a0_paper.py

#!/usr/bin/env python3


def can_combine_for_a0(stock):
    """Determine if different sized sheets of paper can combine to an A0 sheet.

    Given a tuple of A-format paper sizes (A0, A1, A2...), with each entry
    representing the number of sheets for a given size (i.e., element 0 is
    number of A0, element 1 is number of A1, etc), determine whether the
    collection of sheets can be pieced together to produce at least one
    full sheet of A0 paper.

    See https://www.papersizes.org/a-paper-sizes.htm for more information
    about A paper sizes.
    """
    pct = 0.0
    factor = 1.0
    for x in stock:
        pct += x * factor
        if pct >= 1.0:
            return True
        factor /= 2
    return False


def print_collection(collection):
    desc = ""
    for i, n in enumerate(collection):
        if n > 0:
            desc += f"{n} A{i}, "
    return desc[:-2]


if __name__ == "__main__":
    test_cases = [
        (0, 3),
        (0, 1, 2),
        (0, 0, 0, 0, 15),
        (2, 0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 5, 0, 3, 0, 0, 1, 0, 0, 0, 5),
        (0, 1, 1, 1, 2),
    ]
    for x in test_cases:
        result = can_combine_for_a0(x)
        num_sizes = sum([1 for n in x if n > 0])
        print(f"{num_sizes:2d} size{'s' if num_sizes > 1 else ''}: {print_collection(x)}: {result}")