Lecture 4: Sorting Algorithms

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Lecture 4 Sorting Algorithms

• John.Levine_at_cis.strath.ac.uk
• Prof Branestawms
• Sorting Challenge

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Recap of Searching

• Linear search through unordered data is O(n)
• Binary search in ordered data is O(log n)
• Parallel search is even faster
• Search through different combinations is
  exponential if were not smart
• More on graph searching later

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The Problem

• Prof Branestawm has 1,024 books, which he usually
  keeps in alphabetical order
• Bubbles the experimental monkey has gone loopy
  and thrown them all around the room
• How can we get them back into order on the
  bookshelves as efficiently as possible?
• Comparison of titles is the slow step

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Random Sort

1. Put the books back on the shelves in a random
   order.
2. Check to see if they are in alphabetical order.
3. If they are, stop.
4. Else throw them on the floor and repeat from Step
   1.

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Naïve Sort

1. Go through the pile and find the book with the
   title which comes first.
2. Put it on the shelf in first place.
3. Find the second book and put it in second place
   on the shelf.
4. Repeat until all the books are done.

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Bubblesort

1. Put the books on the shelves in a random order.
2. Go through the books comparing the book at
   position i with the book at position i1. If they
   are in the wrong order swap them.
3. Repeat step 2 until a pass is made over the books
   where no swapping occurs.

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Quicksort

1. Partition the books into two piles one pile for
   titles that start with A-M, one for N-Z.
2. Partition each pile into a further two piles,
   trying to keep the piles of equal size.
3. Repeat until the all the piles are of size 1,
   then put all the books onto the shelves in order.

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The Challenge

• What is the complexity of each of these sorting
  algorithms?
• How long will each take on average for 1024 books
  if the comparison step takes 1 second? How
  about for 2048 books?
• Can you think of an algorithm that could do
  better than any of these?