The **conversion from infix notation to prefix **notation involves reversing the order of the expression, replacing each operator with its corresponding prefix operator, and swapping the positions of each operand.

• The final result is a prefix expression with the operator appearing before the operands.

**Here’s an overview of how you can implement the conversion algorithm:**

## Conversion from Infix to Postfix:

- Initialize an empty stack to hold operators.
- Initialize an empty string to store the postfix expression.
- Iterate through each character in the infix expression:
- If the character is an operand (a digit or letter), add it to the postfix string.
- If the character is an opening parenthesis ‘(‘, push it onto the stack.
- If the character is a closing parenthesis ‘)’, pop operators from the stack and append them to the postfix string until an opening parenthesis is encountered. Discard the opening parenthesis.
- If the character is an operator (+, -, *, /, etc.):
- Pop operators from the stack and append them to the postfix string if they have higher or equal precedence compared to the current operator.
- Push the current operator onto the stack.

- After processing all characters, pop any remaining operators from the stack and append them to the postfix string.
- The resulting string is the postfix expression.

## Conversion from Infix to Prefix:

The conversion algorithm for prefix is similar to postfix, but the order of operators and operands is reversed.

**To convert infix to prefix:**

- Reverse the infix expression.
- Convert the reversed infix expression to postfix using the algorithm described above.
- Reverse the resulting postfix expression to obtain the prefix expression.

**Here’s a Java implementation of the conversion from infix to postfix:**

```
import java.util.*;
public class InfixToPostfix {
public static String infixToPostfix(String infix) {
StringBuilder postfix = new StringBuilder();
Stack<Character> stack = new Stack<>();
// Define operator precedence
Map<Character, Integer> precedence = new HashMap<>();
precedence.put('+', 1);
precedence.put('-', 1);
precedence.put('*', 2);
precedence.put('/', 2);
precedence.put('^', 3);
for (char c : infix.toCharArray()) {
if (Character.isLetterOrDigit(c)) {
postfix.append(c);
} else if (c == '(') {
stack.push(c);
} else if (c == ')') {
while (!stack.isEmpty() && stack.peek() != '(') {
postfix.append(stack.pop());
}
stack.pop(); // Discard the '('
} else { // Operator
while (!stack.isEmpty() && precedence.getOrDefault(c, 0) <= precedence.getOrDefault(stack.peek(), 0)) {
postfix.append(stack.pop());
}
stack.push(c);
}
}
while (!stack.isEmpty()) {
postfix.append(stack.pop());
}
return postfix.toString();
}
public static void main(String[] args) {
String infixExpression = "a + b * (c - d) / e";
String postfixExpression = infixToPostfix(infixExpression);
System.out.println("Infix Expression: " + infixExpression);
System.out.println("Postfix Expression: " + postfixExpression);
}
}
```