UE Algorithmen und Datenstrukturen 1 UE Praktische Informatik 1. Übung 9. Sorting

Transcription

1 UE Algorithmen und Datenstrukturen 1 UE Praktische Informatik 1 Übung 9 Sorting Institut für Pervasive Computing Johannes Kepler Universität Linz Altenberger Straße 69, A-4040 Linz

2 Sorting :: Problem given: Record a[1:n] with: type Record = { KeyType key Data... Sorting Criterion The Key is the Sorting Criterion with a full transitive order relation (i.e.: x y && y z à x z) searched: Permutation of a, such that: i j à a[i].key a[j].key The sorting methods discussed here are based on comparisons i j à a[i] a[j] UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

3 Sorting :: Known Sorting Methods Bubble sort Insertion sort Shellsort Selection sort Quicksort < 3 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

4 Sorting :: Bubble sort - Principle One of the simplest sorting methods The array to be sorted is traversed starting from the front Adjacent Elements are swapped, when they are not in the sorted order The Array is repeatedly traversed, until no more swaps are needed The largest Element bubbles to the end of the array < 4 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

5 Sorting :: Bubble sort - Illustration < 5 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik Current value Comparative value

6 Sorting :: Bubble sort - Illustration Involved in exchange Current Value Comparative Value < 6 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

7 Sorting :: Bubble sort - Algorithm bubblesort(!list[1:n] int n) { boolean reverse int help repeat { reverse = false for (i = 1.. n 1) { if (list[i] > list[i + 1]) { help = list[i + 1] list[i + 1] = list[i] list[i] = help reverse = true until (!reverse) < 7 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

8 Sorting :: Insertion Sort - Principle Each element of the unsorted array is once the current element (starting from the front) It searches from the current element towards the front the index of the first element that has a value that is larger than the current element From this index on all elements until the current element will be shifted one position to the right The current element is copied to the new available position (i.e. inserted sorted) < > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

9 Sorting :: Insertion Sort Illustration Current Element.. With.. inverted Element.. Shifted Elements < 9 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

10 Sorting :: Insertion Sort - Algorithm insertionsort(!list[1:n] int n) { int i, j, h for (i = 1.. n - 1) { h = list[i + 1] // current Element j = i while ((j > 0) && (h < list[j])) { list[j + 1] = list[j] // list[j] is made available j = j - 1 // list[j+1] is available list[j + 1] = h // list[1:i+1] is sorted < 10 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

11 Sorting :: Shellsort - Principle Improved version of the Insertion Sort method Insertion-Sort is repeatedly applied to sub- array Comparisons, swaps and shifts only within the sub-arrays Considering sub-arrays (Elements with bigger distance m à increment) Result Almost only swaps Almost no shifts < 11 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

12 Sorting :: Shellsort - Principle First Step: Sub-arrays are those lists of elements, that have n/ 2 distance from each other Second Step: Sub-lists are those lists of elements that have n/ 4 distance from each other Third Step : n/ n/16, n/32... to distance = 1 à Increment < 12 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

13 Sorting :: Shellsort Illustration m = m = m = 1 == Insertionsort Current Element.. Permuted Elements.. Moved Elements.. < 13 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

14 Sorting :: Shellsort - Algorithm shellsort(!list[1:n] int n) { int m, i, j, h m = n/2 while (m > 0) { for (i = 1.. n - m) { h = list[i + m] j = i while ((j > 0) && (h < list[j])) { list[j + m] = list[j] j = j - m list[j + m] = h m = m/2 Insertionsort < 14 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

15 Sorting :: Selection sort - Principle Each Element of the unsorted List is once the current Element (starting from the front) Search the smallest Element of the sub-array from the current element If the current element is larger than the smallest element found Swap these two elements Advantage: Few number of swaps < 15 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

16 Sorting :: Selection sort - Illustration Current Element.. Swapped Elements.. Smallest Element < 16 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

17 Sorting :: Selection sort - Algorithm selectionsort(!list[1:n] int n) { int i, j, min, help for (i = 1.. n - 1) { min = i for (j = i n) { if (list[j] < list[min]) { min = j help = list[i] list[i] = list[min] list[min] = help < 17 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

18 Sorting :: Quicksort - Principle Fastest known sorting method 1) Select a Pivot-Element In practice often the first Element or central Element Better algorithms exist 2) Rearranging the Array (Partitioning) All Elements smaller than the Pivot in left sub-array All Elements larger than the Pivot in right sub-array 3) Recursively apply this rearrangement procedure on the generated sub-arrays Where the Pivot is taken can be chosen freely Termination Condition: The number of elements in the sub-arrays is either 1, 2 or 3 (sort manually) < 1 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

19 Übung 9 :: Information < 19 > UE Algorithmen und Datenstrukturen1, UE Praktische Informatik 1

20 Übung 9 :: Beispiel 1

21 Übung 9 :: Beispiel 2