Topic 7
Standard Algorithms
Learning Objectives

Describe and exemplify the following standard
algorithms in pseudocode and an appropriate high
level language




Binary search
Describe and compare simple linear and binary
search algorithms
Describe and compare sort algorithms for simple
sort, bubble sort and selection sort in terms of
number of comparisons and use of memory
Describe and exemplify user-defined module
libraries
Linear Search
Linear Search


Simplest search method to implement
Scanning takes place from left to right until the
search key is found
16 9 34 76 85 2 25 82 55 60
Search key is 76
Linear Search Algorithm
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Set found to false
Input search key
Point to first element in list
Do while (not end of list) and (not found)
if array(value) = key then
found=true
output suitable message
else
look at next element in list
end if
loop
If (not found) then
key not in list
End if
Linear Search





Not a bad algorithm for short lists
Easier to implement than other methods
List does not need to be sorted
Might be only method for large unordered
tables of data and files
Inefficient since each array element has to be
compared with search key until a match is
found
Analysis





One comparison required to find target at
start of list
Two comparisons for target in second
position
etc
Maximum comparisons is N for a list of N
items
Therefore average number of comparisons is
N/2
Exercise

Implement the Linear search algorithm given
on page 145 in VB 2005
Binary Search
Binary Search



Faster method
BUT list must be ordered
Sometimes called a binary chop as it splits
the data list into two sublists and repeats the
process until a search key is found
Binary Search Example
16 29 34 48 57 59 72 82 90 91
Binary Search Example
16 29 34 48 57 59 72 82 90 91
Search Key is 90
Binary Search Example
Left List
Right List
16 29 34 48 57 59 72 82 90 91
Mid Value
Binary Search Example
Left List
Right List
16 29 34 48 57 59 72 82 90 91
Mid Value
Binary Search Example
Left List
Right List
16 29 34 48 57 59 72 82 90 91
Mid Value
Target Found
Binary Search Algorithm ascending
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Set found=false
Set first_location to start of list
Set last_location to end of list
Input search target
Repeat
Set pointer to middle of list…. integer(first+last)/2
If array(middle)=target then
found=true
Output suitable message
Else
if array(middle)>target then
last_location=middle-1
else
first_location = middle+1
end if
End if
Until found = true or first>last
Exercise 1



With a partner, use the cards given to
exemplify the binary search algorithm
Use cards for different search keys
Make sure that you know how this algorithm
works
Exercise 2


Implement the algorithm given on page 150
You cannot use code given on next pages as
version of VB is different!
Summary of Searches
Linear Search
Binary Search
Is simple to code and implement
Is more complex to code
Quite efficient for short length data
lists
Efficient for any length of data list
Very slow on large lists since each
data element has to be compared
Fast on any length of data list since it
only deals with half sub-lists. Hence
the name is binary chop
Does not require data to be ordered
Data has to be ordered
Average search length is N/2 where N
is the number of data elements
Search length is log2N
Plays a part in other algorithms such
as finding maximum, minimum and
also in selection sort
Binary chop is used in fast searching
routines
Sorting
Sorting

Important process in computing, especially in
data processing




Telephone directories
Sports league tables
Lottery numbers
Etc.
Sorting
Efficient sorting is important to optimizing the
use of other algorithms (such as search and
merge algorithms) that require sorted lists to
work correctly; it is also often useful for
canonicalizing data and for producing humanreadable output.
Sorting
Since the dawn of computing, the sorting
problem has attracted a great deal of research,
perhaps due to the complexity of solving it
efficiently despite its simple, familiar statement.
Sorting

External Sorts



External storage devices used
Large amounts of data
Internal Sorts


Fairly small lists
Uses internal memory (RAM)
Sorting
Three algorithms described and compared
1. Simple sort
2. Bubble sort
3. Selection sort using two lists
Simple Sort


In the first pass, each item in the list is
compared with the first item in the list
If the first item in the list is bigger then the
item being compared then they are swapped.
Simple Sort
Swap
7
5
9
1st Comparison
6
1
8
2
0
3
4
Simple Sort
5
7
9
6
1
8
2
0
3
4
Simple Sort
5
7
9
2nd Comparison
6
1
8
2
0
3
4
Simple Sort
5
7
9
3rd Comparison
6
1
8
2
0
3
4
Simple Sort
Swap
5
7
9
4th Comparison
6
1
8
2
0
3
4
Simple Sort
1
7
9
5th Comparison
6
5
8
2
0
3
4
Simple Sort
1
7
9
6th Comparison
6
5
8
2
0
3
4
Simple Sort
Swap
1
7
9
7th Comparison
6
5
8
2
0
3
4
Simple Sort
0
7
9
6
5
8
2
1
3
4
Simple Sort
0
7
9
8th Comparison
6
5
8
2
1
3
4
Simple Sort
0
7
9
9th Comparison
6
5
8
2
1
3
4
Simple Sort
0
7
9
1st Comparison
6
5
8
2
1
3
4
Simple Sort
Swap
0
7
9
2nd Comparison
6
5
8
2
1
3
4
Simple Sort
0
6
9
7
5
8
2
1
3
4
Simple Sort
Swap
0
6
9
7
3rd Comparison
5
8
2
1
3
4
Simple Sort
0
5
9
7
6
8
2
1
3
4
Simple Sort
0
5
9
7
4th Comparison
6
8
2
1
3
4
Simple Sort
Swap
0
5
9
7
5th Comparison
6
8
2
1
3
4
Simple Sort
0
2
9
7
6
8
5
1
3
4
Simple Sort
And so on…
0
2
9
7
6
8
5
1
3
4
Simple Sort
until…
0
1
2
3
4
5
6
7
8
9
Simple Sort
1.
2.
Performs fewer exchanges on a randomly
ordered list
Must make N-1 passes through list even
when fully sorted or partially sorted
Simple Sort Algorithm
1.
2.
3.
4.
5.
6.
7.
for outer = 1 to n
for inner = outer + 1 to n
if List (outer) > List(inner) then
swap values
end if
next inner
next outer
Simple Sort Task



