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Algorithm Engineering „Schnelles Sortieren“

Algorithm Engineering „Schnelles Sortieren“. Stefan Edelkamp. Überblick. Kriterien für Sortierverfahren State- of - the -Art Clever- Quicksort Heapsort Weak-Heapsort Quick- Heapsort Radix-Exchange- Sort Sortieren durch Fachverteilung. Kriterien für Sortierverfahren.

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Algorithm Engineering „Schnelles Sortieren“

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  1. Algorithm Engineering „Schnelles Sortieren“ Stefan Edelkamp

  2. Überblick • Kriterien für Sortierverfahren • State-of-the-Art • Clever-Quicksort • Heapsort • Weak-Heapsort • Quick-Heapsort • Radix-Exchange-Sort • Sortieren durch Fachverteilung

  3. Kriterien für Sortierverfahren

  4. State-of-the-Art

  5. State-of-the-Art (2)

  6. State-of-the-Art (3)

  7. Clever-Quicksort (Median-of-3)

  8. Clever-Quicksort (Median-of-3) Σ

  9. ImplementierungSieheSedgewick: The analysis of quicksortprograms, ActaInformatica, Journal of Algorithms,15(1):76-100, 1993

  10. Heapsort

  11. Definition

  12. Veranschaulichung

  13. Entfernen des Maximums

  14. Versickern

  15. Pseudo-Code

  16. Erstellung eines Heaps

  17. Äußere Schleife

  18. Analyse Iteriertes Versickern Σ

  19. Analyse

  20. Beobachtung

  21. Bottom-Up-Heapsort

  22. Pseudo-Code (1)

  23. Pseudo-Code (2)

  24. Worst-Case

  25. Average Case

  26. Weak-Heap-Sort

  27. Verschmelzen

  28. Generiereneines Weak-Heaps

  29. Sortierung

  30. Arrayeinbettung

  31. 3 Fälle

  32. PseudoCode

  33. Analyse Σ

  34. Engineering

  35. Quick-Heapsort

  36. Quick-Heapsort Σ Σ

  37. Pseudo-Code

  38. Pseudo-Code (2)

  39. Pseudo-Code (3)

  40. Radix-Sort

  41. Radix-Exchange-Sort

  42. Beispiel

  43. UnterscheidenePräfixe

  44. Analyse

  45. Sortieren durch Fachverteilen

  46. Analyse

  47. Illustration

  48. Pseudo-Code (1)

  49. Pseudo-Code (2)

  50. Adaptives Sortieren Inversionen Inv(X) = {(i,j) | • 1 <= i < j <= n und • xi > xj} Ziel AE: 1*n log (Inv(X)/n)+O(n) Wenn Inv(X) = O(n²)  n log n + O(n) Inversions-optimal := Laufzeit • O(n log (Inv(X)/n)+n) Informationstheoretische Grenze: • Ω(n log (Inv(X)/n)+n)

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