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Lecture 25: Quick Sort

or. CSC 213 – Large Scale Programming. Lecture 25: Quick Sort. Today’s Goals. Begin by discussing basic approach of quick sort Divide-and-conquer used , but how does this help? Merge sort also divides-and-conquers, what differs? Show execution tree & discuss meaning for quick sort

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Lecture 25: Quick Sort

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  1. or CSC 213 – Large Scale Programming Lecture 25:Quick Sort

  2. Today’s Goals • Begin by discussing basic approach of quick sort • Divide-and-conquer used, but how does this help? • Merge sort also divides-and-conquers, what differs? • Show execution tree & discuss meaning for quick sort • Consider selection and important of the pivot • Quick sort rocks for which pivots and why? • If we get really unlucky, when would quick sort suck? • How can we affect choice to insure we get lucky • Given all these facts: is quick sort worth the risk?

  3. Quick (ungraded) Quiz • For what cases does quick sort suck? • When would quick sort execute fastest? • How does quick sort use divide-and-conquer?

  4. Divide-and-Conquer • Like all recursive algorithms, need base case • Has immediate solution to a simple problem • Work is not easy and sorting 2+ items takes work • Already sorted 1 item since it cannot be out of order • Sorting a list with 0 items even easer • Recursive step simplifies problem & combines it • Begins by splitting data into two Sequences • Combine subSequencesonce they are sorted

  5. Quick Sort • Divide: Partition by pivot • L has values <= p • G uses values >= p • Recur: Sort L and G • Conquer: Merge L, p, G p

  6. Quick Sort • Divide: Partition by pivot • L has values <= p • G uses values >= p • Recur: Sort L and G • Conquer: Merge L, p, G p

  7. Quick Sort • Divide: Partition by pivot • L has values <= p • G uses values >= p • Recur: Sort L and G • Conquer: Merge L, p, G p p G L

  8. Quick Sort • Divide: Partition by pivot • L has values <= p • G uses values >= p • Recur: Sort L and G • Conquer: Merge L, p, G p p G L p

  9. Quick Sort v. Merge Sort Quick Sort Merge Sort • Work mostly splitting data • Cannot guarantee even split • Should skip some comparisons • Does not need extra space • Less work allocating arrays • Blindly merges all the data • Data already in sorted order! • Blindly splits data in half • Always gets even split • Needs* to use other arrays • Wastes time in allocation • Complex workaround exists • Work mostly in merge step • Combines two (sorted) halves • Always skips some comparisons

  10. Execution Tree • Depicts divide-and-conquer execution • Recursive call represented by each oval node • Original Sequence shown at start • At the end of the oval, sorted Sequence shown • Initial call at root of the (binary) tree • Bottom of the tree has leaves for base cases

  11. Execution Example • Each call starts by selecting the pivot 7 2 9 4 3 7 6 1  1 2 3 4 6 7 7 9

  12. Execution Example • Each call starts by selecting the pivot 7 2 9 4 3 7 61 1 2 3 4 6 7 7 9

  13. Execution Example • Split into L & Gpartitions around pivot 7 2 9 4 3 7 6 1  1 2 3 4 6 7 7 9

  14. Execution Example • Split into L &Gpartitions around pivot 7294 3761 1 2 3 4 6 7 7 9

  15. Execution Example • Recursively solve L partition first 7294 3761 1 2 3 4 6 7 7 9

  16. Execution Example • Recursively solve L partition first 7294 3761 1 2 3 4 6 7 7 9 2 4 3 1 1 2 3 4

  17. Execution Example • Select new pivotand split into L &Gpartitions 7294 3761 1 2 3 4 6 7 7 9 24 3 1 1 2 3 4

  18. Execution Example • Recursively solve for L 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 11

  19. Execution Example • Recursively solve for L & enjoy base case 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 11

  20. Execution Example • Now solve for Gpartition and select pivot 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 11 43 3 4

  21. Execution Example • Recursively solve for L 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 11 43 3 4

  22. Execution Example • Recursively solve for L & enjoy base case 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 11 43 3 4

  23. Execution Example • Now solve for G& enjoy base case 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 11 43 3 4 44

  24. Execution Example • Add L,pivot,&Gto complete previous call 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 11 433 4 44

  25. Execution Example • Add L,pivot,&Gto complete previous call 7294 3761 1 2 3 4 6 7 7 9 24 3 1 1 2 3 4 11 433 4 44

  26. Execution Example • Recursively sort Gfrom original call 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 11 433 4 44

  27. Execution Example • Recursively sort Gfrom original call 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 7 9 7 7 7 9 11 433 4 44

  28. Execution Example • Select pivot& partition intoL & G 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 7 9 7 7 7 9 11 433 4 44

  29. Execution Example • SolveLrecursively via base case & move to G 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 7 9 7 7 7 9 11 433 4 7 9 7 9 44

  30. Execution Example • Select pivot& partition intoL & G 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 7 9 7 7 7 9 11 433 4 797 9 44

  31. Execution Example • Solve through two base cases in L&G 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 7 9 7 7 7 9 11 433 4 797 9 44 99

  32. Execution Example • Add L,pivot,&Gto complete the call 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 7 9 7 7 7 9 11 433 4 797 9 44 99

  33. Execution Example • Add L,pivot,&Gto complete the call 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 7 9 77 7 9 11 433 4 797 9 44 99

  34. Execution Example • Add L,pivot,&Gto complete final call 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 7 9 77 7 9 11 433 4 797 9 44 99

  35. Execution Example • Sorts data, but only as good as pivotchoice 7294 3761 1 2 3 4 6 7 7 9 24 3 1  1 2 3 4 7 9 77 7 9 11 433 4 797 9 44 99

  36. Quick-Sort’s Pivot • Can select any element as pivot • Pivot's existence required only, not where or what it is • Quick-Sort's ideal pivot is median element • Equal-sizedL&Gwhen median element selected • Makes complexity equal to Merge-Sort • Must sort data first to find the median, however • Smallest (or largest element) worst pivot • G (or L) holds all elements & other partition empty • Complexity becomes equal to Insertion-Sort

  37. Simple Pivot Selection • Could use first (or last) element as pivot • It’s easy to code… • …but also makes sorted data the worst case… • …which is common so this is a really bad idea • Could choose random element as pivot • Little harder to code, but expected to work well • Best is median of first, mid, & last items in list • Nearly eliminates worst case, but much harder to code

  38. For Next Lecture • Week #9 assignment posted so get working • Keep reviewing requirements for program #2 • 2nd preliminary deadline coming up so get started • Time developing good tests saves coding time later • Reading on radix sort for Monday • Is it possible to sort without comparisons? • How is radix sort faster than O(n log n) lower bound?

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