GATE CS 2024 Set 1 Q23 — Parsing (LL, LR)

To evaluate the expression, we apply the operators step-by-step in decreasing order of their precedence, respecting their associativity rules.

The given expression is:
$$3+1+5 * 2 / 7+2-4-7-6 / 2$$

1. Evaluate + (Highest Precedence, Left-Associative):

   We group the + operators from left to right:

   • $3 + 1 + 5 \implies ((3 + 1) + 5) = 9$
   • $7 + 2 \implies 9$

   Substituting these back, the expression becomes:
   $$9 * 2 / 9 - 4 - 7 - 6 / 2$$

2. Evaluate - (High Precedence, Right-Associative):

   Since - has higher precedence than * and /, the subtraction chain $9 - 4 - 7 - 6$ is grouped first, from right to left:

   $$9 - (4 - (7 - 6)) = 9 - (4 - 1) = 9 - 3 = 6$$

   Substituting this back, the expression becomes:
   $$9 * 2 / 6 / 2$$

3. Evaluate * (Medium Precedence, Right-Associative):

   Since * has higher precedence than /, we evaluate $9 * 2$ first:

   $$9 * 2 = 18$$

   The expression becomes:
   $$18 / 6 / 2$$

4. Evaluate / (Low Precedence, Right-Associative):

   Since / is right-associative, we group from right to left:

   $$18 / (6 / 2) = 18 / 3 = 6$$

Thus, the final value of the expression is 6.