#Alternating Hitting Set





    # Try all possible combinations of size at most k



# Example usage


if __name__ == '__main__':
    def is_hitting_set(C, H):
        for s in C:
            if len(set(s) & set(H)) % 2 == 0:
                return False
        return True
    def find_alternating_hitting_set(C, k):
        n = len(C)
        elements = set()
        for s in C:
            elements.update(s)
        for i in range(1, k + 1):
            for subset in itertools.combinations(elements, i):
                H = list(subset)
                if is_hitting_set(C, H):
                    return H
        return None
    C = [['A', 'B', 'C'], ['B', 'D'], ['A', 'C', 'D'], ['B', 'D', 'E']]
    k = 3
    hitting_set = find_alternating_hitting_set(C, k)
    if hitting_set is not None:
        print("Found hitting set:", hitting_set)
    else:
        print("No hitting set of size at most", k, "found.")
