from functools import lru_cache


def lev_dist(prediction, ground_truth):
    @lru_cache(None)  # for memorization
    def min_dist(s1, s2):
        if s1 == len(prediction) or s2 == len(ground_truth):
            return len(prediction) - s1 + len(ground_truth) - s2
        # no change required
        if prediction[s1] == ground_truth[s2]:
            return min_dist(s1 + 1, s2 + 1)
        return 1 + min(
            min_dist(s1, s2 + 1),      # insert character
            min_dist(s1 + 1, s2),      # delete character
            min_dist(s1 + 1, s2 + 1),  # replace character
        )
    return min_dist(0, 0)


def edit_sim_score(a, b):
    return 1 - lev_dist(a, b) / max(len(a), len(b))


def metric_max_over_ground_truths(metric_fn, prediction, ground_truths):
    scores_for_ground_truths = []
    for ground_truth in ground_truths:
        score = metric_fn(prediction, ground_truth)
        scores_for_ground_truths.append(score)
    return max(scores_for_ground_truths)


def compute_edit_sim(predictions, references):
    edit_sim = 0
    for prediction, ground_truths in zip(predictions, references):
        edit_sim += metric_max_over_ground_truths(edit_sim_score, prediction, ground_truths)
    return 100.0 * edit_sim / len(predictions)