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GATE CSE 2024 | Set 2 | Question: 33

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22 22 votes

​Consider the following expression: $x[i]=(p+r) *-s[i]+u / w$. The following sequence shows the list of triples representing the given expression, with entries missing for triples $(1), (3)$, and $(6)$.

$$\begin{array}{|c|c|c|c|}
\hline(0) & + & p & r \\
\hline(1) & & & \\
\hline(2) & \text{uminus} & (1) & \\
\hline(3) & & & \\
\hline(4) & / & u & w \\
\hline(5) & + & (3) & (4) \\
\hline(6) & & & \\
\hline(7) & = & (6) & (5) \\
\hline
\end{array}$$
Which one of the following options fills in the missing entries CORRECTLY?

  1. $(1)$ $\text{=}$$\text{[ ] s } i \quad(3)$ $\text{*}$ $(0)(2) $ $\quad(6) $$\text{[ ]=}$ $\textit{x }i$
  2. $(1)$ $\text{[ ]}$$=\text{s } i \quad(3)-(0)(2) \quad(6) =$$\text{[ ]}$ $\textit{x }(5)$
  3. $(1)$ $\text{=}$$\text{[ ] s } i \quad(3)$ $\text{*}$ $(0)(2) $ $\quad(6) $$\text{[ ]=}$ $\textit{x }(5)$
  4. $(1)$ $\text{[ ]}$$=\text{s } i \quad(3)-(0)(2) \quad(6) =$$\text{[ ]}$ $\textit{x }i$

5 Answers

26 26 votes

We can do this question as option elimination also as @Cxdr suggested on comments.

But, let's actually try to build this table.
Given expression is:  x[i] =  (p+r)*-s[i]+u/w.
converting x[i] and s[i] is little overwhelming, so try to think like this

since, we are using value of s[i], let's write it in this way,
t1 = s[i] ( we have two operands apart from temporary variable and two operator)
in triple symbol table it could be written as,
=[]  s  i  

also, we are putting computed value in x[i], let's write it in this way
x[i] = t1 
In symbol table it could be written as, 
[]=  x  i ( we have two operands apart from temporary variable and two operator)

Now, everything is easy anyways, let's build the table
 

(0)+pr
(1)=[]si
(2)uminus(1) 
(3)*(0)(2)
(4)/uw
(5)+(3)(4)
(6)[]=xi
(7)=(6)(5)


 

4 4 votes
A is the correct answer.

Expalnation: Going from left to right we resolve the brackets first. (p+r) is already given, now we solve s[i]. then comes unary minus as per operator preference. Then we solve * which acts between 0 & 2 (B & D eliminated) and / , + subsequently. Then x[i] address is calculated(step 6) where the final result (obtained in step 5) is stored in the last step (7). The assignment operator has lowest preference so it is done at last.
• edited by
4 4 votes

  • To solve these types of questions, analytical skills are key. From the given expression and table we can see following two 

    • (0) : p + r
    • (4) : u / w

  • I derived these expressions simply by analyzing the given expression. From this, we can conclude:

    • (5) : (3) + (4) and (7) : (6) = (5)

  • Therefore:

    • (5) = (3) + (4), where (4) is fixed as u/v.
    • This implies (3) must be (p + r) * -s[i].

  • Additionally:

    • (2) is -(1) because "-" here is unary.

  • Consequently:

    • (3) must be *(0)(2), as the unary "-" is already associated with (2).

  • With this information:

    • Options B and D are eliminated.

  • Therefore:

    • (1) must be s[i].
    • The same logic applied to s[i] should also be applied to x[i].
    • This also eliminates option D.

  • Conclusion: Option A is correct

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