Download Presentation on Operators and Notation

5. Abstract Data
Structures & Algorithms
5.1 Data Structure Fundamentals
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5.1.1 Operators and
Notation
Operator
• An operator is a mathematical instruction that
manipulates data,
‣
e.g. + means ‘add’, * means ‘multiply’, /, %.
• They are the equivalent of verbs in language.
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Unary operator
• Unary operators act on a single data item,
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e.g. the negation operator used to
represent negative numbers e.g. -4,
e.g. the factorial operator, 8!,
e.g. the percentage operator.
• [Are these not just shorthand for two dat
items?]
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Binary operators
• Binary operators work on two items of data,
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e.g. the addition operator (+), 3 + 4 = 7
combines 3 and 4 by addition
e.g. - (minus), * (multiply), / (divide), ^ (to
the power of), div (whole number division),
mod (divide and use remainder).
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Operand
• An operand is a data item that the operators
act on,
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e.g. in the expression y = x + 1, y, x and 1
are the operands.
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Expression
• An expression is a combination of operators
and operands,
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e.g. 3x + y = 29.
• The equivalent of a sentence in language.
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Recap
• Operator (unary and binary)
• Operand
• Expression
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Identifier
• An identifier is a label chosen by the
programmer to represent an item in the
program e.g. a variable, method, object or
class.
• They should always have a meaningful name
e.g. totalSalary, dayOfWeek,
findAverage(), Student.
• You have seen the Java error message
‘identifier expected’.
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Arguments
• An argument is a value passed to a method
for it to act upon e.g.
drawLine(2,2,10,50) has 4 arguments.
• setPosn(x,y) has 2 arguments, whatever
the values of x and y happen to be at the time
of the call.
• Sometimes called an actual parameter, but
best to use the term argument.
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Parameters
• A (formal) parameter is the variable name
and type in the method definition e.g. for
public int calculateAverage (int
x, int y, int z) the parameters are int
x, int y and int z.
• When the code is run, each parameter is
replaced by the value of the variable, and
becomes the argument of the method.
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Parameters
• Note that in calling a method, no type is
needed e.g. answer = average
(numbers);
• However, in defining a method the type is
needed (i.e. formal parameters) e.g. public
static double average (int no1,
int no2, int no3) {... etc.
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What gets passed?
• Primitives (int, double, etc.) are passed-byvalue i.e. the value of the argument is copied
before being sent to the method and any
changes to it do not affect the original variable
(two different memory locations).
• Objects are passed-by-reference i.e. a
pointer at its memory location is passed, not a
copy, and any changes the called method
makes change the original object.
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Infix notation
• Infix notation is the usual way that we write
algebraic expressions, i.e. the operator is
written between the operands,
• e.g. ‘the sum of x and y multiplied by
z is
written ( x + y ) * z.
• It is also the usual word order in English: ‘the
dog bites the man’ = noun - verb - noun.
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Postfix notation
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In postfix notation, the operator is written after the
operands to which it is applied,
e.g. x y + z * means ‘x plus y multiplied by z’.
It is a more logical order for a processor to work in and
requires no brackets.
It is sometimes known as reverse Polish notation (RPN).
In Latin, the verb comes at the end of the sentence: ‘canis
hominem mordet’.
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Prefix notation
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In prefix notation, the operator comes before the
operands
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e.g. + x y * z.
It is also known as Polish notation.
The processor has warning of the operator to be
executed before the operands arrive.
It also requires no brackets
Commands in English can be prefix e.g. ‘add together
x and y’.
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Converting between notations
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If asked to convert a complex expression between
notations, put in all implied brackets first,
e.g. converting 4 * ( 1 + 2 ) – 3 (which is infix) into
postfix,
insert all implied brackets: ((4 * ( 1 + 2 )) – 3),
convert each element to prefix: (- (* 4 (+ 1 2)) 3),
remove the brackets: - * 4 - 1 2 3
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Static vs. dynamic data
structures
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A static data structure has its size and nature
determined before a program is executed e.g. an
array
A dynamic data structure can vary in size to suit the
data it has to contain - they are faster and more
efficient to use but harder to program.
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