Data StructuresData Structures

Chapter 8Chapter 8SortingSorting

Andreas Savva

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SortingSorting

SmithSanchez Roberts

KennedyJones

JohnsonJackson

Brown

George BrownGeorge Brown32 Cyprus Road32 Cyprus Road

Good GreenGood GreenLondon NW4 1NWLondon NW4 1NW

Records and their keysRecords and their keys

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Sorting AlgorithmsSorting Algorithms The purpose of sort is to produce a list of elements The purpose of sort is to produce a list of elements

sorted in either ascending or descending order.sorted in either ascending or descending order. A list can be sorted by a different key:A list can be sorted by a different key:

NameName SurnameSurname IDID GradeGrade

Sorting is often a very time-consuming action in a Sorting is often a very time-consuming action in a program, and therefore, program, and therefore, the choice of method used the choice of method used for searching for searching can make a substantial deference in can make a substantial deference in the program’s performance.the program’s performance.

Algorithms:Algorithms: Insertion sortInsertion sort Bubble sortBubble sort Quick sortQuick sort

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998877665544332211

SortingSorting

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Insertion SortInsertion Sort

Algorithm:Algorithm:

1.1. Put the first Put the first kk elements of a list in elements of a list in order.order.

2.2. Move the Move the k + 1k + 1 element into element into TempTemp..

3.3. Move the sorted elements (1 to k) Move the sorted elements (1 to k) down, one at a time, until the value in down, one at a time, until the value in TempTemp can be placed in order in the can be placed in order in the previously sorted portion of the list.previously sorted portion of the list.

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TempTemp

Insertion Sort ExampleInsertion Sort Example

998877665544332211

K+1

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Insertion Insertion Sort Sort

ExampleExample881515004422 22

881515002244 22TempTemp

881515004422 00

881515442200 00

881515442200 1515

881515442200 1515

881515442200 88

151588442200 88

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Insertion Sort ProcedureInsertion Sort Procedurevoid InsertionSort(List_entry List[], int size){ int i, k; List_entry temp; bool done;

for (k = 1; k < size; k++) { temp = List[k]; i = k; done = false; while ((i > 0) && !done) if (temp < List[i – 1]) { List[i] = List[i – 1]; i--; } else done = true; List[i] = temp; } }

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Bubble SortBubble Sort

Algorithm:Algorithm:1.1. Starting at the beginning of the list each Starting at the beginning of the list each

time, successive passes are made time, successive passes are made through the list until it is sorted.through the list until it is sorted.

2.2. A flag is needed to indicate whether or A flag is needed to indicate whether or not an exchange is made during a given not an exchange is made during a given pass through the list.pass through the list.

3.3. Since each pass filters the largest (or Since each pass filters the largest (or smallest) element to the end of the list, smallest) element to the end of the list, the length of what remains to be sorted the length of what remains to be sorted can be decrease by 1 after each pass.can be decrease by 1 after each pass.

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5544332211

5544332211

5544332211

5544332211

5544332211

5544332211

5544332211

5544332211

1111

Bubble Sort Bubble Sort ExampleExample

882233001212

882233121200

882212123300

881212223300

121288223300

121288223300

121288332200

121288332200

11stst Pass Pass

121288223300

22ndnd Pass Pass

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Bubble Sort Example (continue)Bubble Sort Example (continue)

121288332200

121288332200

121288332200

33rdrd Pass Pass

No exchange was made in the 3No exchange was made in the 3rdrd pass, pass,thus the list is sorted and we STOP.thus the list is sorted and we STOP.

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Bubble Sort ProcedureBubble Sort Procedurevoid BubbleSort(List_entry List[], int size){ bool exchange_made;

size = size – 1;

do { exchange_made = false;

for (int i = 0; i < size; i++) if (List[i] > List[i + 1]) { swap(List[i], List[i + 1]); exchange_made = true; } size = size – 1; } while (exchange_made && (size > 0);}

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Quick SortQuick Sort Quick-sort is one of the fastest sorting techniques Quick-sort is one of the fastest sorting techniques

available. It uses available. It uses recursionrecursion and is based upon the and is based upon the idea of separating a list into to parts. One part contains idea of separating a list into to parts. One part contains items smaller than some item in the list called items smaller than some item in the list called PivotPivot; ; the other part contains items larger than the other part contains items larger than PivotPivot..

Algorithm:Algorithm:1.1. Select the element in the middle of the array (in position Select the element in the middle of the array (in position

(FIRST + LAST) DIV 2) to be the (FIRST + LAST) DIV 2) to be the pivotpivot value. value.2.2. Move all the items on the left position of the pivot position that Move all the items on the left position of the pivot position that

they are bigger than the pivot value to the right of the pivot they are bigger than the pivot value to the right of the pivot position, and all the items that they are smaller than the pivot position, and all the items that they are smaller than the pivot value to the left of the pivot position. (The pivot can also value to the left of the pivot position. (The pivot can also change position).change position).

3.3. Split the table to two other tables and repeat steps 1 and 2 for Split the table to two other tables and repeat steps 1 and 2 for 1.1. FIRST = FIRST; LAST = Pivot Position – 1FIRST = FIRST; LAST = Pivot Position – 12.2. FIRST = Pivot Position + 1; LAST = LASTFIRST = Pivot Position + 1; LAST = LAST

1515Pivot

RightArrowRightArrow

Pivot

Pivot

Quick Sort ExampleQuick Sort Example

LeftArrow RightArrow

LeftArrow RightArrow

LeftArrowLeftArrow

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RightArrowRightArrow

Pivot

RightArrowRightArrow

Pivot

Quick Sort Example (continue)Quick Sort Example (continue)

RightArrowRightArrow

LeftArrowLeftArrow

LeftArrow RightArrowLeftArrow Pivot

RightArrowRightArrow

Pivot

LeftArrowLeftArrow

RightArrowRightArrow

LeftArrowPivot

Pivot

LeftArrowLeftArrow

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Pivot

RightArrowRightArrow

LeftArrowLeftArrow

Quick Sort Example (continue)Quick Sort Example (continue)

RightArrowRightArrow

Pivot

LeftArrowLeftArrow

RightArrowLeftArrow Pivot

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Quick Sort ProcedureQuick Sort Procedurevoid QuickSort(List_entry List[], int Left, int Right) { int Pivot, LeftArrow = Left, RightArrow = Right;

Pivot = List[(Left + Right) / 2];

do { while (List[LeftArrow] <= Pivot) LeftArrow++; while (List[RightArrow] >= Pivot) RightArrow--; if (LeftArrow < RightArrow) Swap(List[LeftArrow++], List[RightArrow--]); } while (LeftArrow < RightArrow)

if (Left < RightArrow) QuickSort(List, Left, RightArrow); if (LeftArrow < Right) QuickSort(List, LeftArrow, Right);}

main() { List_entry A[MAX]; int size; . . . QuickSort(A, 0, size – 1);}