Computer Science 101 A Survey of Computer Science

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Computer Science 101A Survey of Computer Science

• QuickSort

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Divide and Conquer
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Divide and Conquer

• Divide and Conquer is a common strategy used in
  computer science.
• The idea is that for a given problem, we try to
  break it into smaller problems (perhaps of the
  same type and then solve the smaller problems)
• Of course, we must consider how to solve the
  smaller problems.

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Sorting -Quicksort

• Strategy - Divide and Conquer
• Partition list with small elements in first part
  and large elements in second part
• Sort the first part.
• Sort the second part.

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Quicksort (cont.)

• Question - How do we sort the sections?Answer -
  Apply Quicksort to them.
• Recursive algorithm - one which makes use of
  itself to solve smaller problems of the same type.

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Quicksort (cont.)

• Question - Will this recursive process ever
  stop?
• Answer - Yes, when the problem is small enough
  , we no longer use recursion. Such cases are
  called anchor cases.

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Recursion Example

• The factorial function could be defined this
  way n! 1 if n1 n ((n-1)!)
  otherwise
• Example 4! 4 x 3! 4 x 3 x 2! 4 x 3 x 2
  x 1! 4 x 3 x 2 x 1

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Quicksort - Partitioning

• To partition, we choose a pivot element from
  the list.
• The elements which are less than or equal to the
  pivot go into the first section.
• The elements larger than the pivot go into the
  second section.

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Quicksort - The Pivot

• Ideal would be to choose the median as the pivot,
  but this would take too long.
• Some programs just choose the first element.
• Our choice - choose the median of the first three
  elements.

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Quicksort Partition

• Variables
• N(I),N(I1), , N(K) - list to partition
• P - position of the pivot element
• L - Right hand marker for the first section
• U - Left hand marker for the second section

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Quicksort Partition Algorithm

• Exchange the median of the first 3 elements
  with the first elementSet P to first position of
  listSet L to second position of listSet U to
  last position of listWhile L U do While N(L)
  ? N(P) do Set L to L1 end-of-loop While N(U)
  gt N(P) do Set U to U-1 end-of-loop If L lt U
  then Exchange N(L) and N(U)end-of-loopExchange
  N(P) and N(U)

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QuickSort - The Algorithm

• If the list to sort has more than 1 element
  then If the list has exactly two elements then
  If the elements are out of order
  then Exchange them else Perform the
  Partition Algorithm on list Apply QuickSort
  to the first section Apply QuickSort to the
  second section
• Note Anchor cases are when the list has 1 or 2
  elements recursion is used for 3 or more.

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Quicksort Example
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Quicksort Example (Cont.)
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Quicksort Example (Cont.)
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Quicksort Example (Cont.)
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Quicksort Example (Cont.)
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Quicksort Example (Cont.)
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Quicksort Example (Cont.)
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Quicksort Example (Cont.)
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Quicksort Example (Cont.)
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Student(?) sorts exam papers
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If your way's so good, then prove it!