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Concept
Shunting Yard Algorithm
The
Shunting Yard Algorithm
, developed by Edsger Dijkstra, is used to convert
infix expressions
to postfix (
Reverse Polish Notation
) or
prefix notation
, facilitating easier evaluation by computers. It efficiently handles
operator precedence
and associativity using a
stack-based approach
, making it a fundamental tool in
compiler design
and
expression evaluation
.
Relevant Fields:
Software Engineering and Development 70%
Computer Architecture and Design 20%
Computational Mathematics 10%
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Concept
Infix Notation
Infix notation
is a common arithmetic and
logical formula notation
where operators are placed between operands, such as in 'A + B'. This notation is widely used in mathematics and
programming languages
for its readability and
natural expression of operations
, but it requires
operator precedence
and
associativity rules
to be properly evaluated by computers.
Concept
Postfix Notation
Postfix notation
, also known as
Reverse Polish Notation
(RPN), is a
mathematical notation
in which
operators follow their operands
, eliminating the
need for parentheses
to denote
operation order
. This notation is particularly useful in
computer science
for
stack-based calculations
and is employed in
certain calculators
and
programming languages
to simplify
expression evaluation
.
Concept
Prefix Notation
Prefix notation
, also known as
Polish notation
, is a
mathematical notation
in which
operators precede their operands
, eliminating the need for parentheses to denote
operation precedence
. This notation is particularly useful in
computer science
for
parsing expressions
efficiently, as it allows for easier
implementation of compilers
and calculators.
Concept
Operator Precedence
Operator precedence
determines the order in which operators are evaluated in expressions, ensuring consistent and
predictable results
. Understanding these rules is essential for writing accurate and
efficient code
, as it affects
how expressions are parsed
and executed by
programming languages
.
Concept
Operator Associativity
Concept
Stack Data Structure
A stack is a
linear data structure
that follows the
Last In, First Out
(LIFO) principle, where the last element added is the first to be removed. It is commonly used in scenarios like
function call management
, undo mechanisms in applications, and
syntax parsing
in compilers.
Concept
Expression Parsing
Expression parsing
is the process of analyzing a sequence of tokens to determine its
grammatical structure
with respect to a given
formal grammar
. It is crucial in the
implementation of compilers
and interpreters, enabling the translation of
high-level programming code
into
executable machine code
or
intermediate representations
.
Concept
Compiler Design
Compiler design
is the process of creating software that translates
high-level programming languages
into
machine code
that a
computer's processor
can execute. It involves multiple stages including
lexical analysis
, syntax analysis,
semantic analysis
, optimization, and
code generation
, each critical for ensuring the correctness and efficiency of the resulting program.
Concept
Algorithm Design
Algorithm design
is the process of defining a
step-by-step procedure
to solve a problem efficiently, optimizing for factors like time and
space complexity
. It involves understanding the
problem requirements
, choosing the right
data structures
, and applying suitable
design paradigms
to create
effective solutions
.
Concept
Infix To Postfix Conversion
Infix to postfix conversion
is a process used in computer science to transform
arithmetic expressions
written in
infix notation
(where operators are placed between operands) into
postfix notation
(where operators follow their operands), which is more suitable for
stack-based evaluation
. This conversion facilitates easier computation by eliminating the need for parentheses and
operator precedence
rules, allowing for straightforward evaluation using a
stack data structure
.
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