GATE CS 2018 Q.48 (CS Q.38): Parsing and Syntax Analysis (LL and LR)

Consider the following parse tree for the expression a#b$c$d#e#f, involving two binary operators $ and #.

Which one of the following is correct for the given parse tree?

$ has higher precedence and is left associative; # is right associative

# has higher precedence and is left associative; $ is right associative

$ has higher precedence and is left associative; # is left associative

# has higher precedence and is right associative; $ is left associative

Official answer and solution

Solution

Deduce operator precedence from tree depth and operator associativity from branch direction.

In a parse tree for an arithmetic expression:

Precedence: Operators evaluated deeper in the tree have higher precedence because their results are computed first and passed upward. In the given tree, the subexpression containing $ operations ( $(b \$ c) \$ d$ ) is nested inside the # operations. Therefore, operator $ has higher precedence than #.

For $: The subtree evaluating $b \$ c \$ d$ is structured as $((b \$ c) \$ d)$ , which grows to the left. Hence, $ is left associative.
For #: The expression evaluates $a \# (\dots)$ , with # grouping to the right as $a \# (T \# (e \# f))$ . Hence, # is right associative.

Thus, $ has higher precedence and is left associative; # is right associative, matching option A.

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.