GATE CS 2011 Q27 — Parsing (LL, LR)

To find the correct parse tree for the expression $(7 \downarrow 3 \uparrow 4 \uparrow 3 \downarrow 2)$, we must evaluate the expression step-by-step based on the given precedence and associativity rules.

1. Analyze Precedence and Associativity

• Precedence: $\uparrow$ has higher precedence than $\downarrow$.
• Associativity of $\uparrow$: Right-associative.
• Associativity of $\downarrow$: Left-associative.

2. Parenthesize the Expression

First, we group the higher precedence operator $\uparrow$. Since $\uparrow$ is right-associative, we group from right to left:

Substituting this back into the expression gives:

Next, we group the lower precedence operator $\downarrow$. Since $\downarrow$ is left-associative, we group from left to right:

3. Construct the Parse Tree

In a parse tree, operators that are evaluated last appear closest to the root (higher up in the tree):

• The root of the tree is the outermost operator, which is the second $\downarrow$. Its right child is $2$, and its left child is the subexpression $(7 \downarrow (3 \uparrow (4 \uparrow 3)))$.
• For the left child $(7 \downarrow (3 \uparrow (4 \uparrow 3)))$, the operator is $\downarrow$. Its left child is $7$, and its right child is the subexpression $(3 \uparrow (4 \uparrow 3))$.
• For the subexpression $(3 \uparrow (4 \uparrow 3))$, the operator is the first $\uparrow$. Its left child is $3$, and its right child is $(4 \uparrow 3)$.
• For $(4 \uparrow 3)$, the operator is $\uparrow$ with left child $4$ and right child $3$.

This hierarchical structure corresponds exactly to the tree shown in Option B.