GATE CS 1995 Q2.21 — Arrays, Stacks and Queues

To convert the infix expression $A + B * (C + D) / F + D * E$ to its postfix form, we follow the standard operator precedence and associativity rules:

1. Parentheses have the highest precedence.
2. Multiplication ($*$) and Division ($/$) have the next highest precedence and are left-associative.
3. Addition ($+$) has the lowest precedence and is left-associative.

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

• Step 1: Parentheses
  Convert $(C + D) \rightarrow CD+$
  The expression becomes: $A + B * [CD+] / F + D * E$
• Step 2: Multiplication and Division (from left to right)
  First, evaluate $B * [CD+] \rightarrow BCD+*$
  The expression becomes: $A + [BCD+*] / F + D * E$
  
  Next, evaluate $[BCD+*] / F \rightarrow BCD+*F/$
  The expression becomes: $A + [BCD+*F/] + D * E$
  
  Next, evaluate $D * E \rightarrow DE*$
  The expression becomes: $A + [BCD+*F/] + [DE*]$
• Step 3: Addition (from left to right)
  First, evaluate $A + [BCD+*F/] \rightarrow ABCD+*F/+$
  The expression becomes: $[ABCD+*F/+] + [DE*]$
  
  Finally, evaluate the last addition: $[ABCD+*F/+] + [DE*] \rightarrow ABCD+*F/DE*++$

Thus, the final postfix expression is $ABCD+*F/DE*++$, which corresponds to Option B.