Converting Infix Expression to Postfix Expression Using Stack
How can you manually convert an infix expression to postfix expression using a stack?
Given the following infix expression: (3 + 4) * 5 - 6 / 2, what are the steps to transform it into postfix expression?
Steps to Convert Infix Expression to Postfix Expression:
1. Create an empty stack to store operators temporarily.
2. Start reading the expression from left to right.
3. If the character is an operand (a number or variable), add it directly to the output.
4. If the character is an opening parenthesis '(', push it onto the stack.
5. If the character is an operator (+, -, *, /), compare its precedence with the top of the stack. If the stack is empty or the top of the stack is an opening parenthesis, push the operator onto the stack.
6. If the character is a closing parenthesis ')', pop operators from the stack and add them to the output until an opening parenthesis is encountered. Discard both the opening and closing parentheses.
7. If the character is an operator (+, -, *, /), compare its precedence with the top of the stack. If the top of the stack has higher precedence, pop the operators from the stack and add them to the output.
8. After reading the entire expression, pop any remaining operators from the stack and add them to the output.
When converting an infix expression to postfix expression using a stack, you need to follow a specific set of rules. The process involves pushing operators onto the stack, popping operators from the stack, and adding operands to the output. Let's apply these steps to the given infix expression:
Infix Expression: (3 + 4) * 5 - 6 / 2
Output: 3 4 + 5 * 6 2 / -
Explanation:
- Read the expression from left to right.
- Add operands and push operators onto the stack according to the rules mentioned above.
- When encountering a closing parenthesis, pop operators until an opening parenthesis is found.
- Repeat steps 2 and 3 until the entire expression is processed.
In conclusion, by following the steps outlined above, you can successfully convert an infix expression to a postfix expression using a stack. This method ensures the correct order of operands and operators in the resulting postfix expression.