This Java program demonstrates how to evaluate postfix expressions using a stack. Postfix notation, also known as Reverse Polish Notation (RPN), is a mathematical notation in which every operator follows all of its operands. It does not need any parentheses as long as each operator has a fixed number of operands.

Program Explanation

The program is structured as follows:

• Main Class and Method: The main method where we define the postfix expression and call the evaluation method.
• Evaluation Method: This method processes the postfix expression using a stack to handle the operands and apply the operators.

Java Code

import java.util.Stack;

public class PostfixEvaluator {
    public static void main(String[] args) {
        String postfix = "53+82-*";
        System.out.println("Postfix Expression: " + postfix);
        System.out.println("Evaluation Result: " + evaluatePostfix(postfix));
    }

    public static int evaluatePostfix(String postfix) {
        Stack<Integer> stack = new Stack<>();

        for (int i = 0; i < postfix.length(); i++) {
            char c = postfix.charAt(i);

            if (Character.isDigit(c)) {
                stack.push(c - '0'); // Convert character to integer
            } else {
                int val1 = stack.pop();
                int val2 = stack.pop();
                switch (c) {
                    case '+':
                        stack.push(val2 + val1);
                        break;
                    case '-':
                        stack.push(val2 - val1);
                        break;
                    case '*':
                        stack.push(val2 * val1);
                        break;
                    case '/':
                        stack.push(val2 / val1);
                        break;
                }
            }
        }
        return stack.pop();
    }
}

How the Program Works

1. The program reads characters of the postfix expression one by one.
2. If the character is a digit, it is pushed onto the stack as an integer.
3. If the character is an operator, two elements are popped from the stack. The operation is performed, and the result is pushed back onto the stack.

The final result in the stack after the expression has been processed is the result of the postfix expression.

Explanation

• Main Method: This method initializes the postfix expression and invokes the evaluatePostfix method to perform the evaluation.
• evaluatePostfix Method: This method uses a Stack<Integer> to manage the operands. For each character in the string:
  • If it’s a digit, it converts it to an integer and pushes it onto the stack.
  • If it’s an operator, it pops the required operands from the stack, applies the operation, and pushes the result back onto the stack.
• The method returns the last item in the stack, which is the result of the postfix expression evaluation.

This structured approach clearly separates the logic for parsing and evaluating the expression, making the program easy to understand and maintain.

Conclusion

This implementation allows the evaluation of postfix expressions using a stack, illustrating the utility of the stack data structure in managing order of operations in expressions without the need for parentheses.