36 lines
1.2 KiB
Markdown
Executable File
36 lines
1.2 KiB
Markdown
Executable File
# Convert the Infix Expression A * (B + C) / D to a Postfix Expression
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To convert the infix expression `A * (B + C) / D` into postfix notation, we use the following rules:
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1. **Operator Precedence**: Parentheses have the highest precedence, followed by multiplication (`*`) and division (`/`), and then addition (`+`).
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2. **Associativity**: Operators like `*` and `/` are left-associative, meaning operations are performed left to right if they have the same precedence.
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3. **Conversion Rules**:
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- Operands (like `A`, `B`, `C`, `D`) are output immediately.
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- Operators are pushed onto a stack.
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- Parentheses dictate the priority: Solve what's inside the parentheses first.
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---
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### **Step-by-Step Conversion**
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#### Infix Expression: `A * (B + C) / D`
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1. Start with the subexpression inside the parentheses `(B + C)`:
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- Convert `B + C` to postfix: `BC+`.
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2. Substitute the postfix for `(B + C)` back into the original expression:
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- The expression becomes `A * BC+ / D`.
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3. Process the multiplication (`*`) and division (`/`):
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- `A * BC+` becomes `ABC+*`.
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- `ABC+* / D` becomes `ABC+*D/`.
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---
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### **Final Postfix Expression**:
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```
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ABC+*D/
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```
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