Bubble Sorting

1
Bubble Sorting

• Comp 208 Computers in Engineering
• Yi Lin
• Winter, 2007

2
Analogy to buoyancy

• Bubble sort is an analogy
• Light elements rise to the top
• Heavy elements sink to the bottom
• Top / bottom can arbitrarily be defined to be
  the beginning or end of array to obtain
  increasing / decreasing orders

3
One pass bubbling

• One pass bubbling
• go through the list comparing each adjacent
  elements,
• if they're not in order swap them,
• doing one pass of this guarantees that the
  smallest element will end up at the beginning of
  the list.

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2
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Multiple passes

• Go through the list again until all the elements
  are in order. A total of N-1 passes need to be
  made for all the list to be in order.

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2nd pass
3rd pass
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Bubble sort

• First pass bubbling

32
15
38
56
23
35
74
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35
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Bubble sort

• 2nd pass

15
32
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35
74
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Bubble sort function example 4

• void bubbleSort(int a, int size)
• int i, j
• for(i0 iltsize i)
• for(jsize-1 jgt0 j--)
• if(aj lt aj-1)
• swap(aj, aj-1)

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Two optimizations

• We know that after X passes the X smaller
  elements are at the beginning of the list, it
  therefore isn't useful to pass through these
  elements again, therefore pass X will have N-X
  comparisons instead of N
• If we haven't swapped in a pass then the list is
  in order, therefore we can finish sorting

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Bubble sort optimization 1Example 5

• void bubbleSort(int a, int size)
• int i, j
• for(i0 iltsize-1 i)
• for(jsize-1 jgti j--) // only need to
  check ai to asize-1
• if(aj lt aj-1)
• swap(aj, aj-1)

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Bubble sort optimization 2Example 6

• void bubbleSort(int a, int size)
• int i, j
• int swapped
• for(i0 iltsize-1 i)
• swapped0
• for(jsize-1 jgti j--)
• if(aj lt aj-1)
• swap(aj, aj-1)
• swapped1
• if(swapped0)
• break

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Insertion Sorting

• Comp 208 Computers in Engineering
• Yi Lin
• Winter, 2007

12
How do you update a sorted list?

• What if you already had a sorted list and wanted
  to add one more member to it?
• If you cant arbitrarily insert (as we cant)
• Put the element at the beginning / end
• Use a single bubble pass to move it to its
  final location
• This can be used to sorted completely unsorted
  lists too!

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Insertion sort

• First pass

• 2nd pass

32
15
38
56
23
35
74
15
32
38
56
23
35
74
15
32
38
56
23
35
74
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Insertion sort

• 3rd pass

• 4th pass

15
32
38
56
23
35
74
15
23
32
38
56
35
74
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32
38
56
23
35
74
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38
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74
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Insertion sort

• 5th pass

15
23
32
38
56
35
74
15
23
32
38
35
56
74
15
23
32
38
35
56
74
15
23
32
35
38
56
74
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Insertion sort, example 7

• void insertionSort(int a, int size)
• int i, j
• for(i1 iltsize i) // i0 also works fine.
• for(ji jgt0 j--)
• if(aj lt aj-1)
• swap(aj, aj-1)

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Insertion sort optimizationExample 8

• void insertionSort(int a, int size)
• int i, j
• for(i1 iltsize i) // i0 also works fine.
• for(ji jgt0 j--)
• if(aj lt aj-1)
• swap(aj, aj-1)
• else
• break