23730874 Comparison of All Sorting Algorithms

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Comparison Of All SortingAlgorithms

PresentationBy

G.Gopi Krishna Reddy



Sorting

• The Process of rearranging the elementsso that they are in ascending order or

descending order is called sorting.• E ample! arranging of n"m#ers$ st"dent records.

%ery essential for searching the dictionaries$ telephone directories.



PropertiesThe t&o 'ain properties of sorting techni("es are!

• Stable ! )f the sorting algorithm preser%esthe relati%e order of any t&o e("al elements$thenthe sorting algorithm is sta#le.

• In Place ! )f an algorithm does not re("ire ane tra memory space e cept for fe& memory"nits$then the algorithm is said to #e in place.



Sorting Algorithms

*ario"s sorting algorithms are

B"##le Sort Selection Sort )nsertion Sort +"ic, Sort 'erge Sort



B"##le Sort

• This is one of the most simplest sortingtechni("e and most straight for&ard

method of sorting.• )n this sorting techni("e$ the ad-acent

elements in the list are compared and

e changed if they are o"t of order.• This is also called as Sinking Sort



Time Comple ity B"##le sort/• The time comple ity of #"##le sort in all

three cases #est$a%erage 0 &orst/is

1hich is not efficient compare to other

sorting techni("es.

T n/ 2 3 n45/



Selection Sort• )n this techni("e first &e find the smallest item in

the list and &e e change it &ith the first item.• 6e t$o#tain the second smallest item in the list 0

e change it &ith the second element and so on.• Since$ the ne t least item is selected and

e changed appropriately so that elements are

finally sorted $this techni("e is called Selection Sort



Time Comple ity Selection sort/• The time comple ity of selection sort in all

three cases #est$a%erage0&orst/ is

1hich is not efficient compare to other

sorting techni("es.

T n/ 2 3 n45/



)nsertion Sort• )n this techni("e the gi%en list is di%ided into t&o

parts! sorted part( left ) 0 unsorted part( right ).• The "nsorted elements can #e placed any of the

positions in the sorted part so that elementsto&ards left of #o"ndary are sorted.• As each item is inserted to&ards the sorted left

part$ the #o"ndary mo%es to the right decreasingthe "nsorted list.

• 7inally$once the #o"ndary mo%es to the rightmost position$the elements to&ards the left of

#o"ndary represent the sorted list.



Time Comple ity )nsertion sort/• The Time comple ity of insertion sort is! 1orst case!

A%erage case!

Best case!

T n/ 2 3 n45/

T n/ 2 O n45/

T n/ 2 8 n/



+"ic, sort

• )n ("ic, sort$ partition the array into t&o parts s"ch that elements to&ards left of ,ey

element are less than ,ey element andelements to&ards right of ,ey element aregreater than ,ey element.

• Sort the left part of the array rec"rsi%ely.• Sort the right part of the array rec"rsi%ely.



Time Comple ity +"ic, sort/• The time comple ity of +"ic, sort is! 1orst case!

A%erage case!

Best case!

T n/ 2 O n log n/

T n/ 2 O n log n/

T n/ 2 3 nlog5n/



'erge sort• )n merge sort$ a gi%en array of elements is

di%ided into t&o parts.•

The left part of the array as &ell as the right partof the array is sorted rec"rsi%ely.• 9ater$ the sorted left part and the sorted right part

are finally merged into a single sorted %ector.

• The process of merging of t&o sorted %ectors intoa single sorted %ector is called simple merge.



Time comple ity 'erge sort/• The time comple ity of 'erge sort in all

three cases #est$a%erage0&orst/ is!

T n/ 2 3 nlog 5n/



Concl"sion• By comparing all the sorting techni("es

'erge sort time comple ity is less in all

three cases time cons"ming is less/.• So$ Merge sort is the most efficienttechni("e &hen compare to all othersorting techni("es.



T:A6K ;O<

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23730874 Comparison of All Sorting Algorithms