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Quick Sort

Quick Sort. High level version Partition AlmostQuickSort. QuickSort. QuickSort(l,r) If (r-l) < 1 Return i  Partition(l,r) QuickSort(l,i-1) QuickSort(i+1,r) Partition(l,r). r. l. i. Partition. How can you Partition, so that: Partition is O(n)

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Quick Sort

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  1. Quick Sort High level version Partition AlmostQuickSort CS 303 – Quick Sort Lecture 16

  2. QuickSort • QuickSort(l,r) • If (r-l) < 1 Return • i  Partition(l,r) • QuickSort(l,i-1) • QuickSort(i+1,r) • Partition(l,r) r l i CS 303 – Quick Sort Lecture 16

  3. Partition • How can you Partition, so that: • Partition is O(n) • Why? • If both these conditions are met, then QuickSort is O(n log n) • If not...not! • Discuss various Partition techniques • scan from l,r inwards – swap when stuck • scan from l  r – swap when <x • Discuss choice of pivot • use statistical sample to improve odds CS 303 – Quick Sort Lecture 16

  4. AlmostQuickSort • AlmostQuickSort(l,r) • If (r-l) < 15 Return • i  Partition(l,r) • AlmostQuickSort(l,i-1) • AlmostQuickSort(i+1,r) • QuickSort(l,r) • AlmostQuickSort(l,r) • InsertionSort(l,r) • Partition becomes easier to code • Final InsertionSort is O(n) • alas...(Almost)QuickSort is still O(n2) (in theory...but...) CS 303 – Quick Sort Lecture 16

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