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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 Algorithm1. Set found to false2. Input search key3. Point to first element in list4. Do while (not end of list) and (not found)5. if array(value) = key then6. found=true7. output suitable message8. else9. look at next element in list10. end if11. loop12. If (not found) then13. key not in list14. 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
16 29 34 48 57 59 72 82 90 91
Left List Right List
Mid Value
Binary Search Example
16 29 34 48 57 59 72 82 90 91
Mid Value
Left List Right List
Binary Search Example
16 29 34 48 57 59 72 82 90 91
Mid Value
Left ListRight List
Target Found
Binary Search Algorithm - ascending1. Set found=false2. Set first_location to start of list3. Set last_location to end of list4. Input search target5. Repeat6. Set pointer to middle of list…. integer(first+last)/27. If array(middle)=target then8. found=true9. Output suitable message10. Else11. if array(middle)>target then12. last_location=middle-113. else14. first_location = middle+115. end if16. End if17. 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 human-readable 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
7 5 9 6 1 8 2 0 3 4
1st Comparison
Swap
Simple Sort
5 7 9 6 1 8 2 0 3 4
Simple Sort
5 7 9 6 1 8 2 0 3 4
2nd Comparison
Simple Sort
5 7 9 6 1 8 2 0 3 4
3rd Comparison
Simple Sort
5 7 9 6 1 8 2 0 3 4
4th Comparison
Swap
Simple Sort
1 7 9 6 5 8 2 0 3 4
5th Comparison
Simple Sort
1 7 9 6 5 8 2 0 3 4
6th Comparison
Simple Sort
1 7 9 6 5 8 2 0 3 4
7th Comparison
Swap
Simple Sort
0 7 9 6 5 8 2 1 3 4
Simple Sort
0 7 9 6 5 8 2 1 3 4
8th Comparison
Simple Sort
0 7 9 6 5 8 2 1 3 4
9th Comparison
Simple Sort
0 7 9 6 5 8 2 1 3 4
1st Comparison
Simple Sort
0 7 9 6 5 8 2 1 3 4
2nd Comparison
Swap
Simple Sort
0 6 9 7 5 8 2 1 3 4
Simple Sort
0 6 9 7 5 8 2 1 3 4
3rd Comparison
Swap
Simple Sort
0 5 9 7 6 8 2 1 3 4
Simple Sort
0 5 9 7 6 8 2 1 3 4
4th Comparison
Simple Sort
0 5 9 7 6 8 2 1 3 4
5th Comparison
Swap
Simple Sort
0 2 9 7 6 8 5 1 3 4
Simple Sort
0 2 9 7 6 8 5 1 3 4
And so on…
Simple Sortuntil…
0 1 2 3 4 5 6 7 8 9
Simple Sort
1. Performs fewer exchanges on a randomly ordered list
2. Must make N-1 passes through list even when fully sorted or partially sorted
Simple Sort Algorithm
1. for outer = 1 to n
2. for inner = outer + 1 to n
3. if List (outer) > List(inner) then
4. swap values
5. end if
6. next inner
7. 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
7 5 9 6 1 8 2 0 3 4
First Comparison
Swap
Bubble sort
5 7 9 6 1 8 2 0 3 4
Bubble sort
5 7 9 6 1 8 2 0 3 4
Second Comparison
Bubble sort
5 7 9 6 1 8 2 0 3 4
Third Comparison
Swap
Bubble sort
5 7 6 9 1 8 2 0 3 4
Bubble sort
5 7 6 9 1 8 2 0 3 4
Fourth Comparison
Swap
Bubble sort
5 7 6 1 9 8 2 0 3 4
Bubble sort
5 7 6 1 9 8 2 0 3 4
Fifth Comparison
Swap
Bubble sort
5 7 6 1 8 9 2 0 3 4
Bubble sort
5 7 6 1 8 9 2 0 3 4
Sixth Comparison
Swap
Bubble sort
5 7 6 1 8 2 9 0 3 4
Bubble sort
5 7 6 1 8 2 9 0 3 4
Seventh Comparison
Swap
Bubble sort
5 7 6 1 8 2 0 9 3 4
Bubble sort
5 7 6 1 8 2 0 9 3 4
8th Comparison
Swap
Bubble sort
5 7 6 1 8 2 0 3 9 4
Bubble sort
5 7 6 1 8 2 0 3 9 4
9th Comparison
Swap
Bubble sort
5 7 6 1 8 2 0 3 4 9
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.
Bubble sort
5 7 6 1 8 2 0 3 4 9
The process begins again.
1st Comparison Second Pass
Bubble sort
5 7 6 1 8 2 0 3 4 9
2nd Comparison
Swap
Second Pass
Bubble sort
5 6 7 1 8 2 0 3 4 9
Second Pass
Bubble sort
5 6 7 1 8 2 0 3 4 9
3rd Comparison
Swap
Second Pass
Bubble sort
5 6 1 7 8 2 0 3 4 9
Second Pass
Bubble sort
5 6 1 7 8 2 0 3 4 9
4th Comparison Second Pass
Bubble sort
5 6 1 7 8 2 0 3 4 9
5th Comparison
Swap
Second Pass
Bubble Sort
1. for outer = 1 to n-1
2. for inner = 0 to N - 1
3. if list(inner) > list(inner + 1) then
4. swap values
5. end if
6. next inner
7. next outer
Bubble Sort
1. Makes excessive exchanges (but less so in a partially ordered list).
2. Works best on a partially ordered list
3. Can detect when sorted as no swaps take place.
4. 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
7 5 9 6 1 8 2 0 3 4
Selection Sort
7 5 9 6 1 8 2 X 3 4
0 After 1st pass
Selection Sort
7 5 9 6 X 8 2 X 3 4
0 1 After 2nd pass
Selection Sort
7 5 9 6 X 8 X X 3 4
0 1 2 After 3rd pass
Selection Sort
7 5 9 6 X 8 X X X 4
0 1 2 3 After 4th pass
Selection Sort
7 5 9 6 X 8 X X X X
0 1 2 3 4 After 5th pass
Selection Sort
7 X 9 6 X 8 X X X X
0 1 2 3 4 5 After 6th pass
Selection Sort
7 X 9 X X 8 X X X X
0 1 2 3 4 5 6 After 7th pass
Selection Sort
X X 9 X X 8 X X X X
0 1 2 3 4 5 6 7 After 8th pass
Selection Sort
X X 9 X X X X X X X
0 1 2 3 4 5 6 7 8 After 9th pass
Selection Sort
X X X X X X X X X X
0 1 2 3 4 5 6 7 8 9 After 10th pass
Selection Sort
1. for outer = 1 to n-12. minimum = outer 3. for inner = 0 to N {line modified for two lists} 4. if list_A(inner) < list_A(minimum) then 5. minimum = inner 6. end if 7. next inner 8. list_B(outer) = list_A(minimum) 9. list_A(minimum) = dummy value 10. 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 N x N N x N
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
