algorithm - Java RPN (Reverse Polish Notation) infix to postfix

Question

I am pretty sure, that stacks are used for building PRN and '(' are ignored, but it does not seem to be the case. For example:

• input 1: 52+(1+2)*4-3
• input 2: 52+((1+2)*4)-3
• input 3: (52+1+2)*4-3

Input 1 and input 2 output should be the same, and input 1 and input 3 should differ.

• output 1: 52 1 2 + 4 3 - * +
• output 2: 52 1 2 + 4 * 3 - +
• output 3: 52 1 2 + 4 3 - * +

    public static String Infix2(String input) {
        char[] in = input.toCharArray();
        Stack<Character> stack = new Stack<Character>();
        StringBuilder out = new StringBuilder();

        for (int i = 0; i < in.length; i++)
            switch (in[i]) {
            case '+':
            case '*':
            case '-':
                out.append(' ');
                stack.push(in[i]);
                break;
            case ' ':
            case '(':
                break;
            case ')':
                out.append(' ');
                out.append(stack.pop());
                break;
            default:
                out.append(in[i]);
                break;
            }

        while (!stack.isEmpty()) {
            out.append(' ');
            out.append(stack.pop());
        }

        return out.toString();
    }

Assuming that i want input 1 and 3 also to work, what approach should i use?

edit: After the changes '+','-','*' and '/' worked for given inputs.

public static String Infix2(String input) {
    if (input == null)
        return "";
    char[] in = input.toCharArray();
    Stack<Character> stack = new Stack<Character>();
    StringBuilder out = new StringBuilder();

    for (int i = 0; i < in.length; i++)
        switch (in[i]) {
        case '+':
        case '-':
            while (!stack.empty()
                    && (stack.peek() == '*' || stack.peek() == '/'))
                out.append(' ').append(stack.pop());
        case '*':
        case '/':
            out.append(' ');
        case '(':
            stack.push(in[i]);
        case ' ':
            break;
        case ')':
            while (!stack.empty() && stack.peek() != '(')
                out.append(' ').append(stack.pop());
            if (!stack.empty())
                stack.pop();
            break;
        default:
            out.append(in[i]);
            break;
        }

    while (!stack.isEmpty())
        out.append(' ').append(stack.pop());

    return out.toString();
}

Answer 1

The algorithm is pretty simple (and here is a good explanation). Every operation has a binding weight, with + and - being the lowest. There are two rules:

• print out numbers immediately
• never put a lighter item on a heavier item
• left parentheses go on the stack
• right parentheses pop off the stack until you hit a left parentheses, and then remove the left parentheses

Given your first example, 52+(1+2)*4-3, here is the stack:

 52+          => +
 52+(         => + (
 52+(1+       => + ( + 
 52+(1+2)     => +       //right parentheses popped +
 52+(1+2)*4   => + * 
 52+(1+2)*4-3 => + -     //can't put - on top of *, so pop off *
 ... and then pop the stack until it's empty.

Replacing your switch loop with the following (closest analog to what you had) will give correct answers for your three examples. In a real parser you would give each operator a weight and generalize the pop mechanism.

for (int i = 0; i < in.length; i++)
        switch (in[i]) {
        case '+':
        case '-':
            while (!stack.empty() && (stack.peek() == '*' || stack.peek() == '/')) {
                out.append(' ');
                out.append(stack.pop());
            }
            out.append(' ');
            stack.push(in[i]);
            break;
        case '*':
        case '/':
            out.append(' ');
            stack.push(in[i]);
            break;
        case '(':
            stack.push(in[i]);
            break;
        case ')':
            while (!stack.empty() && stack.peek() != '(') {
                out.append(' ');
                out.append(stack.pop());
            }
            stack.pop();
            break;
        default:
            out.append(in[i]);
            break;
        }