Internal dan Eksternal Sorting

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1 Internal dan Eksternal Sorting

2 Outline Pembagian algoritma sorting Algoritma sorting Paradigma Contoh
Running Time Outline

3 Sorting Sorting = pengurutan Sorted = terurut menurut kaidah tertentu
Data pada umumnya disajikan dalam bentuk sorted Why? Sorting

4 Sort by special key (s) A B C D E F G ascending A B C D E F G
descending

5 Faster and easier in accessing data find “L”!
D-F G-I J-L M-O P-R S-U V-X Y-Z A-C D-F G-I J-L M-O P-R S-U V-X Y-Z Efficient job !

6 Menyusun sekelompok elemen data yang tidak terurut menjadi terurut berdasarkan suatu kriteria tertentu. Mempermudah dan mempercepat proses pencarian data Jika pencarian data mudah, maka proses manipulasi data juga akan lebih cepat. Why Sorting?

7 Internal sorting:refers to the sorting of an array of data that is in RAM
External sorting:refer to sorting methods that are employed when the data to be sorted is too large to fit in primary memory. Internal Vs External

8 Metode Sorting berdasarkan kriteria sorting yang digunakan dibedakan menjadi :

9 Transposition Insert & Keep Sorted
Didasarkan pada perbandingan elemen dan pertukaran posisi elemen Bubble Sort Insert & Keep Sorted Pemasukan sekumpulan data yang belum terurut ke dalam sekumpulan data yang sudah terurut. Mempertahankan keterurutan data yang sudah ada sebelumnya Insertion Sort, Tree Sort

10 Priority Queue Divide & Conquer
Cari elemen yang sesuai dengan kriteria pencarian dari seluruh elemen yang ada (elemen prioritas). Tempatkan pada posisi yang sesuai Ulangi sampai semua elemen telah terurut Selection Sort, Heap Sort Divide & Conquer Pecah masalah ke dalam sub-sub masalah Sort masing-masing sub masalah Gabungkan masing-masing bagian Merge Sort, Quick Sort

11 Diminishing Increment
Penukaran tempat sepasang elemen dengan jarak tertentu. Jarak antar elemen akan terus berkurang sampai dihasilkan keadaan terurut. Shell Sort Addres Calculation Membuat pemetaan atas key yang ingin di sortir,dimana pemetaan itu akan mengirimkan key tersebut ke lokasi yang paling mendekati final di output array Proxmap Sort dan Radix Sort

12 Bubble Sort Ide: bubble = busa/udara dalam air How?
Busa dalam air akan naik ke atas. Ketika busa naik ke atas, maka air yang di atasnya akan turun memenuhi tempat bekas busa tersebut. Bubble Sort

13 Bubble Sort Example

14 void bubbleSort(int numbers[], int n) { int i, j, bubble, temp; for (i = 0; i < n-1; i++) { bubble=numbers[0]; for (j = 1; j < n-i; j++) { if (bubble < numbers[j]){ numbers[j-1]=bubble; bubble=numbers[j]; } else numbers[j-1]=numbers[j]; Bubble Sort Algorithm

15 Bubble Sort Running Time
Kompleksitas: O(n2) Bubble Sort Running Time

16 Selection Sort Lakukan terus sampai kelompok tersebut habis Ide:
Memilih nilai terkecil/terbesar dalam array (sesuai kriteria) dan ditempatkan pada posisi yang sesuai (Pegang index, telusuri nilai array yang sesuai untuk menempati index tersebut ). Lakukan terus sampai kelompok tersebut habis Selection Sort

17 Selection Sort Example

18 Selection Sort Program
void selectionSort(int numbers[], int n) { int i, j; int min, temp; for (i = 0; i < n-1; i++) { min = i; for (j = i+1; j < n; j++) { if (numbers[j] < numbers[min]) min = j; } temp = numbers[i]; numbers[i] = numbers[min]; numbers[min] = temp; Selection Sort Program

19 Selection Sort Running Time
Worst case: O(n2) Best case: O(n2) Based on big-oh analysis, is selection sort better than bubble sort? Selection Sort Running Time

20 Ide: Mengurutkan kartu-kartu??? Insertion Sort

21 Insertion Sort Example

22 Insertion Sort Program
void insertionSort(int numbers[], int n) { int i, j, temp; for (i=1; i < n; i++) { temp = numbers[i]; j = i; while ((j>0) && (numbers[j-1]>temp)) numbers[j] = numbers[j-1]; j = j - 1; } numbers[j] = temp; Insertion Sort Program

23 Insertion Sort Running Time
Running time analysis: Worst case: O(n2) Best case: O(n) Is insertion sort faster than selection sort? Notice the similarity and the difference between insertion sort and selection sort. Insertion Sort Running Time

24 Merge Sort Divide and Conquer approach Ide: Algorithm
Merging two sorted array takes O(n) time Split an array into two takes O(1) time Algorithm If the number of items to sort is 0 or 1, return. Recursively sort the first and second half separately. Merge the two sorted halves into a sorted group. Merge Sort

25 Merge Sort Example

26 MergeSort program Mergesort (elements) if (length <=1) return ;
split(&first, &second) ; first = mergesort(first) ; second= mergesort(second) ; return merge(first, second) ; O(1) O(N) T(N/2) MergeSort program

