Transcript Hardware - Griffith University

Algorithms
Recipes for disaster?
Topics Covered
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Programming vs. problem solving
What is an algorithm?
Algorithm development
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common constructs (loops, conditionals, etc)
Representing algorithms
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flowcharts
pseudocode
Programming vs. Problem Solving
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Two very distinct tasks!
Problem solving:
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Programming:
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developing a solution to a problem
result is an algorithm or a plan for the solution
converting the solution into a computer readable form (C,
assembly, VB, Delphi, etc..)
Programmers are cheap – problem solvers are
not!
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eg, architect, engineer vs. bricklayers, carpenters, etc..
What is an Algorithm?
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Formal definition:
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An algorithm is a step-by-step procedure for accomplishing a
stated task
A recipe for solving a problem
History:
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derived from 9th century mathematician Abu Abdullah
Muhammad ibn Musa al-Khwarizmi
initially referred only to solving arithmetic problems
(multiplication, division, etc) known as algorism
definition expanded to include all mathematical procedures
formalised by Alan Turing in 1936 (Turing Machine)
the foundation of computer science
Algorithm Examples
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Humans solve problems intuitively without
usually formalising the steps involved
Consider:
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passing this course
making a cup of tea
multiplying two numbers
determining if a number is prime
finding the largest number in a list
Properties of Algorithms
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Finiteness: must eventually terminate
Definiteness: each step is precisely defined, there
is no ambiguity
Input: information which is required in order to
start the algorithm
Output: result of the algorithm, with some relation
to the input
Effectiveness: should be able to be emulated
manually (paper and pencil)
Types of Algorithms
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Iterative or Recursive:
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Serial or Parallel:
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identical execution for identical input or some randomness
involved
Exact or Approximate:
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one instruction at a time or multiple instructions
Deterministic or Stochastic:
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recursive algorithms call themselves, iterative algorithms do not
is the solution exact or merely good enough
Complexity:
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how long the algorithm takes to run (for a given size input)
Algorithmic Constructs
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There are a number of standard ‘tools’ used when
developing algorithms
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variables
statements
loops
conditional statements
modules
These are the same actions we use for every
activity
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you just don’t realise it!
Variables
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Variables are areas of storage used to keep track of data
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Each variable requires a distinct name
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should be related to what the variable is holding, eg. age, iq,
student_number, etc
The equivalent of writing something down for later
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in an algorithm, the size or type of the data in a variable is not
necessarily defined, but should be consistent
can hold numbers, letters, words, etc..
when manually running through an algorithm, it is helpful to use
labelled boxes for variables
Input/Output values are also considered variables
Variables are the only data that is available to the algorithm!
Statements
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Statements are the building blocks of algorithms
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each statement is an instruction to perform an action
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Statements should be either:
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set or change a variable’s value
perform calculations
write data to the screen, read from keyboard
call another module
simple, atomic actions that are easily understood
module calls which are defined elsewhere
ALL relevant information needs to be included in the statement!
Read a, b, c from keyboard
SET r1 = (-b + b2-4ac) / 2
Print r1 to screen
Conditional Statements
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Most non-trivial algorithms are not simply a
sequence of statements
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require some decisions at some point!
Conditional statements are used to branch the
execution of an algorithm
logical expressions are used to make such decisions
IF ( something is true ) THEN do something
ELSE do something else
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Loops and Repetition
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Most algorithms require some actions to be
repeated numerous times, either:
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a fixed number of times, OR
until a condition is met (or no longer met)
Such constructs are known as loops, and
are a powerful tool in algorithm design
Representing Algorithms
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Algorithms can be represented in numerous ways
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plain English descriptions
graphically (flowcharts, Nasi-Schneiderman diagrams,
etc)
structured English (pseudocode)
Each approach has advantages and
disadvantages
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ease of understanding
ambiguity
speed of creation
ease of conversion to actual source code
Plain English Descriptions
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As name implies, a plain language description of
the algorithm
Usually in the form of an English paragraph
Advantages:
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easy for layperson to understand
quick to create
Disadvantages:
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often ambiguous
does not convert easily to code
no well defined structure, so large variations between
authors
Graphical Representations
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Visual representation of algorithm
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Flowcharts are one of the earliest and most popular forms
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boxes = actions
diamonds = decisions
arrows = program flow
Advantages:
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each structure has a set of symbols to represent it
some people find visual approach easy to understand
unambiguous
Disadvantages:
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can be large and difficult to create
direct conversion to code is possible, but not always simple
Structured English
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Known as pseudocode
A cross between English and program language
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Advantages:
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rules, conventions and structures similar to programming
languages
statements are written in plain English statements
very easy to convert to program code
unambiguous in most cases
Disadvantages:
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not as easy to read as plain language
can be ambiguous if written poorly
Algorithm Representation Examples
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Simple directions to a destination:
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Plain English:
Go straight on to the traffic lights, turn left and take
the third turning on the right. If the red gate is
open then go through it, otherwise go through the
green gate.
