how to implement this algorithm in python? [closed]

Answer 1

You can use itertools.product for Cartesian products in general. Specifically, I would implement your algorithm in two separate steps:

1. Parse the input string (e.g. "1 0^ 1* 0^ 1") into a list of lists of integers; and
2. Produce the product of the list of lists.

A relatively simple generator-based implementation, with a helper function for clarity, would look like:

def algorithm(input_):
    # Step 1
    instructions = []
    for s in input_.split():
        try:
            instructions.append([int(s)])
        except ValueError:
            instructions.append(list(values(s)))
    # Step 2
    for prod in itertools.product(*instructions):
        yield prod

def values(s):
    RULES = {'*': 4, '^': 2}
    n = int(s[:-1])
    for x in range(RULES[s[-1]]):
        yield n + x

For example:

>>> print("\n".join(" ".join(map(str, t)) for t in algorithm("1 0^ 1* 1")))
1 0 1 1
1 0 2 1
1 0 3 1
1 0 4 1
1 1 1 1
1 1 2 1
1 1 3 1
1 1 4 1

You will have to tinker with it to get the precise order (you appear to have an operator, rather than left-to-right, precedence) and formatting (e.g. spaces between groups) you're looking for.