GATE CSE 2024 | Set 1 | Question: 23

Question

Consider the operator precedence and associativity rules for the integer arithmetic operators given in the table below. $$\begin{array}{|c|l|}\hline \textbf{Operator}  &  \textbf{Precedence} & \textbf{Associativity} \\\hline  \text{$+$} & \text{Highest} & \text{Left} \\\hline  \text{$-$} & \text{High} & \text{Right} \\\hline  \text{$*$} & \text{Medium} & \text{Right}  \\\hline \text{$/$} & \text{Low} & \text{Right}  \\\hline \end{array}$$

The value of the expression $3+1+5 * 2 / 7+2-4-7-6 / 2$ as per the above rules is ________.

Comments

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All questions related to Expression grammar: Associativity, Precedence & (Ambiguity elimination):

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Compiler Design: GATE CSE 2016 Set 1 | Question: 45

Compiler Design: GATE CSE 2024 | Set 1 | Question: 23

Answer 1

The given expression is evaluated as follows:

$\implies \underbrace{\underbrace{3+1}+5}*2/\underbrace{7+2}-4-7-6/2\; [ \text{As '+' has higher predence with left associative in the operators present in the expression.}]$

$\implies(3+1)+5*2/7+2-4-7-6/2$

$\implies(4+5)*2/7+2-4-7-6/2$

$\implies9*2/(7+2)-4-7-6/2$

$\implies9*2/\underbrace{9-\underbrace{4-\underbrace{7-6}}}/2\; [ \text{As '-' has higher predence with right associative in the operators present in the expression.}]$

$\implies9*2/9-4-(7-6)/2$

$\implies9*2/9-(4-1)/2$

$\implies9*2/(9-3)/2$

$\implies \underbrace{9*2}/6/2 \; [ \text{As '*' has higher predence with right associative in the operators present in the expression.}]$

$\implies(9*2)/6/2$

$\implies \underbrace{18/\underbrace{6/2}} \; [ \text{As '/' has higher predence with right associative in the operators present in the expression.}]$

$\implies18/(6/2)$

$\implies18/3=6$

Similar kind of questions  asked in GATE CSE 2016 Set 1 | Question: 45

Comments

But we are saying that -7-6 is -(7-6).

How does that make sense? They have not given precedence of unary (-) operator. So -7-6 should be -13, and so on.

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Agreed

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I think that is because of the associativity,

• For a left–associative operator you group from left to right. (For example, if “+” were the only operator then a+b+c means (a+b)+c .
• For a right–associative operator you group from right to left. (For example, if “−” is right–associative then a−b−c means a−(b−c) . source: ChatGPT

Answer 2

Step by Step Procedure 

 

Answer 3

There was no graph based answer, Here is one, Correct me if you find an imporvement.

Answer 4

{ (((3+1)+5)*2) / ((7+2)-(4-(7-6))) / 2 }

this evaluates to 6