What determines the order of operations in Polish notation?
The positions of the operators and operands in the expression.
What role do stacks play in subprograms?
They process subprogram function calls.
In the C++ display function, what is printed when the stack is not empty?
"Display elements are:" followed by the elements of the stack.
How can a stack be used in evaluating expressions?
To evaluate postfix expressions.
How can stacks help in checking parentheses?
By checking for well-formed (nested) parentheses.
What happens if the stack is not underflow?
Print "deleted element" and decrement top.
What happens if the stack is full during the push operation?
It writes 'Stack is Overflow'.
p.12
Basic Operations on Stacks
Which operator typically has the highest priority?
Exponentiation (^) or similar operators, depending on the programming language.
What does the command 'cin >> x;' do in the push() function?
It reads the input value for 'x'.
Why are postfix expressions useful for computers?
They are very useful for evaluating formulas using stacks.
What is the initial condition of the stack in the provided example?
The stack initially has three elements.
What occurs if the stack is not empty when attempting to pop an element?
The element is removed from the stack.
What is the procedure to add a new element to the stack?
Read data value 'x', increment top, and assign stack[top] = x.
p.17
Infix to Postfix Conversion Algorithm
What is the infix expression to be converted to postfix?
A + B * C / D - F + A ^ E
p.15
Review Questions on Infix Expressions
What is a characteristic of infix operators?
Infix operators have precedence.
p.3
Basic Operations on Stacks
What must be checked before performing push and pop operations?
Whether the stack is empty or full.
What does Polish Notation refer to?
A mathematical notation in which every operator follows all of its operands.
p.12
Basic Operations on Stacks
What is operator priority?
The rules that determine the order in which operations are performed in an expression.
What does the pop operation do?
Deletes elements from the stack.
p.16
Infix to Postfix Conversion Algorithm
What should be done if the scanned character is an operand?
Put it into the output stack.
What are the two ways to represent a stack?
1. Stack using array 2. Stack using linked list.
What happens if the stack is not empty during the display operation?
The list of elements in the stack is displayed.
What should be checked before deleting an element from the stack?
Whether the stack is empty (top == -1).
p.4
Basic Operations on Stacks
What condition occurs if you attempt to remove elements beyond the base of the stack?
You will reach a stack underflow condition.
What happens if you try to push onto a full stack?
It generates an error message 'stack overflow'.
p.16
Infix to Postfix Conversion Algorithm
What is the first step in converting infix to postfix expression?
Scan the input string from left to right character by character.
p.16
Infix to Postfix Conversion Algorithm
What happens if the operator's stack is not empty?
Check the precedence of the scanned operator against the topmost operator of the stack.
p.17
Infix to Postfix Conversion Algorithm
What is the role of parentheses in infix expressions?
To override the default precedence of operators.
p.18
Infix to Postfix Conversion Algorithm
What operator has the highest precedence in the expression (A/(B-C)*D+E)?
Division and multiplication (both have the same precedence).
p.2
Basic Operations on Stacks
Where can items be added or removed in a stack?
Only from the top of the stack.
What is one application of a stack in expression conversion?
Converting infix expressions to postfix and prefix expressions.
What is a key advantage of using Polish notation?
Parentheses are not required while writing expressions.
p.18
Infix to Postfix Conversion Algorithm
What is the first step in converting the infix expression (A/(B-C)*D+E) to postfix notation?
Identify the operators and their precedence.
p.5
Basic Operations on Stacks
What condition must be checked before inserting an element into the stack?
Whether the stack is full (top >= size - 1).
What happens if the stack is not full when trying to add an element?
The element is added to the stack.
p.18
Infix to Postfix Conversion Algorithm
What is the role of the stack in converting infix to postfix notation?
To temporarily hold operators and manage precedence.
p.16
Infix to Postfix Conversion Algorithm
What action is taken if the precedence of the scanned operator is less than or equal to the topmost operator?
Pop operators from the stack until a lower precedence operator is found, without popping '(' or ')'.
p.16
Infix to Postfix Conversion Algorithm
What should be done when encountering an opening round bracket '('?
Push it into the operator's stack.
What happens to the top value after popping an element from the stack?
It is decremented (top = top - 1).
p.4
Basic Operations on Stacks
What happens if you try to add an element beyond the maximum size of the stack?
You will encounter a stack overflow condition.
How do unary operators appear in infix notation?
They precede their operand.
p.12
Basic Operations on Stacks
What is the priority of multiplication and division compared to addition and subtraction?
Multiplication and division have higher priority than addition and subtraction.
p.17
Infix to Postfix Conversion Algorithm
What is the postfix notation for the expression A + B * C / D - F + A ^ E?
A B C D / * + F - A E ^ +
What is a key benefit of postfix expressions regarding parentheses?
Any formula can be expressed without parentheses.
What condition is checked before displaying elements in the stack?
Whether the stack is empty (i.e., top == -1).
p.2
Introduction to Stacks
What is a stack?
A linear data structure where elements can be inserted or deleted only at one end, called the top.
p.12
Basic Operations on Stacks
What are operators in programming?
Symbols that perform operations on variables and values.
What does the push operation do?
Adds new elements to the stack.
p.19
Infix to Postfix Conversion Algorithm
What is the postfix expression for the infix expression A * (B + D)/E - F * (G + H/K)?
A B D + E / F G H K / + * -
p.16
Infix to Postfix Conversion Algorithm
What should be done if the precedence of the scanned operator is greater than the topmost operator?
Push this operator into the operator's stack.
What does the pop() function do in the provided algorithm?
Removes the top element from the stack.
p.18
Infix to Postfix Conversion Algorithm
How do parentheses affect the conversion from infix to postfix notation?
They dictate the order of operations and must be processed first.
What happens if you try to pop from an empty stack?
It generates an error message 'stack underflow'.
p.16
Infix to Postfix Conversion Algorithm
What action is taken if the operator's stack is empty?
Push the operator into the operators' stack.
What does the display() operation do in a stack?
It displays the elements in the stack.
What does the Display procedure check for in Step 2?
If top == -1, indicating the stack is empty.
What happens in Step 3 of the Display procedure if the stack is not empty?
It prints "Display elements are" and then iterates from top to 0 to print the stack elements.
How does the LIFO principle work in a stack?
The last element inserted is the first one to be deleted.
What is the loop structure used to display stack elements in the C++ code?
for(i = top; i >= 0; i--).
What happens to the last item added to a stack?
It is the first item to be removed.
p.12
Basic Operations on Stacks
How can parentheses affect operator priority?
Parentheses can override the default priority, forcing the operations within them to be performed first.
p.16
Infix to Postfix Conversion Algorithm
What is the procedure when a closing round bracket ')' is encountered?
Pop operators from the stack until an opening bracket '(' is found.
What is the purpose of converting expressions to postfix and prefix notations?
To facilitate easier computation and evaluation of expressions.
What message is displayed after successfully pushing data into the stack?
'Data Pushed into the stack'.
p.17
Infix to Postfix Conversion Algorithm
What is the first step in converting the infix expression A + B * C / D - F + A ^ E to postfix?
Identify the operators and their precedence.
p.16
Infix to Postfix Conversion Algorithm
What is the final step after processing all characters?
Pop all remaining operators from the operator's stack and push them into the output stack.
