/---------------------\
| Notes for lecture09 |
| 2 November 1999     |
| CS 125-609          |
| Michael Goldwasser  |
\---------------------/

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  ELEMENTARY SORTING ALGORITHMS
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Preface:   Chapter 4.2 of the text discusses sorting (in particular,
it discusses 'bubble sort').

We will discuss several elementary methods for sorting an array, in
particular 'insertion sort', 'selection sort', as well as 'bubble
sort'.

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SELECTION SORT

The general idea is to go through the entire array looking for the
smallest item.  Once you have found this item, you can place this item
in the first array location (swapping whatever used to be there into
the vacated spot so as not to lose track of that item).  Now go
through and select the second-smallest item, and so on.

------------------------------------------------------------------------
Pseudocode:

Dim Selection As Integer     '  we are selecting the <blank> smallest
Dim Look As Integer          '  loop variable when looking at remaining items
Dim SoFar As Integer         '  index of smallest item found thus far

For Selection = 1 to size-1            '   ? why only size-1 ? 

  SoFar = Selection                    '   a default value
  For Look = Selection+1 to size       '   ? why those loop values ?
    If Array(Look) < Array(SoFar) Then
      SoFar = Look                     '   found an even smaller item!
    End If 
  Next Look

  Swap Array(SoFar) and Array(Selection)  ' place the selected item
                                          '  into its correct location
Next Selection
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INSERTION SORT

General idea is to look at only the beginning part of the array,
adding one new item at a time while keeping the beginning of the array
sorted.

------------------------------------------------------------------------
Pseudocode:

For NewIndex = 2 to size    '  we want Array(1 to NewIndex) to be sorted

  NewValue = Array(NewIndex)       ' must open up correct spot to place
                                   '   item currently at Array(NewIndex)
  i = NewIndex-1                   ' starting one spot to the left
  Do While NewValue < Array(i)     ' go until we find the correct place:
    Array(i+1)  = Array(i)         '   slide item i to the right
    i = i-1                        '   keep moving left
  Loop

  Array(i+1) = NewValue            ' place NewItem to the right of where
                                   '   we finally got stuck
Next Partial
------------------------------------------------------------------------

Bug as written --- what if the current item is the smallest so far?!
 

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BUBBLE SORT

General idea is to do selection sort, but do a little extra work while
scanning down the list (in hopes that the extra work will pay off later).

To be consistent with the book, instead of selecting starting with the
smallest, we consider selection starting with the largest element.

Scan from left to right, but instead of just keeping track of the
largest thus far, whenever you see two neighbors that are out of
order, swap them and continue.  Notice that whereever the biggest item
is in the array, it will always be out of place compared to its
neighbor and so it will keep getting swapped (bubbling) to the far end
of the array.

Now repeat this process to place the second largest item, and so on...

------------------------------------------------------------------------
Pseudocode:


For Pass = 1 to size-1                    '  ? why only size-1 passes ?

  For Walk = 1 to size - pass             '  ? are limits correct ?
    If Array(Walk) > Array(Walk+1) Then
      Swap Array(Walk) and Array(Walk+1)  '  swap the neighbors
    End If
  Next Walk

Next Pass

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DISCLAIMER:
  All of the pseudocode given here is just that (did you know that
  'pseudo' is Greek for 'lie').

  If you want to see code that works, please look at the program which
  is provided as part of lab9.

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