What determines the order of operations in Polish notation?
Click to see answer
The positions of the operators and operands in the expression.
Click to see question
What determines the order of operations in Polish notation?
The positions of the operators and operands in the expression.
What is the maximum size of a stack with 6 elements called?
The size of the stack.
What message is displayed if the stack is underflow?
"Stack is Underflow".
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.
What condition is checked to determine if the stack is underflow?
If top == -1.
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 is the postfix expression for the infix expression (A + B ^ D)/(E - F) + G?
A B D ^ + E F - / G +
What happens if the stack is full during the push operation?
It writes 'Stack is Overflow'.
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 operation is performed to take an element off from the stack?
pop()
What is the postfix notation for the expression X = ((A/(B ^ C)) + (D * E) - (A * C))?
ABC ^/ DE * + AC * -
What is the postfix expression for the infix expression (A - B) * (D/E)?
A B - D E / *
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.
What is the infix expression to be converted to postfix?
A + B * C / D - F + A ^ E
In the expression A + B * C / D - F + A ^ E, which operation is performed first?
B * C
What is a characteristic of infix operators?
Infix operators have precedence.
What is a common use of stacks in string manipulation?
Reversing a string.
What are the two basic operations associated with stacks?
Push and Pop.
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.
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.
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?
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).
What condition occurs if you attempt to remove elements beyond the base of the stack?
You will reach a stack underflow condition.
Give an example of an infix expression.
((A + B) * C) / D.
What happens if you try to push onto a full stack?
It generates an error message 'stack overflow'.
What is the first step in converting infix to postfix expression?
Scan the input string from left to right character by character.
What happens if the operator's stack is not empty?
Check the precedence of the scanned operator against the topmost operator of the stack.
What is the role of parentheses in infix expressions?
To override the default precedence of operators.
What is the first step in the pop() algorithm?
START.
What is the conventional way of writing expressions called?
Infix notation.
In infix notation, where do binary operators occur?
Between the operands.
What is the postfix notation for the expression (A/(B-C)*D+E)?
A B C - D * E + /
What operator has the highest precedence in the expression (A/(B-C)*D+E)?
Division and multiplication (both have the same precedence).
Where can items be added or removed in a stack?
Only from the top of the stack.
What is the data type of the variable 'x' in the push() function?
int.
What operator has the highest precedence in the expression A + B * C / D - F + A ^ E?
^ (exponentiation)
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.
What is the first step in converting the infix expression (A/(B-C)*D+E) to postfix notation?
Identify the operators and their precedence.
What is the prefix notation for the expression X = ((A/(B ^ C)) + (D * E) - (A * C))?
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.
What is the role of the stack in converting infix to postfix notation?
To temporarily hold operators and manage precedence.
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 ')'.
What should be done when encountering an opening round bracket '('?
Push it into the operator's stack.
What operation is used to add an element to a stack?
push()
What happens to the top value after popping an element from the stack?
It is decremented (top = top - 1).
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.
What condition checks for stack overflow in the push() algorithm?
if top >= size - 1.
What is the final step of the pop() algorithm?
END.
What is the priority of multiplication and division compared to addition and subtraction?
Multiplication and division have higher priority than addition and subtraction.
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).
What is a stack?
A linear data structure where elements can be inserted or deleted only at one end, called the top.
What does LIFO stand for?
Last In, First Out.
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.
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 / + * -
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 is the first step in the Display procedure for a stack?
START.
What is the initial value of 'top' in a stack?
-1
How do you increment the 'top' value when adding an element to the stack?
top = top + 1
What is the first step in the push() algorithm for a stack?
START.
What does the pop() function do in the provided algorithm?
Removes the top element from the stack.
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'.
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 message is displayed if the stack is underflow?
"Stack is Underflow".
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.
How can parentheses affect operator priority?
Parentheses can override the default priority, forcing the operations within them to be performed first.
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'.
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.
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.
