35 lines
1.2 KiB
Markdown
35 lines
1.2 KiB
Markdown
# 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/
|
|
```
|