FEN 30-9-2008NOEA/IT: Advanced Computer Studies 1 Patterns The concept of patterns originates from...

FEN 30-9-2008 NOEA/IT:Advanced Computer Studies

1

Patterns

• The concept of patterns originates from architecture (Christopher Alexander, 1977):

“Each pattern describes a problem which occurs over and over again in our environment, and then

describes the core of the solution to that problem, in such a way that you can use this solution a million

times over, without ever doing it the same way twice”

(Christopher Alexander e. a.: “A Pattern Language”. Oxford University Press, New York, 1977.)


2

(OO) Design Patterns

• A well known and widely accepted concept in software engineering

• Developed in the early 1990s and published by Gamma e.a. (“Gang of Four”, GoF) in 1995:

“(…) design patterns (…) are descriptions of communicating objects and classes that are customized to solve a general

design problem in a particular context.”

(Erich Gamma e.a.:”Design Patterns. Elements of Reusable Object-Oriented Software”. Addison-Wesley. 1995.)


3

The Benefits of Patterns

• A pattern captures a proven good design:– A pattern is based on experience– A pattern is discovered – not invented

• It introduces a new (and higher) level of abstraction, which makes it easier:– to talk and reason about design on a higher level– to document and communicate design

• One doesn’t have to reinvent solutions over and over again

• Patterns facilitate reuse not only of code fragments, but of ideas.


4

Patterns as a Learning Tool

• It is often said that good skills in software construction require experience and talent

• …and neither can be taught or learned at school• Patterns capture experience (and talent) in a way that

is communicable and comprehensible• …and hence experience can be taught (and learned)

• So we should rely heavily on patterns in our teaching


5

Algorithm Patterns

• The term is not commonly used in literature, but the concept is well known.

• Terms used in textbooks are:– Algorithm paradigms

– Algorithm (or solution) strategies

– Methodologies

• For several years we have used the the term “Algoritmeskabeloner” in Danish

• I propose that we introduce the term “Algorithm Patterns” in our international programme


6

Algorithm Patterns

• Many different problems from many different problem domains may be solved by algorithms that possess a common structure – or a common pattern.

• By abstracting and formalizing this structure it becomes a reusable pattern with all the desired properties connected to patterns.

• Patterns have names – within the field of algorithms the following – among others – may be identified:– Sweep algorithms

– Search algorithms

– Merge algorithms

– Divide and Conquer algorithms

– Greedy algorithms

– Backtracking algorithms

– Dynamic programming etc. etc.…


7

The Sweep Algorithm Pattern

• Purpose:– inspects all elements in a collection (senselessly

sweeping through the collection) and doing something according to the characteristics of the current element.

• Benefits:– separates operations depending on the

collection (loop control) from operations depending on the actual problem at hand.


8

The Sweep Algorithm Pattern

• Examples:• counting the number of students older than 25 years

in of list of students

• increasing the value of a discount percentage by 10 on all elements with a balance of more than DKK 10,000 in a set of customers

• calculating the average number of words per sentence in a text

• etc. etc.


9

The Sweep Pattern - StructureNotation:• US: Unvisited set

< DO_INIT: initialisation necessary due to the DO operation >;

< INIT: initialise unvisited set, US >;

while < ! DONE (id: US is not empty)> {

< SELECT current element from US >;

< DO something according to current element>;

< REMOVE current element from US>

} // end while Please note:•INIT, DONE, SELECT and REMOVE depends only on the data representation•The realisation of DO_INIT and DO depends on the concrete task to be accomplished by the algorithm as well as the data representation•The structure is independent of the task and data representation


10

Sweep Algorithms on Sequences of Integers

visited US a:

i

Data representation (Java):

An array, a and a counter, i:

int i; int a[]; •INIT, DONE, SELECT and REMOVE may be concretised by a counter: i

•Concretisation of the abstract operations then yields:

– INIT: i = 0

– DONE: i >= a.length

– SELECT: a[i]

– REMOVE: i++

< DO_INIT >;

int i = 0;

while ( i < a.length ) {

< DO something to a[i]) >;

i++;

} // end while


11

Sweep Algorithms on Sequences of Integers

visited US a:

i

Data representation (Java):

int i; int a[];

< DO_INIT >;

int i = 0;

while ( i < a.length ) {


i++;

} // end while

< DO_INIT >;

for (int i= 0 ; i < a.length ; i++ ) {


} // end forIn Java a counter controlled loop may be written simpler

using the for-statement.


12

Applying the Sweep Pattern

Counting zeros in an array:

DO_INIT: int count= 0;

DO: if (a[i] = = 0) count++;

int count= 0;

for (int i= 0 ; i < a.length; i++){

if (a[i] = = 0)

count++;

} // end for

< DO_INIT >;



} // end for


13

Applying the Sweep Pattern

Increasing all elements by one:

DO_INIT: no concretising is needed.

