Algorithms

1
Algorithms
2
Topics to Cover

• Recall Algorithm Definition
• An Algorithm Average
• Fundamental Algorithmic Constructs
• Another Algorithm Euclids
• Recall Algorithm Characteristics
• From Pseudo-Code to Java
• Algorithmic Constructs Java Syntax
• A Java Program Average
• Another Java Program Euclid
• The Program Development Algorithm
• Stepwise Refinement
• Algorithm vs. Program

3
Recall Algorithm Definition

• An ordered set of effective, unambiguous,
  commands for a task which, when executed,
  terminates.
• Where does the term algorithm come from then?
• From mathematics, actually

4
Recall Algorithm Definition

• Historians generally believe the word algorithm
  came from an Arabic author of textbooks in the
  9th century
• Abu Abdullah Muhammad bin Musa al-Khwarizmi
• Examples from mathematics
• Long division algorithm
• Euclidean algorithm for finding the greatest
  common divisor of 2 positive integers

5
An Algorithm Average
Average Algorithm This algorithm computes the
average of three numbers.  ASSIGN howmany
3ASSIGN sum 0 FOR howmany repetitions DO
GET number ADD number to sumEND of
repetitions REPORT average is sum DIVIDED BY
howmany
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An Algorithm Average

• Observe
• Once an algorithm is specified, one no longer
  requires an understanding of the principles of
  the algorithm to solve the problem
• Rather, one only needs to blindly follow the
  steps of the algorithm (which is exactly what a
  computer does with a computer program!)
• Recall an algorithm is written in a pseudo-code
  form. (Like code, but not quite translation to
  code for a particular programming language would
  be fairly simple though.)

7
An Algorithm Average

• The Average Algorithm, although simple, provides
  examples of some of the following algorithmic
  constructs provided by high-level programming
  languages
• Data storage/retrieval
• Data manipulation
• Sequential execution
• Conditional execution
• Repetition
• We will look at each of these fundamental
  algorithm (and, therefore, programming)
  constructs, in turn

8
Fundamental Algorithm Constructs

• Data storage/retrieval (aka input/output)
• Information (data) is stored in variables so that
  it can be retrieved and used later.
• Pseudo-code keywords
• GET ltvariable namegt
• obtain a value (e.g. from the user) and store it
  in main memory
• REPORT ltvariable namegt
• display a value stored in main memory to the user
  
• ASSIGN ltvariable namegt ltvaluegt
• store a value in a location in main memory
• LET ltvariable namegt BE ltvaluegt
• store a value in a location in main memory
• Examples from the Average Algorithm?

9
Fundamental Algorithm Constructs

• Data manipulation
• Information is used to create new or additional
  information
• Pseudo-code keyword
• none data to be manipulated is obtained simply
  by giving the location of its storage (i.e. its
  variable name)
• Example from the Average Algorithm?

10
Fundamental Algorithm Constructs

• The previous algorithmic constructs deal with
  data. The remaining constructs deal with flow of
  control
• Which instruction is executed next?
• Sequential execution
• Instructions are executed one after another in
  the order given
• Pseudo-code keyword
• none - default mode of execution
• Example from the Average Algorithm?

11
Fundamental Algorithm Constructs

• Conditional execution (aka selection)
• Instruction(s) may or may not be executed,
  depending on some condition(s) at time of
  execution (aka run time).
• Pseudo-code keywords
• IF-THEN
• IF-THEN-ELSE
• Example from the Average Algorithm?

12
Fundamental Algorithm Constructs

• Observe Three types of conditionals
• IF-THEN
• Decides whether or not some sequence of
  instructions will be executed
• IF-THEN-ELSE
• Selects one of two sequences of instructions to
  be executed
• How is one of many sequences of instructions
  selected to be executed? ( nested IF-THEN-ELSE)
• Examples?

13
Fundamental Algorithm Constructs

• Repetition
• A sequence of instructions is executed 0, 1, or
  more times
• Also called a loop
• Pseudo-code keywords
• WHILE
• FOR
• DO-WHILE
• Example from the Average Algorithm?

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Fundamental Algorithm Constructs

• Important loop design considerations
• How many repetitions?
• Termination condition?
• If the loop never terminates, we have what is
  called an infinite loop.
• What happens if an infinite loop is present in
  an algorithm? in a program?
• Initial conditions?

