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Hausuebung_10_Hashtabellen
Course: HKJLHKJL 565, Spring 2009School: University of Graz
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MatNr. HausuebungNr.10Hastabellen DatenstrukturenAlgorithmen 11.02.2008 Angabe i A[i] 0 6 19 1 3 16 2 9 22 3 0 13 4 3 16 5 6 19 6 0 13 Bsp1 A[i] % 5 4 1 2 3 1 i 0 1 2 16 22 16 Kollision 3 13 4 19 Bsp2 - linear probing A[i] % 5 4 1 2 3 1 2 3 4 0 4 19 A[i] A[i] A[i] A[i] + + + + 1 2 3 4 i 0 16 1 16 2 22 3 13 Bsp3 quadratic - probing f(i) = 3i^3+2i^2+i h(w,i) i 0 4 0 13 6 2 1 22 34 1 2 16 102 0 3 228...
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MatNr. HausuebungNr.10Hastabellen
DatenstrukturenAlgorithmen
11.02.2008
Angabe
i A[i] 0 6 19 1 3 16 2 9 22 3 0 13 4 3 16 5 6 19 6 0 13
Bsp1
A[i] % 5 4 1 2 3 1
i
0
1 2 16 22 16 Kollision
3 13
4 19
Bsp2 - linear probing
A[i] % 5 4 1 2 3 1 2 3 4 0 4 19 A[i] A[i] A[i] A[i] + + + + 1 2 3 4
i
0 16
1 16
2 22
3 13
Bsp3 quadratic - probing
f(i) = 3i^3+2i^2+i h(w,i) i 0 4 0 13 6 2 1 22 34 1 2 16 102 0 3 228 4 4 19 16 Kollision
Bsp4 - double Hashing
i A[i] h2(k) h1(k) h1(k)+i*h2(k) h(w) i 0 19 2 4 4 4 0 1 16 2 1 3 3 1 22 2 22 2 2 6 1 2 16 3 13 2 3 9 4 3 16 4 16 2 1 9 4 4 19 13 16 Kollision
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HaraldAltinger2008 MatNr.0630936
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University of Graz - HKJLHKJL - 565
Altinger Harald 0630936INTSUCH(von,bis,x) IF A[von] < A[bis] THEN t = floor(sqrt(x-A[von]*(von^2 - bis^2) / (A[von] - A[bis]) + von^2) IF x = A[t] then RETURN t ELSE IF x < A[t] THEN RETURN INTSUCH(von,t-1,x) ELSE RETURN INTSUCH(t+1,bis,x) ELSE IF x = A[
University of Graz - HKJLHKJL - 565
05AltingerHarald0630936Altinger Harald 0630936/-/funktion searches for the min branch within a binary tree /the idea is to seek per node; first all left elements, afterwards all left int seekRecursive(int currentDepth, int minLength, currentNode) cfw
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.03104.10.2007helmut.hauser@igi.tugraz.atUm was geht es?DatenstrukturenAlgorithmen04.10.2007helmut.hauser@igi.tugraz.atAlgorithmusVersuch einer Erklrung: Ein Algorithmus nimmt bestimmte Daten als Input und tran
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 2. Vorlesung, am 12.Okt 200611.10.2007helmut.hauser@IGI1Kleine WiederholungKennenlernen grundlegender Datenstrukturen und Algorithmen (Basis und Bausatz fr Sie). Wir wollen Algorithmen auch analysieren und unt
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 3. Vorlesung, am 18.Okt 2007Kleine Wiederholung Mathematische Definition von Komplexittsklassen Asymptotische Betrachtungsweise ( n O-Notation -Notation -Notation beschrnkt von oben beschrnkt von unten ) worst ca
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 4. Vorlesung, am 25.Okt. 200725.10.2007helmut.hauser@IGI1Kleine Wiederholung - Rekursionen Beschreibung durch Rekursionsgleichungen Lsen von Rekursionen Iteratives Einsetzen Induktion Schranken finden (siehe F
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 5. Vorlesung, am 08.Nov. 2007Kleine WiederholungElementare Datenstrukturen- Lineares Feld A[n] LIFO - Stapel (Stack)- Anwendungen: - Infix-Postfix - Postfix-Auswertung - Rekursionen abbilden - etc. - Schlange (
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 6. Vorlesung, am 15.Nov. 2007Wiederholung - HaldeEine Halde (Heap) ist ein lineares Feld A[1.n], wobei gilt:A[i] max cfw_A[2i], A[2i+1], fr i=1,2,floor(n/2) Haldenbedingung- Maximum steht an erster Position 976
