Recursive structure

Lesson 9 of 29 in Coddy's Calculator project using Python course.

The real power of the structure we saw last lesson comes with recursion.

Consider calculation with more than one operator, for example:

2 + 3 * 4 + 5

There is an order according to math rules, first we need to calculate 3 * 4 and then all the rest.

The following calculation will be formatted into recursive structure in the possible ways,

['+', ['+', 2, ['*', 3, 4]], 5]
['+', 2, ['+', 5, ['*', 3, 4]]]
['+', 5, ['+', ['*', 3, 4], 2]]

Notice that the deepest simple structure is always ['*', 3, 4] which is the first to calculate, also note that everything is the basic structure [op, num1, num2].

Some more examples of calculations to recursive structure:

2 - 3 -> ['-', 2, 3]
1 - 2 + 3 -> ['+', ['-', 1, 2], 3]
1 * 2 - 3 -> ['-', ['*', 1, 2], 3]
2.3 + 3 / 4.2 - 2 -> ['-', ['+', 2.3, ['/', 3, 4.2]], 2]

Challenge

Medium

Upgrade the eval function to support recursive structures as described above.

Notes:

call calc function when the structure is simple structure, operator with two numbers .
call eval recursively if one of the arguments is another structure (list).

Try it yourself

def calc(op, n1, n2=None):
    if not isinstance(n1, int) and not isinstance(n1, float):
        raise Exception('Invalid number "' + str(n1) + '"')

    if n2 is None:
        if op == '+' or op == 'add':
            return n1
        if op == '-' or op == 'sub':
            return -n1

        raise Exception('Invalid operator "' + op + '"')

    if not isinstance(n2, int) and not isinstance(n2, float):
        raise Exception('Invalid number "' + str(n2) + '"')

    if op == '+' or op == 'add':
        return n1 + n2
    if op == '-' or op == 'sub':
        return n1 - n2
    if op == '*' or op == 'mul':
        return n1 * n2
    if op == '/' or op == 'div':
        if n2 == 0:
            raise Exception("Division by zero")
        return n1 / n2
    if op == '%' or op == 'mod':
        if n2 == 0:
            raise Exception("Division by zero")
        return n1 % n2
    if op == '^' or op == 'pow':
        return n1 ** n2

    raise Exception('Invalid operator "' + op + '"')


def eval(lst):
    op = lst[0]
    n1 = lst[1]
    n2 = lst[2]
    return calc(op, n1, n2)