15
Fundamental Algorithm Constructs

• There are 2 types of loops
• Pre-tested
• Body executed 0 or more times
• Two main forms
• FOR ltnumber of repetitionsgt DO ltloop
  body statementsgt
• Useful when the number of times the loop body
  must be executed is known when the looping starts
• Executes the ltloop body statementsgt ltnumber of
  repetitionsgt times
• Example?

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Fundamental Algorithm Constructs

• The other form
• WHILE ltconditiongt DO ltloop body statementsgt
• Useful when the number of repetitions is unknown
  when the looping starts
• Continues to repeat the execution of the ltloop
  body statementsgt as long as ltconditiongt is true
• Example?

17
Fundamental Algorithm Constructs

• Post-tested
• Loop body executed 1 or more times
• Continues to repeat the execution of the ltloop
  body statementsgt as long as ltconditiongt is
  trueDO ltloop body statementsgt WHILE
  ltconditiongt
• Example?

18
Fundamental Algorithm Constructs

• Notes
• The WHILE and DO-WHILE loops are indefinite
  loops.
• The FOR loop, on the other hand, is a definite
  loop.
• Why?

19
Algorithms with Flow Charts

• It can be useful to model flow of control with
  flow charts.
• Flow charts can help to visualize algorithms and
  how they would beexecuted.
• Other diagramming techniques are more expressive
  and more commonly used these days.
• But, flow charting tends to be the simplest.
• You will see some of the other approaches later,
  in other courses.

20
Algorithms with Flow Charts
21
Algorithms with Flow Charts
Flow chart of the Average Algorithm
22
Another Algorithm Euclids
Euclids Algorithm This algorithm computes the
greatest common divisor. GET two integers
biggest, smallest DO DIVIDE biggest by
smallest LET remainder be the remainder of
the division IF remainder is not zero
THEN LET biggest take the value of the
smallest LET smallest take
the value of the remainderWHILE remainder is not
zero REPORT greatest common divisor is smallest
23
Another Algorithm Euclids
Flow chart of Euclids Algorithm
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Another Algorithm Euclids

• First step understand the problem GCD
• Next, identify
• Keywords
• Variables
• Assignments (i.e. when a value is stored in
  memory)
• I/O (input/output)
• Selection
• Repetition
• Observe
• Indentation, spacing, fonts (Are they
  important? Why? Why not?)

25
Another Algorithm Euclids

• Discussion points
• Is the loop pre-tested or post-tested?
• Can a post-tested loop be written as a pre-tested
  loop?
• Can a pre-tested loop be written as a post-tested
  loop?
• What kind of selection is involved?
• When the last statement is executed is one of the
  original numbers reported?
• Desk-check (aka trace) the algorithm.

26
Recall Algorithm Characteristics

• Those characteristics were
• Ordered set of instructions
• Effective instructions
• Unambiguous instructions
• Terminates
• Does Euclids Algorithm fulfill these
  requirements? does the Average Algorithm?
• Give of a sequence of steps that is not an
  algorithm.

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Recall Algorithm Characteristics

• There are other concerns for algorithms besides
  those characteristics.
• Efficiency This can be a very important concern
  for algorithms. Two key types
• Time efficiency
• Space efficiency
• Correctness Of course, this tends to be the
  most important concern!
• If the algorithm is not correct, and does notdo
  the task it was intended for, what goodis it?

28
From Pseudo-Code to Java

• Once satisfied with an algorithm, the programmer
  translates the algorithm into a program.
• The algorithm was written in pseudo-code.
• The program is to be written in a programming
  language of some kind.
• In our case, we are particularly interested in
  translating algorithms into Java.

29
From Pseudo-Code to Java

• To do this, one needs to know how each
  algorithmic construct
• data storage/retrieval
• data manipulation
• sequential execution
• conditional execution
• repetition
• is represented in Java that is Java syntax.
• We will now briefly see how some algorithmic
  constructs are represented in Java.
• We will be seeing these in more detail later
  this is just a first look

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Algorithmic Constructs Java Syntax

• Important to distinguish
• Semantics vs. syntax
• Meaning vs. representation
• Concept vs. symbol

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Algorithmic Constructs Java Syntax

• Data storage/retrieval
• REPORT
• System.out.println displays items separated by
  (called the concatenation operator) to the
  screen.