DO: a[i]++; < DO_INIT >;



} // end forfor (int i= 0 ; i < a.length; i++) {

a[i]++;

} // end for


14

The Sweep Pattern in C#

Loops may be written more simply using the foreach loop:

ArrayList a = new ArrayList(); foreach (int x in a) System.Console.WriteLine(x);

The foreach loop can only be used if:

1. The collection implements IEnumerable

2. The elements in the collection are not changed

The reason for this is that the foreach is implemented using an iterator:


15

Iterators in C#

• An iterator is an object that encapsulations the internal structure of a collection and still allowing iteration through the collection

• In C# iterators are called enumerators

• Example: IList a = new ArrayList();

IEnumerator it = a.GetEnumerator();

while (it.MoveNext())

{

//it.Current = (int)it.Current * 3;

System.Console.WriteLine(it.Current);

}

Current is a read-only property


16

The Search Algorithm Pattern

• Purpose:– The algorithm looks for an element (target, t) with some specified

property in a collection

• Benefits: – The search terminates when the first occurrence of the target is

discovered

– Loop control is separated from the testing for the desired property

• Examples:– Searching for a customer with a balance greater than DKK 10,000

– Searching for a student older than 30

– Searching for the word “algorithm” in a text.


17

The Search Pattern - StructureNotation:• CC: Candidate Collection• c: Element to be examined• t: The target element

< Initialise CC >;

boolean found= false;

while ( ! found && <CC Ø > ) {

< Select c from CC >;

if ( < c==t > )

found = true;

else {

< Split CC >

}

}

Only the abstract operations (in red)

are problem specific

The structure is general

and reusable


18

Formalism

The abstract operations ought to

be formally specified, but in this

context we will rely on intuition.


19

initialise: int i = 0

select: c = a[i]

CC Ø: i < a.length

split: i ++ CC

a:

i

int c;

int i= 0;

boolean found= false;

while ( !found && i<a.length ) {

c = a[i];

if (c == target)

found= true;

else

i ++;

} // end while

Does this realisation meet

the requirements?

Applying the pattern to an int[] a

Conditions connected to loop control

Conditions connected to the actual search


20

Binary Search:

A "smart" realisation of the search pattern on a sorted sequence • The strategy:

– Select an element in the middle of the candidate set:

• If this is the element we are looking for – we are done • If the target comes after the middle element, then look

in the upper part (remember the collection is sorted) • If the target comes before the middle element, then

look in the lower part (again remember the collection is sorted)

– Repeat this until the target has been found or there are no more candidate elements


21

CC

a:

low high

Binary Search:

Applied to a sorted array of integers

int low = 0;int high = a.length -1;int c , middle;boolean found = false;while ( ! found && low<=high ) {

middle = (high + low) / 2;c= a[middle];if (c == t)

found= true;else if ( c<t )low = middle+1; else high= middle-1;

} // end while

INITIALISE: int low = 0;

int high= a.length;

SELECT: middle= (low´+high)/2

c = a[i]

CC Ø: low <= highSPLIT: if (k<m) low= middle + 1;

else high:= middle – 1;

INITIALISE: int low = 0;

int high= a.length;

SELECT: middle= (low+high)/2

c = a[middle]

CC Ø: low <= highSPLIT: if (c<t) low= middle + 1;

else high= middle – 1;


22

Binary Search

• Please note:– Binary search is very efficient (logarithmic in

execution time), but: • The realisation of SPLIT relies heavily on the

precondition that the array is sorted.• The realisation of SELECT requires that the data

representation provides random access to elements.• Binary search is not to be applied otherwise (don’t ever

use it on linked lists)


23

Merge Pattern

• The Merge Pattern deals with the problem of joining two sorted sequences into one sorted sequence. The following example illustrates merging two sequences s and t into a third sequence r:

• Let• s = [1, 3, 6, 7, 9] and t = [1, 2, 5, 7, 11, 17]• Then

• r = [1, 1, 2, 3, 5, 6, 7, 7, 9, 11, 17]


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Merge Pattern s.reset(); t.reset(); while(s.hasMore() && t.hasMore()){

if(s.getCurrent()<t.getCurrent()){<Move s>s.next();

}else {

if(s.getCurrent() > t.getCurrent()){<Move t>t.next();

}else{

<Move st>s.next();t.next();

}}

}if(s.hasMore()) <MoveTail s> else <MoveTail t>


25

Merge Pattern

View the code:

MergePattern.zip


26

Opgave

• Brug Merge Pattern til at realisere følgende metoder:

public static int[] MergeUnion(int[] s, int[] t)

//returnerer fletning af s og t uden dubletter

//dvs. foreningsmængde

public static int[] MergeIntersect(int[] s, int[] t)

//returnerer elementer som er i både s og t

//dvs. fællesmængde

public static int[] MergeDifference(int[] s, int[] t)

//returnerer elementer som er i s, men ikke i t

//dvs. mængdedifferens

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