Solution about player marking algorithm.

optimal_marking.py

def optimal_markings(input_graph):
    """
    The following function will return the most optimal marking for an input graph. 
    To do it, we will try all possibles markings, and check if they are valid markings by using the previous function. 
    Once all valid markings are found,
    we need to sort them according to the number of the element it required to achieve a full marking. 
    The most optimal markings are the markings with the lowest number of players.
    """

    results_counts = []
    for combination in itertools.product([1, 0], repeat=len(input_graph)):
        results = combination
        if valid_markings(results, input_graph):
            results_counts.append((results.count(1), results))
    optimal_required = sorted(results_counts, key = lambda x : x[0] )[0][0]
    optimal_marking = list(filter( lambda x : x[0] == optimal_required, results_counts))
    return optimal_marking[0]