System.out.println("The average of the numbers is
" (float) sum /
howmany)
32
Algorithmic Constructs Java Syntax

• GET consists of two Java statements a prompt
  statement and an input statement
• System.out.print - displays a message to the
  screen
• parseInt - a method that obtains an integer from
  a line of keyboard input
• Integer - the class where the parseInt method
  is found
• keyboard.readLine() reads in a line of input
  typed by the user

System.out.print("Please enter number " i "
")aNumber Integer.parseInt(keyboard.readLine()
)
33
Algorithmic Constructs Java Syntax

• LET is represented in Java by the assignment
  statement
• is the assignment operator
• Note it does not represent equals in the
  mathematical sense!
• int indicates the type of variable

int howmany3
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Algorithmic Constructs Java Syntax

• Data manipulations
• A mathematical operation shown here division
• (float) is called a type cast, which deals with
  a conversion of the representation of data
  (float implies a real number as opposed to an
  integer)
• Sequential execution default
• Statements are executed in the order given, one
  after the other

(float) sum / howmany
35
Algorithmic Constructs Java Syntax

• Conditional execution
• keyword if represents a decision to be made
  based on the condition following it in
  parentheses
• remainder is a variable (storage place in memory)
• ! represents not equal
• represents a block of code
• If the condition is true, the statements in the
  associated block are executed if the condition
  is not true, the statements in the associated
  block are not executed

if (remainder ! 0) biggest smallest
smallest remainder
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Algorithmic Constructs Java Syntax

• Repetition
• An example of a loop, indicated by the keyword
  for
• (int i1 i lt howmany i) indicates
• a start condition (initialization)
• termination condition (when to quit repeating)
• a statement to be executed every time
• The loop body
• is located inside the curly brackets
• contains the statements to be repeatedly executed
• Observe this is a pre-tested loop

for (int i1 i lt howmany i)
System.out.print("Please enter number " i "
") aNumber Integer.parseInt(keyboard.r
eadLine()) sum sum aNumber

37
A Java Program Average

• The following slide presents a Java program
  developed from the Average Algorithm.

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/ Average.java CS026 Lecture Notes Example
Task calculates the average of three
numbers using fundamental programming
concepts /import java.io.public class
Average public static void main(String
args) throws Exception BufferedReader
keyboard new BufferedReader(
new InputStreamReader(System.in),1)
int howmany3 int sum0 int
aNumber for (int i1 i lt howmany i)
System.out.print("Please enter number
" i " ") aNumber
Integer.parseInt(keyboard.readLine())
sum sum aNumber
System.out.println() System.out.println("Th
e average of the numbers is "
(float) sum / howmany)
39
A Java Program Average
Screenshot of BlueJ output from running the
Average program.
40
Another Java Program Euclid

• The following slides contain a Java program
  developed from Euclids Algorithm.

41
/ file name Euclid.java CS026 Lecture
Notes Example   Task calculates the greatest
common divisor of two integers, using
fundamental programming concepts and
Euclid's algorithm /   import
java.io. public class Euclid
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public static void main(String args) throws
Exception BufferedReader keyboard new
BufferedReader
(new InputStreamReader(System.in),1) int
biggest / first user input largest of 2
integers / int smallest / second user
input smallest of 2 integers /
System.out.print("Please enter an integer ")
biggest Integer.parseInt(keyboard.readLine())
System.out.print("Please enter an
integer smaller than "
biggest " ") smallest
Integer.parseInt(keyboard.readLine())
System.out.print("The greatest common divisor of
" biggest " and "
smallest " is ") int remainder
/ remainder from integer division / do
remainder biggest smallest
if (remainder ! 0) biggest
smallest smallest remainder
while (remainder ! 0)
System.out.println(smallest)
43
Another Java Program Euclid
Screenshot of BlueJ output from running the
Euclid program.
44
Sample Java ProgramsObservations

• Things to observe regarding the programs
• Program names Average, Euclid
• File names Average.java, Euclid.java
• Java statement terminator
• Form spacing, indentation, upper/lower case
• Comments audience, importance
• Compound statements
• How to run (i.e. execute)? (enter with editor,
  compile, run)
• See Program Development Algorithm, coming shortly
• More on this in the labs and your first
  assignment

