GATE CS 2016 Set 1 Q45 — Parsing (LL, LR)

To evaluate the expression $2 - 5 + 1 - 7 * 3$, we must follow the precedence and associativity rules provided in the table:

1. Precedence: $+$ (High) $>$ $-$ (Medium) $>$ $*$ (Low).
2. Associativity:
   • $+$ is Left-associative.
   • $-$ is Right-associative.
   • $*$ is Left-associative.

Let's evaluate the expression step-by-step:

Step 1: Evaluate the highest precedence operator ($+$)
There is only one $+$ operator in the expression: $5 + 1$.
$$5 + 1 = 6$$ Substituting this back, the expression becomes: $$2 - 6 - 7 * 3$$

Step 2: Evaluate the next highest precedence operator ($-$)
We have two $-$ operators: $2 - 6 - 7$. Since $-$ is right-associative, we evaluate them from right to left, grouping as $2 - (6 - 7)$: $$\text{Rightmost } - \implies 6 - 7 = -1$$ Now evaluate the remaining $-$: $$2 - (-1) = 3$$ Substituting this back, the expression becomes: $$3 * 3$$

Step 3: Evaluate the lowest precedence operator ($*$)
$$3 * 3 = 9$$

Thus, the value of the expression is 9.