ion of All Sorting

8/14/2019 ion of All Sorting

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TTECHNIQUESECHNIQUESssortingorting

By

Sukanta behera

Reg. No. 07SBSCA048


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Topic overview:Topic overview:

NOTES ON SORTING.NOTES ON SORTING.

SELECTION SORT ALGORITHM ANDSELECTION SORT ALGORITHM AND

EXAMPLE.EXAMPLE.

BUBBLE SORT ALGORITHM ANDBUBBLE SORT ALGORITHM AND

EXAMPLE.EXAMPLE.

MERGE SORT ALGORITHM ANDMERGE SORT ALGORITHM AND

EXAMPLE.EXAMPLE.

QUICK SORT ALGORITHM AND EXAMPLE.QUICK SORT ALGORITHM AND EXAMPLE.


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SSORTING:ORTING:

The sorting technique asks us to rearrangeThe sorting technique asks us to rearrange

the given items of a given list in ascendingthe given items of a given list in ascending

order.order.

As a practical manner, we usually need toAs a practical manner, we usually need to

sort lists of numbers, characters from ansort lists of numbers, characters from an

alphabet, character strings, and mostalphabet, character strings, and most

important records in an institutions,important records in an institutions,

companies etc.companies etc.

For example, we can choose to sort studentFor example, we can choose to sort student


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SSelection sort:election sort: Selection sort and Bubble sorting techniques areSelection sort and Bubble sorting techniques are

coming under Brute Force method, which is acoming under Brute Force method, which is astraightforward approach to solving a problemsstraightforward approach to solving a problemsstatement and definitions of the concepts involved.statement and definitions of the concepts involved.

ALGORITHMALGORITHM SelectionSort(A[o..n-1])SelectionSort(A[o..n-1])

//The algorithm sorts a given array by selection sort//The algorithm sorts a given array by selection sort

//Input: An array A[0..n-1] of orderable elements//Input: An array A[0..n-1] of orderable elements

//Output: Array A[0..n-1] sorted in ascending order//Output: Array A[0..n-1] sorted in ascending order

for i=0 to n-2 dofor i=0 to n-2 do

min=imin=i

for j=i+1 to n-1 dofor j=i+1 to n-1 do

if A[j] < A[min], min=jif A[j] < A[min], min=j

swa A i and A minswa A[i] and A[min]


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Bubble sort:Bubble sort:

Bubble sort is comes under Brute Force method. TheBubble sort is comes under Brute Force method. The

sorting problem is to compare adjacent elements ofsorting problem is to compare adjacent elements of

the list and exchange them if they are out of order .the list and exchange them if they are out of order .

By doing it repeatedly, we end up bubbling up theBy doing it repeatedly, we end up bubbling up the

largest element to the last position of the list and vicelargest element to the last position of the list and vice

versa.versa.

ALGORITHMALGORITHM BubbleSort(A[0..n-1])BubbleSort(A[0..n-1])

//The algorithm sorts array A[0..n-1] by bubblesort//The algorithm sorts array A[0..n-1] by bubblesort

//Input: An array A[0..n-1] of orderable elements//Input: An array A[0..n-1] of orderable elements

//Output: Array A[0..n-1] sorted in ascending order//Output: Array A[0..n-1] sorted in ascending order

for i=0 to n-2 dofor i=0 to n-2 do

for j=0 to n-2-I dofor j=0 to n-2-I do


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Merge sort:Merge sort: Merge sort is a perfect example of a successful application ofMerge sort is a perfect example of a successful application of

the Divide and Conquer method. It sorts a given array A[0..n-the Divide and Conquer method. It sorts a given array A[0..n-

1] by dividing it into two halves A[0..[n/2]-1] and A[[n/2]n-1] by dividing it into two halves A[0..[n/2]-1] and A[[n/2]n-

1]. Sorting each of them recursively and then merging the two1]. Sorting each of them recursively and then merging the two

smaller sorted arrays into a single sorted one.smaller sorted arrays into a single sorted one.