45
Sample Java ProgramsA Word on Keywords

• Recall a keyword is a word that has special
  meaning in Java.
• Here is a very brief introduction to some of the
  keywords in the programs (we will see all of
  these in much more detail later )
• class the unit of organization for Java
  programs
• public an accessibility modifier indicates
  whether or not the code is available for use by
  other code (other possibilities are private,
  protected)
• static indicates a certain type of subsection
  of code
• void indicates that no value is present here
  (other possibilities are int, double)
• throws Exception deals with error handling
• import tells what predefined Java code is
  required

46
The Program Development Algorithm

• The following is an algorithm used by programmers
  in developing Java programs.
• It isnt a perfect algorithm for doing so,but it
  isnt bad either.

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Java Programming for Programmers DEFINE the
problemDEVELOP an algorithmTRANSLATE the
algorithm into JavaENTER the Java program into a
file, using an editor DO DO
CREATE Java bytecode representation of the
program (i.e.
compile javac) RUN the program with
test input (java) CHECK the output
IF the output is not correct
determine problem
determine correction edit
program with the correction WHILE the
output is not correctWHILE there are more test
cases
48
More On Java Programming

• More details about Java programming
• Regarding file names
• Each Java program has a name
• A program must be stored in a file named with the
  program name and the extension .java
• e.g. program name HelloWorldfile
  HelloWorld.java contains the Java code
• Regarding compiling the source code
• The compiler creates the bytecode version of the
  code and stores it in a file with the extension
  .class
• e.g. javac HelloWorld.javacreates the file
  HelloWorld.class(assuming, of course, there are
  no syntax errors!)

49
More On Java Programming

• Regarding running the code
• Remember, Java is interpreted
• It would be more correct to say interpreting the
  code but, no one does!
• e.g. java HelloWorld.class
• Starts the Java interpreter with the Java
  bytecode in the file HelloWorld.class
• The interpreter then executes the bytecode one
  bytecode instruction at a time

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Discussion Points

• Nested loops pre/post tested?, termination
• Test cases
• Debugging
• Compile time syntax errors
• Run time logic errors
• Algorithm
• Ordered ?
• Terminating ?
• Unambiguous and effective ?
• No! some steps need to be refined (i.e. explained
  further)

51
Stepwise Refinement

• Recall each step of an algorithm must be
  effective.
• Stepwise Refinement (aka Top-down Design )
• General idea attack a large problem by dividing
  it into smaller pieces
• Main algorithm is composed of major logical
  steps details of each of these major steps are
  given separately, in a module that deals only
  with that sub-step.
• If necessary, decompose that module into smaller
  steps and so on
• When to stop? When each individual instruction
  is unambiguous and effective.
• Terminology for modules subroutines, procedures,
  functions, methods (used in Java)

52
Stepwise Refinement

• The first (main) algorithm is said to be at the
  highest level of abstraction
• There may be many levels of abstraction below
  this, depending on the problem
• Once an algorithm is organized by levels of
  abstraction, the details of each logical step can
  be in a separate module, each of which has its
  own name
• Each module represents one task

53
Stepwise Refinement

• When stepwise refinement is used, the resulting
  algorithm (and, eventually, program) is said to
  be modular.
• This is something that all programs should be, to
  allow for
• Ease of design, modification, and correction
• Reuse of modules
• Separate design, writing, and testing of modules
• Information hiding need to know basis

54
Stepwise Refinement

• Examples
• The Java Programming Algorithm what would the
  modules be?
• Create a menu driven algorithm that allows a user
  to either calculate the average of three numbers
  or calculate the greatest common divisor
• What would the modules be for a web browser like
  Internet Explorer or Firefox?

55
Algorithm vs. Program

• Recall
• An algorithm is not written in any particular
  computer language
• A computer program expresses an algorithm in a
  specific programming language
• It should be possible to translate a well-written
  algorithm into any programming language.
• Advice programmers should make sure that their
  algorithm is indeed an algorithm
  (ordered, unambiguous, effective, terminating)
  before it is translated into a computer program!
  (Why?, how?)

56
Further Reading

• The following sections from the Java 5.0 Program
  Design text supplement these notes nicely
• Section 1.7