Virtual Labs

1. Why is it useful to convert an infix expression to postfix before evaluation?

a: It makes the expression easier for humans to read. Explanation

Explanation

b: It makes the evaluation order explicit, so evaluation does not need to repeatedly apply infix precedence and parentheses. Explanation

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c: It changes every operand into an operator. Explanation

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d: It guarantees that no stack is needed during evaluation. Explanation

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2. The postfix evaluation of

1\ 2\ +\ 3\ 9\ -\ +\ 4\ +

is ______.

a: 3 Explanation

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b: 2 Explanation

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c: 1 Explanation

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d: 4 Explanation

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3. Convert the infix expression

1+1-3*4/2+3-8

to postfix.

a: 1 1 + 3 - 4 * 2 / + 3 8 - Explanation

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b: 1 1 + 3 - 4 / 2 * 3 + 8 - Explanation

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c: 1 1 + 3 4 * 2 / - 3 + 8 - Explanation

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d: 1 1 * 3 + 4 - 2 + 3 / 8 - Explanation

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4. Convert the infix expression

a+b*(c^d-e)^(f+g*h)-i

to postfix.

\texttt{ab\textasciicircum{}cd-ef+d*h\textasciicircum{}*-i+}

Explanation

\texttt{ab\textasciicircum{}cd-ef+d*h*\textasciicircum{}-i+}

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\texttt{abcd\textasciicircum{}e-fgh*+\textasciicircum{}*+i-}

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\texttt{abcd\textasciicircum{}e-fgh*+*\textasciicircum{}+i-}

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5. Convert the infix expression

a+b*c-d^{e^f}

to postfix.

\texttt{abc*+def\textasciicircum{}\textasciicircum{}-}

Explanation

\texttt{abc*+de\textasciicircum{}f\textasciicircum{}-}

Explanation

\texttt{ab+c*d-e\textasciicircum{}f\textasciicircum{}}

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\texttt{-+a*bc\textasciicircum{}\textasciicircum{}def}

Explanation

6. During postfix evaluation, what happens when the operator

*

is encountered after two operands have been pushed onto the stack?

a: The operator is pushed as a new operand. Explanation

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b: The two operands are used for multiplication and the result is pushed back onto the stack. Explanation

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c: The stack is cleared without performing the operation. Explanation

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d: The operator is ignored. Explanation

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7. Which postfix expression is equivalent to the infix expression

a*(b+c)-d

a: abc+*d- Explanation

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b: ab+c*d- Explanation

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c: abc*+d- Explanation

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d: a*bc+d- Explanation

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8. In the postfix expression

2\ 3\ 4\ *\ +

, what is the final result?

a: 14 Explanation

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b: 20 Explanation

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c: 9 Explanation

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d: 24 Explanation

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9. For a valid postfix expression containing

n

tokens, what is the auxiliary space complexity of stack-based evaluation in the worst case?

O(1)

Explanation

O(\log n)

Explanation

O(n)

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O(n^2)

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Infix and Postfix