2. Convert the following from postfix to prefix using stacks: c 5 ^ d 3 ^ / e 4 ^ -

C++ Programming: From Problem Analysis to Program Design
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ISBN:9781337102087
Author:D. S. Malik
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Chapter18: Stacks And Queues
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### Exercise 2: Postfix to Prefix Conversion Using Stacks

**Task:** Convert the following expression from postfix notation to prefix notation using stacks.

**Postfix Expression:** `c 5 ^ d 3 ^ / e 4 ^ -`

### Explanation

To convert a postfix expression to a prefix expression using stacks, follow these steps:

1. **Initialize an Empty Stack:** Start with an empty stack.
2. **Scan from Left to Right:** Traverse the postfix expression from left to right.
3. **Operands:** Whenever you encounter an operand (e.g., `c`, `5`, `d`, `3`, `e`, `4`), push it onto the stack.
4. **Operators:** When you encounter an operator (e.g., `^`, `/`, `-`), pop the required number of operands from the stack, apply the operator, and push the resulting expression back onto the stack in prefix form.

### Detailed Steps:

- **Step 1:** `c` is an operand, push it onto the stack. Stack: [`c`]
- **Step 2:** `5` is an operand, push it onto the stack. Stack: [`c`, `5`]
- **Step 3:** `^` is an operator, pop two operands (`c`, `5`), create the expression `^ c 5`, and push it back. Stack: [`^ c 5`]
- **Step 4:** `d` is an operand, push it onto the stack. Stack: [`^ c 5`, `d`]
- **Step 5:** `3` is an operand, push it onto the stack. Stack: [`^ c 5`, `d`, `3`]
- **Step 6:** `^` is an operator, pop two operands (`d`, `3`), create the expression `^ d 3`, and push it back. Stack: [`^ c 5`, `^ d 3`]
- **Step 7:** `/` is an operator, pop two operands (`^ c 5`, `^ d 3`), create the expression `/ ^ c 5 ^ d 3`, and push it back. Stack: [`/ ^ c 5 ^ d 3`]
- **Step 8:** `e` is an operand, push it onto the stack. Stack: [`/ ^ c 5 ^ d
Transcribed Image Text:### Exercise 2: Postfix to Prefix Conversion Using Stacks **Task:** Convert the following expression from postfix notation to prefix notation using stacks. **Postfix Expression:** `c 5 ^ d 3 ^ / e 4 ^ -` ### Explanation To convert a postfix expression to a prefix expression using stacks, follow these steps: 1. **Initialize an Empty Stack:** Start with an empty stack. 2. **Scan from Left to Right:** Traverse the postfix expression from left to right. 3. **Operands:** Whenever you encounter an operand (e.g., `c`, `5`, `d`, `3`, `e`, `4`), push it onto the stack. 4. **Operators:** When you encounter an operator (e.g., `^`, `/`, `-`), pop the required number of operands from the stack, apply the operator, and push the resulting expression back onto the stack in prefix form. ### Detailed Steps: - **Step 1:** `c` is an operand, push it onto the stack. Stack: [`c`] - **Step 2:** `5` is an operand, push it onto the stack. Stack: [`c`, `5`] - **Step 3:** `^` is an operator, pop two operands (`c`, `5`), create the expression `^ c 5`, and push it back. Stack: [`^ c 5`] - **Step 4:** `d` is an operand, push it onto the stack. Stack: [`^ c 5`, `d`] - **Step 5:** `3` is an operand, push it onto the stack. Stack: [`^ c 5`, `d`, `3`] - **Step 6:** `^` is an operator, pop two operands (`d`, `3`), create the expression `^ d 3`, and push it back. Stack: [`^ c 5`, `^ d 3`] - **Step 7:** `/` is an operator, pop two operands (`^ c 5`, `^ d 3`), create the expression `/ ^ c 5 ^ d 3`, and push it back. Stack: [`/ ^ c 5 ^ d 3`] - **Step 8:** `e` is an operand, push it onto the stack. Stack: [`/ ^ c 5 ^ d
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