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Bekti - Rita - Sevenhot

z. Struktur Data & Algoritma 2009. Bekti - Rita - Sevenhot. DEFINISI. DEFINISI. HEAP Sebuah complete binary tree dengan ketentuan sebagai berikut : Perbandingan suatu node dengan suatu nilai node child-nya mempunyai ketentuan tertentu berdasarkan jenis heap-nya Jenis heap

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Bekti - Rita - Sevenhot

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  1. z Struktur Data & Algoritma 2009 Bekti - Rita - Sevenhot

  2. DEFINISI DEFINISI • HEAP • Sebuah complete binary tree dengan ketentuan sebagai berikut : • Perbandingan suatu node dengan suatu nilai node child-nya mempunyai ketentuan • tertentu berdasarkan jenis heap-nya • Jenis heap • MAXHEAP (elemen maksimum di root) : • A[parent(i)] ≥ A[i] • nilai node lebih besar atau sama dengan nilai childnya • MINHEAP (elemen minimum di root) : • A[parent(i)] ≤ A[i] • nilai node lebih kecil atau sama dengan nilai childnya SDA - 2009

  3. CONTOH HEAP MAXHEAP MINHEAP 12 2 10 7 4 7 6 2 4 7 12 4 8 10 nilai node ≥ nilai childnya nilai node ≤ nilai childnya SDA - 2009

  4. Heap adalah suatu priority queue (mempertahankan antrian prioritas). • Dalam antrian prioritas, elemen yang dihapus adalah elemen yang mempunyai prioritas terbesar (atau terkecil, tergantung keperluan), • dan elemen inilah yang selalu terletak di akar (root). • Suatu heap sewaktu-waktu dapat berubah, baik itu dikarenakan penambahan elemen (insert) ataupun penghapusan elemen (delete). • Struktur data heap biasanya diimplementasikan dalam array SDA - 2009

  5. INDEXING INDEXING 1 parent(i) = i/2 left_child(i) = 2·i right_child(i) = 2·i + 1 3 2 4 5 6 7 SDA - 2009

  6. OPERASI HEAP OPERASI HEAP INSERT Memasukkan data baru ke dalam heap tree Contoh : insert 9 Karena 9 < 10, maka 10 tidak terjadi switch Proses insert berhenti 10 10 10 exchange 9 > 1 exchange 9 > 7 7 7 7 7 9 7 1 3 2 4 9 3 2 4 7 3 2 4 9 1 1 SDA - 2009

  7. OPERASI HEAP OPERASI HEAP ROOT DELETION Menghapus root pada heap tree Contoh : delete root 12 2 Elemen dengan indeks terbesar naik menjadi root HEAPIFY 7 10 7 10 1 3 4 2 1 3 4 SDA - 2009

  8. HEAPiFY HEAPIFY Definisi Proses mengubah binary tree menjadi heap tree Algoritma Heapify(A,i) l ← left [i] r ← right [i] if l ≤ heap-size [A] and A[l] > A[i] then largest ← l     else largest ← i if r ≤ heap-size [A] and A[r] > A[largest]     then largest ← r if largest  ≠ i     then exchange A[i] ↔ A[largest] Heapify (A, largest) SDA - 2009

  9. HEAPiFY HEAPIFY Contoh 2 10 10 7 > 2 10 > 7 7 > 2 7 10 7 7 2 7 1 3 4 1 1 3 3 2 7 SDA - 2009

  10. HEAP SORT HEAP SORT • HEAP SORT ALGORITHM • adalah algoritma sorting yang berdasarkan pada struktur data heap tree • Kompleksitas running time-nye : O(nlog(n)) • Langkah : • Susun array A kedalam heap tree • Ambil root pada heap tree, masukkan ke array • Hapus elemen root (dengan mempertahankan sifat heap, lakukan heapify jika tidak memenuhi sifat heap) • Lakukan terus (langkah 2-3) hingga tree menjadi kosong SDA - 2009

  11. ALGORITHM HEAP SORT ALGORITHM HEAPSORT (A) BuildHeap (A) for i ← length (A) down to 2 do exchange A[1] ↔ A[i] heap-size [A] ← heap-size [A] - 1 Heapify (A, 1) SDA - 2009

  12. Heapify(A,i) l ← left [i] r ← right [i] if l ≤ heap-size [A] and A[l] > A[i] then largest ← l     else largest ← i if r ≤ heap-size [A] and A[r] > A[largest]     then largest ← r if largest  ≠ i     then exchange A[i] ↔ A[largest] Heapify (A, largest) BuildHeap(A) heap-size (A) ← length [A] for i ←  floor(length[A]/2) down to 1 do       Heapify (A, i) SDA - 2009

  13. SIMULASI SIMULASI HEAP SORT Array A = [1, 4, 89, 77, 12, 50, 23] BuildHeap(A) SDA - 2009

  14. SIMULASI SIMULASI HEAP SORT Array A = [1, 4, 89, 77, 12, 50, 23] BuildHeap(A) insert 1 1 SDA - 2009

  15. SIMULASI SIMULASI HEAP SORT Array A = [1, 4, 89, 77, 12, 50, 23] BuildHeap(A) insert 4 insert 1 1 4 1 4 1 SDA - 2009

  16. SIMULASI SIMULASI HEAP SORT Array A = [1, 4, 89, 77, 12, 50, 23] BuildHeap(A) insert 4 insert 1 insert 89 1 4 1 4 89 4 1 1 89 1 4 SDA - 2009

  17. SIMULASI SIMULASI HEAP SORT BuildHeap(A) insert 77 89 89 1 4 77 4 1 77 SDA - 2009

  18. SIMULASI SIMULASI HEAP SORT BuildHeap(A) insert 77 insert 12 89 89 89 1 4 77 4 77 4 1 77 12 1 SDA - 2009

  19. SIMULASI SIMULASI HEAP SORT BuildHeap(A) insert 50 insert 77 insert 12 89 89 89 89 89 1 4 77 4 77 4 77 4 77 50 50 4 1 77 12 12 12 1 1 1 SDA - 2009

  20. SIMULASI SIMULASI HEAP SORT BuildHeap(A) insert 23 89 77 50 4 23 12 1 SDA - 2009

  21. SIMULASI SIMULASI HEAP SORT 89 23 77 Delete root Heapify 77 50 77 50 23 50 4 4 4 23 12 12 12 1 1 1 sorted SDA - 2009

  22. SIMULASI SIMULASI HEAP SORT 77 4 50 Delete root Heapify 23 50 23 50 23 4 4 12 12 12 1 1 1 sorted SDA - 2009

  23. SIMULASI SIMULASI HEAP SORT 50 12 23 Delete root Heapify 23 4 23 4 12 4 12 1 1 1 sorted SDA - 2009

  24. SIMULASI SIMULASI HEAP SORT 23 1 12 Delete root Heapify 12 4 12 4 1 4 1 sorted SDA - 2009

  25. SIMULASI SIMULASI HEAP SORT 12 4 Delete root 1 4 1 sorted SDA - 2009

  26. SIMULASI SIMULASI HEAP SORT 12 4 Delete root Delete root 1 1 4 1 sorted SDA - 2009

  27. SIMULASI SIMULASI HEAP SORT 12 4 Delete root Delete root Delete root 1 1 4 1 sorted SDA - 2009

  28. Selesai & Terima kasih SDA - 2009

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