ALGORITHMALGORITHM Mergesort(A[0..n - 1])Mergesort(A[0..n - 1])

//Sorts array A[0..n - 1] by recursive mergesort//Sorts array A[0..n - 1] by recursive mergesort

//Input: An array A[0..n - 1] of orderable elements//Input: An array A[0..n - 1] of orderable elements

// Output: Array A[0..n - 1] sorted in decreasing order// Output: Array A[0..n - 1] sorted in decreasing order

if n > 1if n > 1copy A[0..[n/2] - 1] to B[0[n/2] - 1]copy A[0..[n/2] - 1] to B[0[n/2] - 1]

copy A[[n/2]..n - 1] to C[0[n/2] - 1]copy A[[n/2]..n - 1] to C[0[n/2] - 1]

Mergesort (B[0..[n/2] - 1])Mergesort (B[0..[n/2] - 1])

Mergesort (C[0..[n/2] - 1])Mergesort (C[0..[n/2] - 1])Mer e B C A


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89 45 68 90 29 34 1712

89 45 68 90 29 34 17 12

8945

6890

2934

1712

89

45

68

90

29

34

17

12

4589

6890

29 34 12 17

45 68 89 90 12 17 29 34

12 17 29 34 45 68 8990


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Quick Sort:Quick Sort: Quick sort is another important sorting algorithm that isQuick sort is another important sorting algorithm that is

based on the Divide and Conquer method. It divides thebased on the Divide and Conquer method. It divides the

input elements according to their value. Specifically, itinput elements according to their value. Specifically, it

rearranges elements of a given array A[0..n 1] to achieverearranges elements of a given array A[0..n 1] to achieve

itsits partition.partition.

ALGORITHMALGORITHM Quicksort(A[lr])Quicksort(A[lr])

//Sorts a subarray by quicksort//Sorts a subarray by quicksort

//Input: A subarray A[lr] of A[0..n 1], defined by its left & right//Input: A subarray A[lr] of A[0..n 1], defined by its left & right

indicesindices

//Output: The subarray A[lr] sorted in nondecreasing order//Output: The subarray A[lr] sorted in nondecreasing order

if l < rif l < r==


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ALGORITHMALGORITHM Partition(A[lr])Partition(A[lr])//Partitions a subarray by using its first element as a pivot//Partitions a subarray by using its first element as a pivot

//Input: A subarray A[l..r] of A[on 1], defined by its left//Input: A subarray A[l..r] of A[on 1], defined by its leftand rightand right

// indices l and r (l < r) // indices l and r (l < r)

//Output: A partition of A[l..r], with the split position returned//Output: A partition of A[l..r], with the split position returnedas thisas this

// functions values // functions values

p = A[l]p = A[l]

i = l; j = r + 1i = l; j = r + 1

repeatrepeat

repeatrepeati = i + 1 until A[i] >= pi = i + 1 until A[i] >= prepeatrepeatj = j - 1 until A[j] = j

swap(A[i], A[j]) //undo last swap when i >= jswap(A[i], A[j]) //undo last swap when i >= jswap(A[l],A[j])swap(A[l],A[j])


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0 1 2 3 4 5 6 7 0 1 20 1 2 3 4 5 6 7 0 1 2

3 4 5 6 73 4 5 6 7

55 ii 3 1 9 8 2 4 j 7 13 1 9 8 2 4 j 7 1 22 33

44

5 3 15 3 1

ii9 8 2 j 4 79 8 2 j 4 7 11

5 3 15 3 1 ii 4 8 2 j 9 74 8 2 j 9 7 33

ijij44

5 3 1 45 3 1 4 ii 8 j 2 9 78 j 2 9 7 ii33jj44

5 3 1 4 j 25 3 1 4 j 2 ii 8 9 78 9 7

44


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Insertion sort:Insertion sort: Insertion sort comes under Decrease and ConquerInsertion sort comes under Decrease and Conquer

method. In this method, we consider an application ofmethod. In this method, we consider an application of

the decrease-by-one technique to sorting an array A[0the decrease-by-one technique to sorting an array A[0n 1].n 1].

ALGORITHMALGORITHM Insertionsort(A[0n 1])Insertionsort(A[0n 1])

//Sorts a given array by insertion sort//Sorts a given array by insertion sort

// Input: An array A[0n 1] of n orderable elements// Input: An array A[0n 1] of n orderable elements

// Output: Array A[0n 1] sorted in nondecreasing order// Output: Array A[0n 1] sorted in nondecreasing order

for i =1 to n 1 dofor i =1 to n 1 do

v = A[i]v = A[i]

j = i 1j = i 1

while j >= 0 and A[j ] > v dowhile j >= 0 and A[j ] > v do

A[j + 1] = A[j]A[j + 1] = A[j]

j = j 1j = j 1

A[j + 1] = vA[j + 1] = v


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