The document discusses converting expressions from infix to postfix notation. It explains that stacks are used in compilers to perform this conversion. An infix expression contains operators between operands, while a postfix expression has the operator following its operands. The algorithm scans the infix expression left to right, pushing operands and operators onto a stack based on precedence. Operators are popped off and output once higher precedence operators are encountered.
The document discusses converting expressions from infix to postfix notation. It explains that stacks are used to perform the conversion by pushing and popping operators. The algorithm scans the expression from left to right, pushes operands to the output and compares operator priorities to determine when to push or pop from the stack.
This document discusses applications of stacks, including converting between infix, prefix, and postfix notation. It provides examples of evaluating arithmetic expressions in postfix notation. Key points include:
- Prefix notation places the operator before operands, postfix places after, and infix between.
- Converting infix to prefix moves operators left and removes parentheses. Converting to postfix moves operators to output list in order of evaluation.
- Postfix notation avoids needing parentheses and is evaluated by pushing operands, popping to apply operators, and pushing results back onto the stack.
The document discusses various applications of stacks including reversing data, parsing, postponing operations, and backtracking. It provides examples of converting infix expressions to postfix notation using a stack and evaluating postfix expressions. The key stack operations of push, pop, and accessing the stack top are defined. Implementation of a stack using an array is also mentioned.
The document discusses stacks and converting expressions between infix, postfix, and prefix notation. It provides examples and algorithms for converting infix expressions to postfix. The algorithms involve using an operator stack to determine the order of operations based on precedence rules. Operands are added to the output string and operators are pushed to the stack or popped and added to the output string based on their precedence.
Queues are lists that follow a first-in, first-out (FIFO) policy for insertion and removal. Elements are inserted at the back of the queue and removed from the front. Common queue operations include enqueue, which adds an element to the back, and dequeue, which removes an element from the front. Queues can be implemented using arrays, with front and back pointers to track positions.
This document discusses stack applications and operations. It provides examples of how stacks can be used for reversing data, converting decimal to binary, evaluating arithmetic expressions by converting infix to postfix notation, and backtracking. Basic stack operations include push, pop, and peeking at the top element. Stacks follow LIFO order and are commonly implemented using arrays or linked lists. Common applications include reversing strings or files, evaluating arithmetic expressions, and backtracking to achieve goals.
The document discusses converting expressions from infix to postfix notation. It explains that stacks are used in compilers to perform this conversion. An infix expression contains operators between operands, while a postfix expression has the operator following its operands. The algorithm scans the infix expression left to right, pushing operands and operators onto a stack based on precedence. Operators are popped off and output once higher precedence operators are encountered.
The document discusses converting expressions from infix to postfix notation. It explains that stacks are used to perform the conversion by pushing and popping operators. The algorithm scans the expression from left to right, pushes operands to the output and compares operator priorities to determine when to push or pop from the stack.
This document discusses applications of stacks, including converting between infix, prefix, and postfix notation. It provides examples of evaluating arithmetic expressions in postfix notation. Key points include:
- Prefix notation places the operator before operands, postfix places after, and infix between.
- Converting infix to prefix moves operators left and removes parentheses. Converting to postfix moves operators to output list in order of evaluation.
- Postfix notation avoids needing parentheses and is evaluated by pushing operands, popping to apply operators, and pushing results back onto the stack.
The document discusses various applications of stacks including reversing data, parsing, postponing operations, and backtracking. It provides examples of converting infix expressions to postfix notation using a stack and evaluating postfix expressions. The key stack operations of push, pop, and accessing the stack top are defined. Implementation of a stack using an array is also mentioned.
The document discusses stacks and converting expressions between infix, postfix, and prefix notation. It provides examples and algorithms for converting infix expressions to postfix. The algorithms involve using an operator stack to determine the order of operations based on precedence rules. Operands are added to the output string and operators are pushed to the stack or popped and added to the output string based on their precedence.
Queues are lists that follow a first-in, first-out (FIFO) policy for insertion and removal. Elements are inserted at the back of the queue and removed from the front. Common queue operations include enqueue, which adds an element to the back, and dequeue, which removes an element from the front. Queues can be implemented using arrays, with front and back pointers to track positions.
This document discusses stack applications and operations. It provides examples of how stacks can be used for reversing data, converting decimal to binary, evaluating arithmetic expressions by converting infix to postfix notation, and backtracking. Basic stack operations include push, pop, and peeking at the top element. Stacks follow LIFO order and are commonly implemented using arrays or linked lists. Common applications include reversing strings or files, evaluating arithmetic expressions, and backtracking to achieve goals.
