in a given order.

10 20 30 40 50 60

30 10 60 20 50 40 Unsorted List

Sorted List

BASIC TYPES :Internal Sorting:If all the data to be sorted can be adjusted in main memory then it is called as Internal Sorting.External Sorting:If data to be stored is large and aquires external memory then the type is called as External Sorting.

METHODS OF SORTING:Bubble SortSelection SortInsertion Sort

BUBBLE SORT

ALGORITHMBubble Sort:Algorithm of bubble sort includes two steps repeated until the list is sorted. Compare adjacent elements, if the

element on right side is smaller then swap their positions.

Compare first element, second element and so on on completion of Pass 1 the largest element is at last position.

Pass 1:

50 10 30 20 40

50 10 30 20 40

10 50 30 20 40

10 30 50 20 40

10 30 20 50 40

10 30 20 40 50

0,1

1,2

2,3

3,4

Number Of Passes = Max – 1 = 5 – 1 = 4

Pass 2:10 30 20 40 50

10 30 20 40 50

10 30 20 40 50

10 30 20 40 50

0,1

1,2

2,3

Pass 3:

10 30 20 40 50

10 30 20 40 50

10 30 20 40 50

0,1

1,2

Pass 4:

10 30 20 40 50 0,1

10 30 20 40 50

10 30 20 40 50 Sorted list

SELECTION SORT

ALGORITHMSelection Sort:Here in selection sort the algorithm depends on the zeroth element majorly.

The Zeroth element is compared with the first element and if the element at right is found smaller then their positions are swapped or exchanged.

The same procedure is carried with all elements of the list resulting into a fully sorted list.

23 15 29 11 1

23 15 29 11 1

Pass 1:

Number Of Passes = Max – 1 = 5 – 1 = 4

15 23 29 11 1

15 23 29 11 1

11 23 29 15 1

1 23 29 15 11

0,1

0,3

0,2

0,4

1 23 29 15 11

Pass 2:

1 29 23 15 11

1 15 23 29 11

1 11 23 29 15

1,3

1,2

1,4

1 11 23 29 15

Pass 3:

1 11 23 29 15

1 11 15 29 23

2,3

2,4

Pass 4:

1 11 15 29 23

1 11 15 23 29

1 11 15 23 29 Sorted List

3,4

INSERTION SORT

•Applications using insertion sort Mathematical applications : in the search for greater value, or the smallest value. In many other applications. 

• when we can use Insertion Sort ?This method is effective when dealing with small numbers .

ALGORITHMInsertion SortIn insertion sort the elements are compared and inserted to respective index place. It starts with comparision of 1st and 0th

element in pass 1. In pass 2 the second element is

compared with the 1st and 0th element. Doing so with all the elements in the list

appropriate element is inserted by shifting elements on right.

public insertionSort(int[] arr) { for (int i = 1; i < arr.Length; ++i) { int temp = arr[i]; int pos = i; while (arr[pos-1].CompareTo(temp) > 0 && pos > 0) {

arr[pos] = arr[pos-1]; pos--; } arr[pos] = temp; } }

Select

Comparing

Shift

Insert

Algorithm

Best And Worst Case Best Case

The best case input is an array that is already sorted. In this case insertion sort has a linear running time (i.e., Θ(n)). During each iteration, the first remaining element of the input is only compared with the right-most element of the sorted subsection of the array.

Worst Case

The worst case input is an array sorted in reverse order. In this case every iteration of the inner loop will scan and shift the entire sorted subsection of the array before inserting the next element. For this case insertion sort has a quadratic running time (i.e., O(n2)).

75 57 25 19 4

Pass 1:

75 57 25 19 4

Number Of Passes = Max – 1 = 5 – 1 = 4

57 75 25 19 4

0,1

Pass 2:

57 75 25 19 4

25 57 75 19 4

0,2

25 57 75 19 4

Pass 3:

19 25 57 75 4

0,3

4 19 25 57 75

Pass 4:

19 25 57 75 4 0,4

Thank You…!