Question

What is the postfix form of the infix expression A + B * C − D / E?

• A. A B + C * D E / −
• B. A B + * C D − /
• C. A B C D E + * − /
• D. A B C * + D E / −

Hint:

Handle * and / before + and −. Convert B*C and D/E first, then combine the additive operators left to right.

Answer 1

The Correct Option is D

Idea: Fully parenthesise by precedence, then move each operator after its operands.

Insert the implied brackets according to priority:

\[(A + (B * C)) - (D / E)\]

Convert innermost groups: $B * C \to BC*$ and $D / E \to DE/$. The tree now reads $((A) + (BC*)) - (DE/)$.

Postfix places the operator last. The plus node yields $A\,BC*\,+ = ABC*+$. The top minus node takes that whole left result and the right group $DE/$, appending the operator:

\[ABC*+ \;\; DE/ \;\; - \;=\; ABC*+DE/-\]

\[\boxed{A\,B\,C\,*\,+\,D\,E\,/\,-}\]