The document discusses stack applications for conversion and evaluation of expressions. It describes stacks, different types of expressions (infix, postfix, prefix), and algorithms for converting between these types. Examples are provided to demonstrate converting an infix expression to postfix and evaluating a postfix expression step-by-step using a stack. The postfix expression p=abc*/d+ is evaluated, with the steps shown and final result of 3.4.
The document discusses evaluation of expressions and the conversion between infix and postfix notations. It provides examples of:
1) Evaluating expressions using the order of operations and precedence of operators. Scenarios are worked through step-by-step.
2) Converting infix notation expressions to equivalent postfix notation expressions using a stack-based algorithm.
3) Evaluating postfix notation expressions using a stack to pop operands and operators in order.
Stacks have several application areas including:
1) When functions are called to save return addresses and local variables.
2) To convert infix expressions to postfix form by acting as a placeholder.
3) To evaluate postfix expressions by holding operands and intermediate results.
The document discusses several applications of stacks, including evaluating arithmetic expressions in Polish notation without needing operator precedence or parentheses, converting expressions between infix and postfix notation, matching parentheses in expressions, and other applications like reversing strings and generating code from expressions. Polish notation places operators after operands to simplify evaluation using a stack. Converting expressions to postfix form uses a stack to remove parentheses and preserve operator order.
The document discusses applications of stacks, including reversing strings and lists, Polish notation for mathematical expressions, converting between infix, prefix and postfix notations, evaluating postfix and prefix expressions, recursion, and the Tower of Hanoi problem. Recursion involves defining a function in terms of itself, with a stopping condition. Stacks can be used to remove recursion by saving local variables at each step.
The document discusses applications of stacks, including reversing strings and lists, Polish notation for mathematical expressions, converting between infix, prefix and postfix notations, evaluating postfix and prefix expressions, recursion, and the Tower of Hanoi problem. Recursion involves defining a function in terms of itself, with a stopping condition. Stacks can be used to remove recursion by saving local variables at each step.
This document discusses different notations for representing mathematical expressions: infix, prefix, and postfix. In infix notation, operators are placed between operands (e.g. A + B). In prefix notation, operators come before operands (e.g. + A B). In postfix notation, operators follow operands (e.g. A B +). It notes that infix notation requires parentheses to determine the order of operations, while prefix and postfix notations do not. The document then provides a step-by-step example of converting an infix expression to postfix notation using a stack.
A stack is a last-in, first-out data structure where elements can only be inserted or removed from one end. Stacks follow the LIFO principle. The document discusses stacks and their use in evaluating arithmetic expressions. Expressions can be written in infix, prefix, or postfix notation, and converting an infix expression to postfix notation allows it to be evaluated using a stack, with operators and operands pushed and popped off the stack from left to right.
The document provides an outline for a lecture on applications of stacks and queues, including syntax parsing, expression evaluation, backtracking, and printing jobs. It discusses infix, postfix, and prefix notation and how to convert between them using stacks. It also explains how to check parentheses in an expression and evaluate postfix expressions using stacks and queues.
The document discusses stacks and queues, which are fundamental data structures that can insert and remove items. Stacks follow the LIFO (last in, first out) principle, while queues follow the FIFO (first in, first out) principle. The document provides implementations of stacks and queues using linked lists and arrays and examples of their applications in parsing, compilers, undo functions, and more.
The document discusses converting expressions from infix to postfix notation. It explains that infix notation uses operators between operands, while postfix notation places operators after operands. The algorithm for conversion involves scanning the infix expression token by token, appending operands to the output and handling operators and parentheses by pushing/popping a stack based on precedence. An example demonstrates applying the algorithm to convert the infix expression A * (B + C) - D / E to the postfix form ABC+*DE/-.
The document describes an algorithm to convert a postfix expression to a prefix expression in the following steps:
1) Read the postfix expression from left to right and push operands onto a stack
2) When an operator is encountered, pop two operands and concatenate them with the operator to create a string
3) Push the new string back onto the stack
4) Repeat until the end of the postfix expression, at which point the final string is the prefix expression
The time complexity is O(n) where n is the length of the postfix expression.
