"""
Reverse Polish Nation is also known as Polish postfix notation or simply postfix
notation.
https://en.wikipedia.org/wiki/Reverse_Polish_notation
Classic examples of simple stack implementations.
Valid operators are +, -, *, /.
Each operand may be an integer or another expression.

Output:

Enter a Postfix Equation (space separated) = 5 6 9 * +
 Symbol  |    Action    | Stack
-----------------------------------
       5 | push(5)      | 5
       6 | push(6)      | 5,6
       9 | push(9)      | 5,6,9
         | pop(9)       | 5,6
         | pop(6)       | 5
       * | push(6*9)    | 5,54
         | pop(54)      | 5
         | pop(5)       |
       + | push(5+54)   | 59

        Result =  59
"""

# Defining valid unary operator symbols
UNARY_OP_SYMBOLS = ("-", "+")

# operators & their respective operation
OPERATORS = {
    "^": lambda p, q: p**q,
    "*": lambda p, q: p * q,
    "/": lambda p, q: p / q,
    "+": lambda p, q: p + q,
    "-": lambda p, q: p - q,
}


def parse_token(token: str | float) -> float | str:
    """
    Converts the given data to the appropriate number if it is indeed a number, else
    returns the data as it is with a False flag. This function also serves as a check
    of whether the input is a number or not.

    Parameters
    ----------
    token: The data that needs to be converted to the appropriate operator or number.

    Returns
    -------
    float or str
        Returns a float if `token` is a number or a str if `token` is an operator
    """
    if token in OPERATORS:
        return token
    try:
        return float(token)
    except ValueError:
        msg = f"{token} is neither a number nor a valid operator"
        raise ValueError(msg)


def evaluate(post_fix: list[str], verbose: bool = False) -> float:
    """
    Evaluate postfix expression using a stack.
    >>> evaluate(["0"])
    0.0
    >>> evaluate(["-0"])
    -0.0
    >>> evaluate(["1"])
    1.0
    >>> evaluate(["-1"])
    -1.0
    >>> evaluate(["-1.1"])
    -1.1
    >>> evaluate(["2", "1", "+", "3", "*"])
    9.0
    >>> evaluate(["2", "1.9", "+", "3", "*"])
    11.7
    >>> evaluate(["2", "-1.9", "+", "3", "*"])
    0.30000000000000027
    >>> evaluate(["4", "13", "5", "/", "+"])
    6.6
    >>> evaluate(["2", "-", "3", "+"])
    1.0
    >>> evaluate(["-4", "5", "*", "6", "-"])
    -26.0
    >>> evaluate([])
    0
    >>> evaluate(["4", "-", "6", "7", "/", "9", "8"])
    Traceback (most recent call last):
    ...
    ArithmeticError: Input is not a valid postfix expression

    Parameters
    ----------
    post_fix:
        The postfix expression is tokenized into operators and operands and stored
        as a Python list

    verbose:
        Display stack contents while evaluating the expression if verbose is True

    Returns
    -------
    float
        The evaluated value
    """
    if not post_fix:
        return 0
    # Checking the list to find out whether the postfix expression is valid
    valid_expression = [parse_token(token) for token in post_fix]
    if verbose:
        # print table header
        print("Symbol".center(8), "Action".center(12), "Stack", sep=" | ")
        print("-" * (30 + len(post_fix)))
    stack = []
    for x in valid_expression:
        if x not in OPERATORS:
            stack.append(x)  # append x to stack
            if verbose:
                # output in tabular format
                print(
                    f"{x}".rjust(8),
                    f"push({x})".ljust(12),
                    stack,
                    sep=" | ",
                )
            continue
        # If x is operator
        # If only 1 value is inside the stack and + or - is encountered
        # then this is unary + or - case
        if x in UNARY_OP_SYMBOLS and len(stack) < 2:
            b = stack.pop()  # pop stack
            if x == "-":
                b *= -1  # negate b
            stack.append(b)
            if verbose:
                # output in tabular format
                print(
                    "".rjust(8),
                    f"pop({b})".ljust(12),
                    stack,
                    sep=" | ",
                )
                print(
                    str(x).rjust(8),
                    f"push({x}{b})".ljust(12),
                    stack,
                    sep=" | ",
                )
            continue
        b = stack.pop()  # pop stack
        if verbose:
            # output in tabular format
            print(
                "".rjust(8),
                f"pop({b})".ljust(12),
                stack,
                sep=" | ",
            )

        a = stack.pop()  # pop stack
        if verbose:
            # output in tabular format
            print(
                "".rjust(8),
                f"pop({a})".ljust(12),
                stack,
                sep=" | ",
            )
        # evaluate the 2 values popped from stack & push result to stack
        stack.append(OPERATORS[x](a, b))  # type: ignore[index]
        if verbose:
            # output in tabular format
            print(
                f"{x}".rjust(8),
                f"push({a}{x}{b})".ljust(12),
                stack,
                sep=" | ",
            )
    # If everything is executed correctly, the stack will contain
    # only one element which is the result
    if len(stack) != 1:
        raise ArithmeticError("Input is not a valid postfix expression")
    return float(stack[0])


if __name__ == "__main__":
    # Create a loop so that the user can evaluate postfix expressions multiple times
    while True:
        expression = input("Enter a Postfix Expression (space separated): ").split(" ")
        prompt = "Do you want to see stack contents while evaluating? [y/N]: "
        verbose = input(prompt).strip().lower() == "y"
        output = evaluate(expression, verbose)
        print("Result = ", output)
        prompt = "Do you want to enter another expression? [y/N]: "
        if input(prompt).strip().lower() != "y":
            break