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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/
+```