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Algorithms III

Representing Algorithms

with

pseudo-code

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Goal

A method for representing algorithms that:o Is easy to use (or it won’t be)o Clear and precise (or why bother?)o Understandable by others without

special training.

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Algorithm Definition

• An algorithm for a problem is a sequence of finite number of steps arranged in a specific logical order which, when executed, will produce a correct solution for a specific problem.

“An algorithm is any finite sequence of steps connecting a problem with its solution.”

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Requirements for a Solution Algorithm

– Unambiguous– Finite– Defined Input– Desired Output– Generality– Correctness– Efficiency

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Algorithm Representations

• English• Pseudo-code (“Structured English”)• Flow chart

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Algorithms in English

To find a zero using Newton’s Methodo Begin the procedure by letting x be the current

point.o Using their definitions, calculate f(x) and f’(x).o If f’(x) is less than an error tolerance, e, quit.o If it is not, calculate the next point:

y = x - f(x)/f’(x)o Continue until f(x) is “close enough” to zero. x is

the zero of f.

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Algorithms in English

Easy to understand. Easy to use. Not very clear or precise.

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Pseudo-code

• English like• Semi-formal• Limited vocabulary • Intended specifically to design and describe

algorithms.

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Pseudo-code

• The main purpose of a pseudo-code is to define the procedural logic of an algorithm in a simple, easy-to-understand manner for readers, who may or may not be proficient in computer programming.

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Pseudo-code

• Used in designing algorithms.• Used in communicating to users.• Used in implementing algorithms as

programs.• Used in debugging logic errors in programs.• Used in documenting programs for future

maintenance and expansion purposes.

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Pseudo-code

• Must have a limited vocabulary.• Must be easy to learn.• Must produce simple, English-like narrative

notation.• Must be capable of describing all

algorithms, regardless of their complexity.

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Control Structures of All Computer Programs

• Sequence• Selection• Repetition

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Sequence

• Series of steps or statements that are executed in the order they are written.

• Example:Read taxable incomeRead filing statusCompute income taxPrint income tax

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Sequence

• A sequence can be thought of as one logical step.

In OutSequence

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Selection

• Defines one or two courses of action depending on the evaluation of a condition.

• A condition is an expression that is either true or false.

• Example if condition (is true) then-partelse else-partend_if

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Nested Selection

if status is equal to 1 print “Single”else if status is equal to 2 print “Married filing jointly” else if status is equal to 3 print “Married filing separately end_if end_ifend_if

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Nested Selection

SINGLE = 1; MARRIEDJOINT = 2; MARRIEDSEP = 3if status is equal to SINGLE print “Single”

else if status is equal to MARRIEDJOINT print “Married filing jointly” else if status is equal to MARRIEDSEP print “Married filing separately end_if end_ifend_if

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Nested Selection

Defines a logical block with one entrance, one exit, and two or more paths inside.

If

Endif

Input

Output

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Repetition

• Specifies a block of one or more statements that are repeatedly executed until a condition is satisfied.

• while condition loop-bodyend_while

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Repetition

• Whilewhile m is less than m, … end while

• For loopfor m from 1 to n, … end for

• Untildo … until m is less than n, end do

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Repetition

A logical block with one input, one output, and one return loop.

While

EndWhile

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Conventions

• Each pseudo-code statement consists of keywords that describe operations and some appropriate, English-like description of operands.

• Each statement should be written on a separate line. Continuation lines should be indented.

• Goal is clarity

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Conventions (II)

• Sequence statements should begin with unambiguous words (verbs -- compute, set, initialize).

• Selection statements then-part and else-part should be indented.

• Selection statements end with the keyword end_if.

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Conventions (III)

• Repetition statements end with end_while.• Loop-bodies are indented.• All words in a pseudo-code statement must

be chosen to be unambiguous, and as easy as possible to understand by non-programmers.

• Enclose comments between /* and */

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Example

Set correctIncomeInput to ‘n’

while correctIncomeInput is equal to ‘n’

print “Enter taxable income: Should not be less than 50000 read income

if income is equal to or greater than 50000 set correctIncomeInput to ‘y’ end_if

end_while

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Flowcharting

• Flowcharting is another technique used in designing and representing algorithms.

• A flowchart is a graph consisting of geometric shapes that are connected by flow lines.

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Symbols

Terminal symbol

Process symbol

Input-Output symbol

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Symbols (III)

Flow Lines indicating the logical sequence of statements

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Flowchart

If

Keyboard

Process