27 Merge Program 7 5 4 2 6 3 1  p q r n1 n2 Alg.: MERGE(A, p, q, r)
Compute n1 and n2 Copy the first n1 elements into L[1 . . n1 + 1] and the next n2 elements into R[1 . . n2 + 1] L[n1 + 1] ← ; R[n2 + 1] ←  i ← 1; j ← 1 for k ← p to r do if L[ i ] ≤ R[ j ] then A[k] ← L[ i ] i ←i + 1 else A[k] ← R[ j ] j ← j + 1 1 2 3 4 5 6 7 8 p r q n1 n2 p q 7 5 4 2 6 3 1 r q + 1 L R  Merge Program

28 Example: MERGE(A, 9, 12, 16) p r q

29 Example: MERGE(A, 9, 12, 16)

30 Example (cont.)

31 Example (cont.)

32 Example (cont.) Done!

33 Merge Sort Running Time (28 & 32)

34 Quick Sort Divide and Conquer approach Quicksort(S) algorithm:
If the number of items in S is 0 or 1, return. Pick any element v in S. This element is called the pivot. Partition S – {v} into two disjoint groups: L = {x ∈ S – {v} | x ≤ v} and R = {x ∈ S – {v} | x ≥ v} Return the result of Quicksort(L), followed by v, followed by Quicksort(R). Quick Sort

35 Quick Sort Algorithm Select a pivot Partition
Recursive sort and merge the result Quick Sort Algorithm

36 Quick Sort Example

37 Quick Sort Program

38 Quick Sort Running Time
Partitioning takes O(n) Merging takes O(1) So, for each recursive call, the algorithm takes O(n) How many recursive calls does a quick sort need? n for worst case  if pivot is least or greatest key  O(n2) log n for average case  O(n log n) Quick Sort Running Time

39 Ide: Penukaran tempat sepasang elemen dengan jarak tertentu. Jarak antar elemen akan terus berkurang sampai dihasilkan keadaan terurut. Shell Sort

40 Idea: using a mapkey to locate the item in the proper place
Algorithm: Use mapkey to map the item into sorted linked list Compute hit count H[i] Compute Proxmap P[i] Compute insertion location L[i] into A2  output array Proxmap Sort

41 Proxmap Example & Program
Step 1: sorted linked list 1 2 3 4 5 6 7 8 9 10 11 12 0.4 1.1 1.2 1.8 3.7 4.8 5.9 6.1 6.7 7.3 8.4 10.5 11.5 Step 2: compute hit count /*compute hit counts, H[i], for each position, i, in A*/ for(i=0;i<13;++i) { j=MapKey(A[i]); H[j]++; } 1 2 3 4 5 6 7 8 9 10 11 6.7 5.9 8.4 1.2 7.3 3.7 11.5 1.1 4.8 0.4 10.5 6.1 i A[i] 12 1.8 H[i]

42 Proxmap Example & Program
Step 3: compute proxmap /*convert hit counts to a proxmap*/ Position=0; for(i=0;i<13;++i) { if(H[i]>0) P[i]=Position; Position+=H[i]; } 1 2 3 4 5 6 7 8 9 10 11 6.7 5.9 8.4 1.2 7.3 3.7 11.5 1.1 4.8 0.4 10.5 6.1 i A[i] 12 1.8 H[i] P[i]

43 Proxmap Example & Program
Step 4: Compute insertion location L[i] into A2  output array /*Compute insertion locations, L[i], for each key*/ for(i=0;i<13;++i) { L[i]=P[MapKey(A[i])]; } i 1 2 3 4 5 6 7 8 9 10 11 12 A1[i] 6.7 5.9 8.4 1.2 7.3 3.7 11.5 1.1 4.8 0.4 10.5 6.1 1.8 H[i] 1 3 1 1 1 2 1 1 1 1 P[i] 1 4 5 6 7 9 10 11 12 L[i] 7 6 10 1 9 4 12 1 5 11 7 1 0.4 1.1 1.2 1.8 3.7 4.8 5.9 6.1 6.7 7.3 8.4 10.5 11.5 A2[i]

44 Worst case O(n2)  all keys in A have an equal value.
Best case O(n) Proxmap Running Time

45 Idea:radix sort is a sorting algorithm that sorts integers by processing individual digits
Two classifications of radix sorts: least significant digit (LSD) radix sorts most significant digit (MSD) radix sorts LSD radix sorts process the integer representations starting from the least significant digit and move towards the most significant digit. MSD radix sorts work the other way around Radix Sort

46 Radix Sort Example Original:
516, 223, 323, 413, 416, 723, 813, 626, 616 Using Queues: Final Sorted: 223, 323, 413,416, 516, 616, 626, 723, 813 First Pass: 0: 1: 2: 223 3: 323 4: 413,416 5: 516 6: 616,626 7: 723 8: 813 First Pass: 0: 1: 2: 3: 223, 323, 413, 723,813 4: 5: 6: 516, 416, 626, 616 7: 8: First Pass: 0: 1: 413, 813, 516, 416, 616 2: 223, 323, 723, 626 3: 4: 5: 6: 7: 8: Radix Sort Example

47 Radix Sort Running Time
Worst case and best case = O(n) Radix Sort Running Time