The document describes an algorithm to convert a postfix expression to a prefix expression in the following steps:
1) Read the postfix expression from left to right and push operands onto a stack
2) When an operator is encountered, pop two operands and concatenate them with the operator to create a string
3) Push the new string back onto the stack
4) Repeat until the end of the postfix expression, at which point the final string is the prefix expression
The time complexity is O(n) where n is the length of the postfix expression.
The document discusses evaluating arithmetic expressions in infix notation using stacks. It explains that two stacks will be used - an operand stack to store numbers and an operator stack to store operators. It then provides the step-by-step process for evaluating an expression using these stacks by popping operands, popping operators, and pushing results. An algorithm is given that iterates through the expression character by character, pushing operands and operators to the appropriate stacks according to precedence rules.
This document provides instructions for implementing a basic four-function calculator using stacks and queues. It describes converting an infix expression to postfix notation, evaluating the postfix expression, and handling parentheses. Code is provided to get started, and the tasks are to complete functions to convert infix to postfix, evaluate postfix expressions, and update infix to postfix to handle parentheses. Test cases should be run to demonstrate the functionality.
The document discusses stacks and their implementation using either arrays or linked lists, noting the tradeoffs of each approach. It then covers using stacks to evaluate expressions in postfix notation by pushing operands onto the stack and applying operators to the top two elements before pushing the result back on. Finally, an example is given of evaluating the postfix expression 6 2 3 + - 3 8 2 / + * to demonstrate this process.
The document discusses stacks and their implementation and applications. It defines a stack as a linear data structure for temporary storage where elements can only be inserted or deleted from one end, called the top. Stacks follow the LIFO (last in, first out) principle. Stacks have two main operations - push, which inserts an element, and pop, which removes the top element. Stacks can be implemented using arrays or linked lists. Common applications of stacks include reversing strings, checking matching parentheses, and converting infix, postfix, and prefix expressions.
1. The document discusses stacks and queues as linear data structures. It describes stack operations like push and pop and provides algorithms for implementing these operations.
2. An example program for implementing a stack using an array is presented, with functions defined for push, pop, and display operations on the stack.
3. Applications of stacks discussed include reversing a list or string by pushing characters onto a stack and popping them off in reverse order, and converting infix expressions to postfix using a stack.
The document discusses converting infix expressions to postfix expressions using a stack. It defines infix and postfix expressions, provides examples of each, and presents an algorithm that uses a stack to scan an infix expression from left to right and output an equivalent postfix expression. Key steps include pushing operators to the stack based on precedence and popping operators to the output when encountering operands and parentheses.
The document discusses stack applications for conversion and evaluation of expressions. It describes stacks, different types of expressions (infix, postfix, prefix), and algorithms for converting between these types. Examples are provided to demonstrate converting an infix expression to postfix and evaluating a postfix expression step-by-step using a stack. The postfix expression p=abc*/d+ is evaluated, with the steps shown and final result of 3.4.
The document discusses evaluation of expressions and the conversion between infix and postfix notations. It provides examples of:
1) Evaluating expressions using the order of operations and precedence of operators. Scenarios are worked through step-by-step.
2) Converting infix notation expressions to equivalent postfix notation expressions using a stack-based algorithm.
3) Evaluating postfix notation expressions using a stack to pop operands and operators in order.
Stacks have several application areas including:
1) When functions are called to save return addresses and local variables.
2) To convert infix expressions to postfix form by acting as a placeholder.
3) To evaluate postfix expressions by holding operands and intermediate results.
The document discusses several applications of stacks, including evaluating arithmetic expressions in Polish notation without needing operator precedence or parentheses, converting expressions between infix and postfix notation, matching parentheses in expressions, and other applications like reversing strings and generating code from expressions. Polish notation places operators after operands to simplify evaluation using a stack. Converting expressions to postfix form uses a stack to remove parentheses and preserve operator order.
The document discusses applications of stacks, including reversing strings and lists, Polish notation for mathematical expressions, converting between infix, prefix and postfix notations, evaluating postfix and prefix expressions, recursion, and the Tower of Hanoi problem. Recursion involves defining a function in terms of itself, with a stopping condition. Stacks can be used to remove recursion by saving local variables at each step.
The document discusses applications of stacks, including reversing strings and lists, Polish notation for mathematical expressions, converting between infix, prefix and postfix notations, evaluating postfix and prefix expressions, recursion, and the Tower of Hanoi problem. Recursion involves defining a function in terms of itself, with a stopping condition. Stacks can be used to remove recursion by saving local variables at each step.