Algorithm Representation Examples
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Flowchart:
Algorithm Representation Examples
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Pseudocode:
Go straight on to the traffic lights
Turn left
Take the third turning on the right
IF the red gate is open THEN
go through the red gate
ELSE
go through the green gate
END IF
Examples
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Reconsider these problems:
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passing this course
making a cup of tea
multiplying two numbers
determining if a number is prime
finding the largest number in a list
Now define a solution in each
representation…
Breaking Down a Problem
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Problems are often too complicated to be completely defined
in a single algorithm
In such cases, some steps are defined only in general terms
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Such tasks are not simple
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add milk to tea
study
determine factors of x
cannot be done in one action – one line of code
This is OK, provided that they are expanded upon elsewhere
This is known as a modular approach, and is how all large
software systems are developed
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each module is designed and built separately, and assumes the
other modules will do their job…
Modular Algorithm Examples
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Traditional program breakdown:
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get input
process input
display output
For very simple problems all such steps can be done in one
algorithm
For more complex tasks, each step becomes one or more
modules
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eg, solving quadratic equation:
Read a, b, c
Calculate r1, r2
Display r1, r2
simple, not a module
NOT simple, requires a module
simple, not a module
Defining Modules
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When modules have been identified, it is
necessary to define them
What is required?
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inputs
outputs
their own algorithm!
Note that the calling module doesn’t need to know
the algorithm
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but does need to know the inputs and outputs!!
“Top-Down” Design
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Systematic method of algorithm
development
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start at a high, conceptual level
specify operations in general terms
identify sub-modules
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inputs, outputs
repeat for each sub-module
Can benefit from re-use of some common
modules
Top Down Example
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Missile guidance system
Basic algorithm:
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inputs: target coordinates (t_location)
while ( haven’t hit target yet )
get instrument readings
calculate position and direction
calculate required trajectory
calculate fin/motor adjustments
implement adjustments
end while
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Clearly, all statements here require some refinement…
Top Down Example
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Get_instrument_readings
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outputs: gps, speed, altitude, gyro
activate gps
get gps information
read speed
read altitude from altimeter
read spin from gyro
RETURN ( gps, speed, altitude, spin )
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Calculate_position_and_velocity
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input: gps, speed, altitude, spin
output: position, velocity
Algorithm: who knows?!? (somebody else’s job!)
Top Down Example
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Calculate_trajectory
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Calculate_fin_motor
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inputs: position, velocity, t_location
outputs: req_trajectory
input: position, velocity, req_trajectory
output: fin_adjust, motor_adjust
Implement_adjustments
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input: fin_adjust, motor_adjust
Top Down Example
Missile
Guidance
Get_inst
calc_pos
…
calc_traj
…
calc_fin_adjst imp_fin_adjst
…
When to Break Down Problem?
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In general, an algorithm (module) should be no more than 20 lines
long
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Any moderately lengthy section of an algorithm which is used a
number of times should be made into a module
Modules should be logical!
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>20, probably should be modularised
not a hard and fast rule, but a guideline – many ‘simple’ modules may
contain hundreds of lines
well-defined purpose (make sense independently)
the module should be cohesive
not just to break apart a long module!
Modules should be able to be tested independently!
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must have a good input/output relationship
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testing is done before integration occurs
Types of Modules
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Some languages define different module types
Procedures:
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Functions:
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perform a specific task
do NOT provide an output
can take inputs however
return at least one output
in general, their purpose is to calculate those values, and
nothing else
can of course take input as well
C makes no distinction between these types of modules – all
are called functions