Using the cards provided and
With a partner
Sort the cards into ascending order using the
simple sort methd
Simple Sort Task



Using the cards provided and
With a partner
Sort the cards into ascending order using the
simple sort method
Bubble sort
Swap
7
5
9
First Comparison
6
1
8
2
0
3
4
Bubble sort
5
7
9
6
1
8
2
0
3
4
Bubble sort
5
7
9
6
Second Comparison
1
8
2
0
3
4
Bubble sort
Swap
5
7
9
6
Third Comparison
1
8
2
0
3
4
Bubble sort
5
7
6
9
1
8
2
0
3
4
Bubble sort
Swap
5
7
6
9
1
8
Fourth Comparison
2
0
3
4
Bubble sort
5
7
6
1
9
8
2
0
3
4
Bubble sort
Swap
5
7
6
1
9
8
Fifth Comparison
2
0
3
4
Bubble sort
5
7
6
1
8
9
2
0
3
4
Bubble sort
Swap
5
7
6
1
8
9
2
Sixth Comparison
0
3
4
Bubble sort
5
7
6
1
8
2
9
0
3
4
Bubble sort
Swap
5
7
6
1
8
2
9
0
3
Seventh Comparison
4
Bubble sort
5
7
6
1
8
2
0
9
3
4
Bubble sort
Swap
5
7
6
1
8
2
0
9
3
8th Comparison
4
Bubble sort
5
7
6
1
8
2
0
3
9
4
Bubble sort
Swap
5
7
6
1
8
2
0
3
9
4
9th Comparison
Bubble sort
5
7
6
1
8
2
0
3
4
Notice… we are sorting list into an ascending list. The largest number is
now at the end of the list…where it should be!
This completes the first pass through the list.
9
Bubble sort
5
7
6
1
1st Comparison
The process begins again.
8
2
0
3
4
9
Second Pass
Bubble sort
Swap
5
7
6
2nd Comparison
1
8
2
0
3
4
9
Second Pass
Bubble sort
5
6
7
1
8
2
0
3
4
9
Second Pass
Bubble sort
Swap
5
6
7
1
3rd Comparison
8
2
0
3
4
9
Second Pass
Bubble sort
5
6
1
7
8
2
0
3
4
9
Second Pass
Bubble sort
5
6
1
7
8
4th Comparison
2
0
3
4
9
Second Pass
Bubble sort
Swap
5
6
1
7
8
2
5th Comparison
0
3
4
9
Second Pass
Bubble Sort
1.
2.
3.
4.
5.
6.
7.
for outer = 1 to n-1
for inner = 0 to N - 1
if list(inner) > list(inner + 1) then
swap values
end if
next inner
next outer
Bubble Sort
1.
2.
3.
4.
Makes excessive exchanges (but less so in
a partially ordered list).
Works best on a partially ordered list
Can detect when sorted as no swaps take
place.
Most inefficient when list is randomly
ordered
Bubble Sort task



Using the cards provided and
With a partner
Sort the cards into ascending order using the
bubble sort method
Selection Sort

This version uses two lists…
Selection Sort
7596182034
Selection Sort
7596182X34
0
After 1st pass
Selection Sort
7596X82X34
01
After 2nd pass
Selection Sort
7 5 9 6X8XX3 4
012
After 3rd pass
Selection Sort
7 5 9 6X8XXX4
0123
After 4th pass
Selection Sort
7 5 9 6X8XXXX
01234
After 5th pass
Selection Sort
7X9 6X8XXXX
012345
After 6th pass
Selection Sort
7X9XX8XXXX
0123456
After 7th pass
Selection Sort
XX9XX8XXXX
01234567
After 8th pass
Selection Sort
XX9XXXXXXX
012345678
After 9th pass
Selection Sort
XXXXXXXXXX
0123456789
After 10th pass
Selection Sort
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
for outer = 1 to n-1
minimum = outer
for inner = 0 to N {line modified for two lists}
if list_A(inner) < list_A(minimum) then
minimum = inner
end if
next inner
list_B(outer) = list_A(minimum)
list_A(minimum) = dummy value
next outer
Selection Sort
1.
Makes excessive use of memory as two
lists required.
Selection Sort Task



Using the cards provided and
With a partner
Sort the cards into ascending order using the
selection sort method
Summary of three sorting algorithms
The criteria for measuring algorithm
performance are –
1.Behaviour with different size lists
2.Memory requirements
3.Stability
Summary of three sorting algorithms
Simple sort
Bubble sort
Selection sort
using two lists
Comparisons
N(N-1)/2
NxN
NxN
Passes
N
N
Negligible
Memory
Negligible
Negligible
Small
Uses
Small Lists
None
Lists
stability
Stable
Stable
Stable
Summary of three sorting algorithms



Partially ordered list – use Bubble Sort
Randomly ordered list – use Simple Sort
Simplicity of implementation – use Selection
Sort
User-defined Module Libraries
Module Library

Depositaries of useful software










procedures,
functions,
subroutines,
programs,
applications,
OS routines
Objects
Classes
Type declarations
Etc.
Module Library



If they are all packaged as a DLL file
(dynamic link library) then they can be used
within most programming environments
simply by calling them up
Windows itself is composed of many DLL
files
A DLL contains executable code and will link
to a programming application at run time
rather than at compile time.
Exercise


Create a new folder and call it Module Library
Work through the worked examples on page
169 onwards