import json


def get_min_cache(path: str) -> float:
    """Get the minimum caching time of all the entries in a config file.

    :param path: path of the config file to use
    :type path: str

    :return: float number representing the smallest caching time.
    """
    result = float('inf')

    with open(path, 'r') as config_file:
        file = json.loads(config_file.read())

    for entry in file:
        if 'cache' in entry and entry['cache'] < result:
            result = entry['cache']

    return result