import functools


def memoize(func, cache, num_args):
    """
    Wrap a function so that results for any argument tuple are stored in
    'cache'. Note that the args to the function must be usable as dictionary
    keys.

    Only the first num_args are considered when creating the key.
    """
    @functools.wraps(func)
    def wrapper(*args):
        mem_args = args[:num_args]
        if mem_args in cache:
            return cache[mem_args]
        result = func(*args)
        cache[mem_args] = result
        return result
    return wrapper