GATE CS 2024 Set 1 Q.33: Parsing and Syntax Analysis (LL and LR)

Consider the operator precedence and associativity rules for the integer arithmetic operators given in the table below.

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

Your answer

Official answer and solution

Solution

Parenthesize and evaluate the expression strictly in decreasing order of custom precedence (+, then -, then *, then /).

Evaluating the expression $3 + 1 + 5 * 2 / 7 + 2 - 4 - 7 - 6 / 2$ step by step according to the given precedence table:

+ (Highest precedence, Left-associative):
- $((3 + 1) + 5) = 9$
- $(7 + 2) = 9$
  The expression reduces to: $9 * 2 / 9 - 4 - 7 - 6 / 2$
- (High precedence, Right-associative):
- $(9 - (4 - (7 - 6))) = 9 - (4 - 1) = 9 - 3 = 6$
  The expression reduces to: $9 * 2 / 6 / 2$
* (Medium precedence, Right-associative):
- $(9 * 2) = 18$
  The expression reduces to: $18 / 6 / 2$
/ (Low precedence, Right-associative):
- $18 / (6 / 2) = 18 / 3 = 6$

Final answer

Common trap

Evaluating - or / left-to-right instead of right-to-left as specified in the table.

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

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