This document discusses different notations for representing mathematical expressions: infix, prefix, and postfix. In infix notation, operators are placed between operands (e.g. A + B). In prefix notation, operators come before operands (e.g. + A B). In postfix notation, operators follow operands (e.g. A B +). It notes that infix notation requires parentheses to determine the order of operations, while prefix and postfix notations do not. The document then provides a step-by-step example of converting an infix expression to postfix notation using a stack.
A stack is a last-in, first-out data structure where elements can only be inserted or removed from one end. Stacks follow the LIFO principle. The document discusses stacks and their use in evaluating arithmetic expressions. Expressions can be written in infix, prefix, or postfix notation, and converting an infix expression to postfix notation allows it to be evaluated using a stack, with operators and operands pushed and popped off the stack from left to right.
The document provides an outline for a lecture on applications of stacks and queues, including syntax parsing, expression evaluation, backtracking, and printing jobs. It discusses infix, postfix, and prefix notation and how to convert between them using stacks. It also explains how to check parentheses in an expression and evaluate postfix expressions using stacks and queues.
The document discusses stacks and queues, which are fundamental data structures that can insert and remove items. Stacks follow the LIFO (last in, first out) principle, while queues follow the FIFO (first in, first out) principle. The document provides implementations of stacks and queues using linked lists and arrays and examples of their applications in parsing, compilers, undo functions, and more.
The document discusses converting expressions from infix to postfix notation. It explains that infix notation uses operators between operands, while postfix notation places operators after operands. The algorithm for conversion involves scanning the infix expression token by token, appending operands to the output and handling operators and parentheses by pushing/popping a stack based on precedence. An example demonstrates applying the algorithm to convert the infix expression A * (B + C) - D / E to the postfix form ABC+*DE/-.
The document describes an algorithm to convert a postfix expression to a prefix expression in the following steps:
1) Read the postfix expression from left to right and push operands onto a stack
2) When an operator is encountered, pop two operands and concatenate them with the operator to create a string
3) Push the new string back onto the stack
4) Repeat until the end of the postfix expression, at which point the final string is the prefix expression
The time complexity is O(n) where n is the length of the postfix expression.
The document describes an algorithm to convert a postfix expression to a prefix expression in the following steps:
1) Read the postfix expression from left to right and push operands onto a stack
2) When an operator is encountered, pop two operands and concatenate them with the operator to create a string
3) Push the new string back onto the stack
4) Repeat until the end of the postfix expression, at which point the final string is the prefix expression
The time complexity is O(n) where n is the length of the postfix expression.
The document discusses evaluating arithmetic expressions in infix notation using stacks. It explains that two stacks will be used - an operand stack to store numbers and an operator stack to store operators. It then provides the step-by-step process for evaluating an expression using these stacks by popping operands, popping operators, and pushing results. An algorithm is given that iterates through the expression character by character, pushing operands and operators to the appropriate stacks according to precedence rules.
This document provides instructions for implementing a basic four-function calculator using stacks and queues. It describes converting an infix expression to postfix notation, evaluating the postfix expression, and handling parentheses. Code is provided to get started, and the tasks are to complete functions to convert infix to postfix, evaluate postfix expressions, and update infix to postfix to handle parentheses. Test cases should be run to demonstrate the functionality.
The document discusses stacks and their implementation using either arrays or linked lists, noting the tradeoffs of each approach. It then covers using stacks to evaluate expressions in postfix notation by pushing operands onto the stack and applying operators to the top two elements before pushing the result back on. Finally, an example is given of evaluating the postfix expression 6 2 3 + - 3 8 2 / + * to demonstrate this process.
The document discusses stacks and their implementation and applications. It defines a stack as a linear data structure for temporary storage where elements can only be inserted or deleted from one end, called the top. Stacks follow the LIFO (last in, first out) principle. Stacks have two main operations - push, which inserts an element, and pop, which removes the top element. Stacks can be implemented using arrays or linked lists. Common applications of stacks include reversing strings, checking matching parentheses, and converting infix, postfix, and prefix expressions.
1. The document discusses stacks and queues as linear data structures. It describes stack operations like push and pop and provides algorithms for implementing these operations.
2. An example program for implementing a stack using an array is presented, with functions defined for push, pop, and display operations on the stack.
3. Applications of stacks discussed include reversing a list or string by pushing characters onto a stack and popping them off in reverse order, and converting infix expressions to postfix using a stack.