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 7. Vorlesung, am 22.Nov. 200722.11.2007helmut.hauser@IGIAchtung: Vorlesung nchste Woche (29.Nov) fllt aus !22.11.2007helmut.hauser@IGIWiederholung Partition Zerlegen von FeldernDefinition Zerlegen: Speichere
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 8. Vorlesung, am 13.Dez. 200713.12.2007helmut.hauser@IGIWiederholung - QuicksortT(n) = T(k) + T(n-k) + O(n)Bester Fall:k = n/2Schlechtester Fall:k=1Minimale RekursionstiefeMaximale Rekursionstiefeworst c
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 9. Vorlesung, am 10.Jan. 200810.01.2008helmut.hauser@IGIWiederholungWrterbuchproblem (Suchen, Einfgen, Lschen) Eine gute Lsung: Hashtabellen (Gestreute Speicherung) Wichtig: Eine gute Hashfunktion zu haben, um
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 10. Vorlesung, am 17.Jan. 200817.01.2008helmut.hauser@IGIWiederholung Suchen in linearen FeldernOhne Vorsortierung Mit Vorsortierung Sequentielle Suche Speicherung nach Zugriffswahrscheinlichkeiten Selbstanord
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 11. Vorlesung, am 24.Jan. 200824.01.2008helmut.hauser@IGIBinrbume - WiederholungBinrbume sind spezielle Bume, welcher maximal 2 Shne haben. Knotenreihenfolgen (Symmetrische, Haupt- und Nebenreihenfolge) geordne
University of Graz - HKJLHKJL - 565
Datenstrukturen & AlgorithmenVO 708.031 12. Vorlesung, am 31.Jan. 200731.01.2008helmut.hauser@IGIHinweise: Es gibt weitere Prfungstermine im Laufe des Semesters Nutzen Sie die Wartelisten Wenn Sie die Prfung nicht machen wollen, bitte abmelden! Scha
University of Graz - HKJLHKJL - 565
Insertion-Sort For i=2 to n h=A(j) j=j-1 While A(j)>h and j>0 Do A(j+1) = A(j) j=j-1 A(j=1)=h
University of Graz - HKJLHKJL - 565
University of Graz - HKJLHKJL - 565
Fakultaet(n) if n=1 then return 1 else return(n*Fakultaet(n-1)fibonacci(n) fib = 1 fir_1 = 1 for i = 3 to n fib_2 =fib_1 fig_1 = fib fib = fib_1 + fib_2 return fib
University of Graz - HKJLHKJL - 565
Verhalden(A,i) l-LINKS(i), r=RECHTS(i) index = i if l<=n AND A[l>A[i] then index=l if r<=n AND A[r>A[index then index=r if i!=index then vertausche(A[i],A[index]) verhalde(A,index)Baue_halde(A) for i=n/2 downto 1 verhalde(A,i)Baue_halde(A) for i=n/2 dow
University of Graz - HKJLHKJL - 565
MAXIMUM (A) return A[1] ENTFERNE_MAX (A) A[1] = A[n] n=n-1 Verhalde (A,1) EINFUEGEN (A,x) n = n+1, A[n]=x, i=n While i > 1 and A[i]>A[Vater(i)] do Vertausche (A[i],A[Vater(i)]) i = Vater(i)www.cosc.canterbury.ac.nz/mukundan/dsal/MinHeapAppl.htmlHEAP_SOR
University of Graz - HKJLHKJL - 565
RAND_PARTITION (A,l,r) idx = RANDOM(l,r) VERTAUSCHE(A[i],A[idx]) p = A[l] j = l-1 k = r+1 loop repeat j=j+1 until A[j] => p repeat k=k-1 until A[k] =< p if j < k then vertausche (A[j],A[k]) else return k QUICKSORT(A,l,r) if l < r then k=PARTITION (A,l,r)
University of Graz - HKJLHKJL - 565
University of Graz - HKJLHKJL - 565
Suche (A,x) i = 0; While i < n i=i+1 if (A[i] = x) RETURN i else RETURN -1BINSUCHE(von,bis,x) if von <= bis then m = floor (von + bis)/2) if x = A[m] then return m else if x < A[m] then m = BINSUCHE(von,m -1,x) else then m = BINSUCHE(m+1,bis,x) else m =
University of Graz - HKJLHKJL - 565
University of Graz - HKJLHKJL - 565
Simon Fraser - CS - CMPT 307
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Simon Fraser - CS - CMPT 307
Simon Fraser - CS - CMPT 307
Simon Fraser - CS - CMPT 307
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