GATE CSE 2007 | Question: 38, ISRO2016-27

Question

The following postfix expression with single digit operands is evaluated using a stack:

$$8 \ 2 \ 3 \  {}^\hat{}  ∕  \ 2 \ 3 * + 5 \ 1 * -$$

Note that $^\hat{}$ is the exponentiation operator. The top two elements of the stack after the first $*$ is evaluated are

• A. $6, 1$
• B. $5, 7$
• C. $3, 2$
• D. $1, 5$

Comments

@Arjun sir , this question is still not corrected in go hardcopy 2020.

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missed it. Will check next time as nothing is wrong in HTML. May be an unknown issue.

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It is fixed now.

Answer 1

• $8:$ $\textsf{PUSH}.$  Stack becomes $:8$
• $2:$ $\textsf{PUSH}.$  Stack becomes $:8\;2$
• $3:$ $\textsf{PUSH}.$  Stack becomes $:8\;2\;3$
• $^\hat{}:$ $\textsf{POP}$ $3$ and $2$ and perform the operation $2\; ^\hat{}\; 3$ and push the result to stack. Stack becomes $:8\;8$
• $∕:$ $\textsf{POP}$ $8$ and $8$ and perform the operation $8 ∕8$ and push the result to stack. Stack becomes $:1$
• $2:$ $\textsf{PUSH}.$  Stack becomes $:1\;2$
• $3:$ $\textsf{PUSH}.$  Stack becomes $:1\;2\;3$
• $*:$ $\textsf{POP}$ $3$ and $2$ and perform the operation $2 * 3$ and push the result to stack. Stack becomes $:1\;6$

Hence, answer is A.

Comments

after 823 we've ^ in TOS , so we'll pop last two element & perform the operation that's fine.but my query is that why 2^3 not 3^2 & in case there is ' - ' in place of ' ^ ' then in which order it will be performed.

I mean sometimes for some operator order of the elelment will matter( e.g:' - ' & ' ^ ' as 3-2 or 2-3  and  2^3 or 3^2) Is there any general concept to remove this confusion???

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@MRINMOY_HALDER......bottom of the element is 1st and top element 2nd......i.e    2-3=-1

better take any infix operation solve first then convert that postfix evaluate using postfix evaluation...you will get ans

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what if 1,6 and 6,1 both were in options...

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I guess 6,1 must be the answer.

Since stack elements, in the end, are 1,6 with 6 being at the top. So when popped off, 6 will come first. Then, 1.

Answer 2

Operation	Expression	Stack
	823 ^ /23 * 51 * -	Empty
Push	23 ^ /23 * 51 * -	8
Push	3 ^ /23 * 51 * -	8 2
Push	^ /23 * 51 * -	8 2 3
Pop	/23 * 51 * -	8 (2^3)
Pop	23 * 51 * -	8/8
Push	3 * 51 * -	1 2
Push	* 51 * -	1 2 3
Pop	51 * -	1 (2*3)

So top two elements after 1st * is 6 , 1

Answer 3

The single important thing is, when you pop two elements, first one goes on right side.

Answer 4

Ans is (A) 6 ,1