The document discusses converting infix expressions to postfix expressions using a stack. It defines infix and postfix expressions, provides examples of each, and presents an algorithm that uses a stack to scan an infix expression from left to right and output an equivalent postfix expression. Key steps include pushing operators to the stack based on precedence and popping operators to the output when encountering operands and parentheses.
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2. Objectives Overview
• Notations
• Prefix, Infix and Postfix Notations
• Conversion of one type expression to another
• Evaluation of Prefix and Postfix Notations
3. Notation
The way to write arithmetic expression is known as a notation.
An arithmetic expression can be written in three different but
equivalent notations, i.e., without changing the essence or
output of an expression. These notations are:
• Infix Notation
• Prefix Notation
• Postfix Notation
These notations are named as how they use operator in
expression. The terms infix, prefix, and postfix tell us whether
the operators go between, before, or after the operands.
4. Infix Notation
• We write expression in infix notation, e.g. a - b + c,
where operators are used in-between operands. It is
easy for us humans to read, write, and speak in infix
notation but the same does not go well with
computing devices. An algorithm to process infix
notation could be difficult and costly in terms of time
and space consumption.
6. Prefix Notation
• In this notation, operator is prefixed to operands, i.e.
operator is written ahead of operands. For example,
+ab. This is equivalent to its infix notation a + b.
Prefix notation is also known as Polish Notation.
8. Postfix Notation
• This notation style is known as Reversed Polish
Notation. In this notation style, the operator is
postfixed to the operands i.e., the operator is
written after the operands. For example, ab+. This is
equivalent to its infix notation a + b.
10. Fully Parenthesized Expression
• A FPE has exactly one set of Parentheses enclosing
each operator and its operands.
• Which one is fully parenthesized?
• ( A + B ) * C
• ( ( A + B) * C )
• ( ( A + B) * ( C ) )
12. Conversion from Infix to Postfix
• Infix: ( ( ( A + B ) * C ) - ( ( D + E ) / F ) )
• Postfix: A B + C * D E + F / -
• Operand order does not change!
• Operators are in order of evaluation!
13. Infix to Postfix - Algorithm
• Initialize a Stack for operators, output list.
• Split the input into a list of tokens.
• for each token (left to right):
▫ if it is operand: append to output
▫ if it is '(': push onto Stack
▫ if it is ')': pop & append till '('
14. FPE Infix to Postfix
( ( ( A + B ) * ( C - E ) ) / ( F + G ) )
● stack: <empty>
● output: []
15. FPE Infix to Postfix
( ( A + B ) * ( C - E ) ) / ( F + G ) )
● stack: (
● output: []
16. FPE Infix to Postfix
( A + B ) * ( C - E ) ) / ( F + G ) )
● stack: ( (
● output: []
17. FPE Infix to Postfix
A + B ) * ( C - E ) ) / ( F + G ) )
● stack: ( ( (
● output: []
18. FPE Infix to Postfix
+ B ) * ( C - E ) ) / ( F + G ) )
● stack: ( ( (
● output: [A]
19. FPE Infix to Postfix
B ) * ( C - E ) ) / ( F + G ) )
● stack: ( ( ( +
● output: [A]
20. FPE Infix to Postfix
) * ( C - E ) ) / ( F + G ) )
● stack: ( ( ( +
● output: [A B]
21. FPE Infix to Postfix
* ( C - E ) ) / ( F + G ) )
● stack: ( (
● output: [A B + ]
22. FPE Infix to Postfix
( C - E ) ) / ( F + G ) )
● stack: ( ( *
● output: [A B + ]
23. FPE Infix to Postfix
C - E ) ) / ( F + G ) )
● stack: ( ( * (
● output: [A B + ]
24. FPE Infix to Postfix
- E ) ) / ( F + G ) )
● stack: ( ( * (
● output: [A B + C ]
25. FPE Infix to Postfix
E ) ) / ( F + G ) )
● stack: ( ( * ( -
● output: [A B + C ]
26. FPE Infix to Postfix
) ) / ( F + G ) )
● stack: ( ( * ( -
● output: [A B + C E ]
27. FPE Infix to Postfix
) / ( F + G ) )
● stack: ( ( *
● output: [A B + C E - ]
28. FPE Infix to Postfix
/ ( F + G ) )
● stack: (
● output: [A B + C E - * ]
29. FPE Infix to Postfix
( F + G ) )
● stack: ( /
● output: [A B + C E - * ]
30. FPE Infix to Postfix
F + G ) )
● stack: ( / (
● output: [A B + C E - * ]
31. FPE Infix to Postfix
+ G ) )
● stack: ( / (
● output: [A B + C E - * F ]
32. FPE Infix to Postfix
G ) )
● stack: ( / ( +
● output: [A B + C E - * F ]
33. FPE Infix to Postfix
) )
● stack: ( / ( +
● output: [A B + C E - * F G ]
34. FPE Infix to Postfix
)
● stack: ( /
● output: [A B + C E - * F G + ]
35. FPE Infix to Postfix
● stack: <empty>
● output: [A B + C E - * F G + / ]
38. Infix to Prefix - Algorithm
1. Reverse the infix expression i.e A+B*C will become
C*B+A. Note while reversing each ‘(‘ will become ‘)’
and each ‘)’ becomes ‘(‘.
