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G4G0-2/Data Structures/GPT Answers to Past Paper/Question 5.md
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Convert the Infix Expression A * (B + C) / D to a Postfix Expression

To convert the infix expression A * (B + C) / D into postfix notation, we use the following rules:

  1. Operator Precedence: Parentheses have the highest precedence, followed by multiplication (*) and division (/), and then addition (+).
  2. Associativity: Operators like * and / are left-associative, meaning operations are performed left to right if they have the same precedence.
  3. Conversion Rules:
    • Operands (like A, B, C, D) are output immediately.
    • Operators are pushed onto a stack.
    • Parentheses dictate the priority: Solve what's inside the parentheses first.

Step-by-Step Conversion

Infix Expression: A * (B + C) / D

  1. Start with the subexpression inside the parentheses (B + C):

    • Convert B + C to postfix: BC+.
  2. Substitute the postfix for (B + C) back into the original expression:

    • The expression becomes A * BC+ / D.
  3. Process the multiplication (*) and division (/):

    • A * BC+ becomes ABC+*.
    • ABC+* / D becomes ABC+*D/.

Final Postfix Expression:

ABC+*D/