algorithm engineering schnelles sortieren n.
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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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Presentation Transcript
  • Kriterien für Sortierverfahren
  • State-of-the-Art
  • Clever-Quicksort
  • Heapsort
  • Weak-Heapsort
  • Quick-Heapsort
  • Radix-Exchange-Sort
  • Sortieren durch Fachverteilung
ImplementierungSieheSedgewick: The analysis of quicksortprograms, ActaInformatica, Journal of Algorithms,15(1):76-100, 1993
adaptives sortieren
Adaptives Sortieren


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)


:= Laufzeit

  • O(n log (Inv(X)/n)+n)



  • Ω(n log (Inv(X)/n)+n)
kartesischer baum
Kartesischer Baum
  • Der kartesische Baum TF

von F[1..n] ist ein geordneter „gewurzelter“ Baum mit n Knoten.

  • Der kartesische Baum des leeren Feldes ist der leere Baum. Sei k = min (1,n).
  • Die Wurzel von TF ist markiert mit k, die Kinder sind die kartesischen Bäume von
  • F[1..k −1] und F[k+1..n] (wobei F[i..j] das leere Feld ist, falls j < i).
konstruktion a la wikipedia
Konstruktion (a la wikipedia)

Process the sequence values in left-to-right order, maintaining the Cartesian tree of the nodes processed so far, in a structure that allows both upwards and downwards traversal of the tree.

To process each new value x, start at the node representing the value prior to x in the sequence and follow the path from this node to the root of the tree until finding a value y smaller than x. This node y is the parent of x, and the previous right child of y becomes the new left child of x.

The total time for this procedure is linear, because the time spent searching for the parent y of each new node x can be charged against the number of nodes that are removed from the rightmost path in the tree

levcopoulos petersson algorithmus
  • KonstruiereKarteschenBaumsfür die Eingabe
  • Initialisiere PQ mitderWurzel des kartesischenBaumes
  • Solange PQ nicht leer:
    • Finde und lösche den min. Wert x in PQ (DeleteMin)
    • Gebexaus
    • Füge die Kinder von x imkartesischen Baum zu PQ hinzu (Insert)