2. Obtain the postfix expression of the modified
expression i.e CB*A+.
3. Reverse the postfix expression. Hence in our
example prefix is +A*BC.
39. Infix to Prefix Conversion
Move each operator to the left of its
operands & remove the parentheses:
( ( A + B) * ( C + D ) )
40. Infix to Prefix Conversion
Move each operator to the left of its
operands & remove the parentheses:
( + A B * ( C + D ) )
41. Infix to Prefix Conversion
Move each operator to the left of its
operands & remove the parentheses:
* + A B ( C + D )
42. Infix to Prefix Conversion
Move each operator to the left of its
operands & remove the parentheses:
* + A B + C D
Order of operands does not change!
44. Algorithm
● While there are input symbol left
● Read the next symbol from input.
● If the symbol is an operand
o Push it onto the stack.
● Otherwise,
● the symbol is an operator.
● If there are fewer than 2 values on the stack
● Show Error /* input not sufficient values in the expression */
● Else
● Pop the top 2 values from the stack.
● Put the operator, with the values as arguments and form a string.
● Encapsulate the resulted string with parenthesis.
● Push the resulted string back to stack.
● If there is only one value in the stack
● That value in the stack is the desired infix string.
● If there are more values in the stack
● Show Error /* The user input has too many values */
46. Algorithm
● The reversed input string is completely pushed into a stack.
● prefixToInfix(stack)
● 2.IF stack is not empty
● a. Temp -->pop the stack
● b. IF temp is a operator
● Write a opening parenthesis to output
● prefixToInfix(stack)
● Write temp to output
● prefixToInfix(stack)
● Write a closing parenthesis to output
● c. ELSE IF temp is a space -->prefixToInfix(stack)
● d. ELSE
● Write temp to output
● IF stack.top NOT EQUAL to space -->prefixToInfix(stack)
48. Algorithm
● Read the Prefix expression in reverse order (from right to
left)
● If the symbol is an operand, then push it onto the Stack
● If the symbol is an operator, then pop two operands from
the Stack
Create a string by concatenating the two operands and
the operator after them.
string = operand1 + operand2 + operator
And push the resultant string back to Stack
● Repeat the above steps until end of Prefix expression.
50. Algorithm
● Read the Postfix expression from left to right
● If the symbol is an operand, then push it onto the Stack
● If the symbol is an operator, then pop two operands from
the Stack
Create a string by concatenating the two operands and
the operator before them.
string = operator + operand2 + operand1
And push the resultant string back to Stack
● Repeat the above steps until end of Prefix expression.
52. Postfix Evaluation Algorithm
● Step 1 − scan the expression from left to right
● Step 2 − if it is an operand push it to stack
● Step 3 − if it is an operator pull operand from
stack and perform operation
● Step 4 − store the output of step 3, back to stack
● Step 5 − scan the expression until all operands
are consumed
● Step 6 − pop the stack and perform operation
54. Prefix Evaluation Algorithm
1) Put a pointer P at the end of the end
2) If character at P is an operand push it to Stack
3) If the character at P is an operator pop two elements
from the Stack. Operate on these elements according to
the operator, and push the result back to the Stack
4) Decrement P by 1 and go to Step 2 as long as there are
characters left to be scanned in the expression.
5) The Result is stored at the top of the Stack, return it
6) End
55. Summary
• Notations
• Prefix, Infix and Postfix Notations
• Conversion of one type expression to another
• Evaluation of Prefix and Postfix Notations