Data Structures: Stacks and Notations

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Questions and Answers

Using the described algorithm, what is the postfix notation for the infix expression $A + B * C - D / E$?

AB+C*DE/-

ABC+*DE/-

AB*C+DE/-

ABC*+DE/- (correct)

Given the postfix expression $5\ 2\ +\ 8\ 3\ - *$, what is the result of its evaluation?

35 (correct)

Which of the following infix expressions is correctly represented by the postfix expression $AB+C*D-$?

(A + B) * C - D (correct)

A + (B * C - D)

A + B * (C - D)

A + B * C - D

What is the stack content just before processing 'F' in the infix expression conversion to postfix for $(A+B/C*(D+E)-F)$?

(- (D) Signup and view all the answers

Which of the following statements regarding infix, prefix, and postfix notations is most accurate?

Prefix notation requires no parentheses to define the order of operations. (D) Signup and view all the answers

What is the postfix equivalent of the infix expression $(A + B) * (C + D)$?

AB+CD+* (B) Signup and view all the answers

Given an empty stack, trace the stack operations while converting $A+B+C+D$ to postfix. What does the stack contain just before processing 'C'?

<ul> <li>(A)</li> </ul> Signup and view all the answers

Using the example conversion, determine the postfix equivalent for infix: $(A+B*C)/(D-E-F)$?

ABC*+DEF--/ (C) Signup and view all the answers

If the stack contains `` while converting `AB+CD` to postfix, what are the inputs that caused `` to be on the stack?

A, *, B (A) Signup and view all the answers

What is the final evaluated output of the postfix expression $10\ 6\ 2\ /\ \ 9\ 10\ +\ \ + \ 12\ -$?

178 (C) Signup and view all the answers

Given the expression `abc-+de-+`, which of the following represents the correct evaluation steps using a stack?

Push a, b, c; Pop c, b; Apply -; Push result; Push d, e; Pop e, d; Apply -; Push result; Pop both results; Apply +; Push final result. (B) Signup and view all the answers

What is the prefix expression for the infix expression $A+B*C+D$?

$++A*BCD$ (A) Signup and view all the answers

When converting the infix expression `K+L-MN+(O^P)W/U/V*T+Q` to prefix using a stack, what is the state of the stack when processing the character 'W'?

+-*/ (A) Signup and view all the answers

Given the prefix expression `*+AB+CD`, what is its equivalent infix expression?

(A+B)*(C+D) (B) Signup and view all the answers

You are evaluating the prefix expression `+9*26`. What are the intermediate steps?

Evaluate 2*6=12, evaluate 9+12=21 (C) Signup and view all the answers

When converting `(A+B)*(C+D)` to prefix notation, which of the following is a step along the way?

Converting A+B to +AB and C+D to +CD, then combining as *+AB+CD (A) Signup and view all the answers

What would be the stack contents after processing 'B' and then '+' when converting 'A+B*C' to prefix?

Stack contains '+' (A) Signup and view all the answers

What is the relationship between number of operands with number of operators while converting from infix to postfix?

Operands are always one more than operators. (B) Signup and view all the answers

If an expression contains characters instead of numerical values what is the final output when it is fully evaluated using stack?

The expression will result in a string representing the equivalent expression. (A) Signup and view all the answers

What is the prefix form of `(D+C)*(B+A)`?

*+DC+BA (C) Signup and view all the answers

Flashcards

Operator

A symbol that denotes operations on operands, e.g., +, -.

Operand

An entity on which an operation is performed, e.g., numbers or variables.