#### Postfix Evaluation

p
"""
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:
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("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