from bisect import bisect from math import pi, sqrt, tanh from operator import attrgetter, itemgetter from django.db import transaction from django.db.models import Count, OuterRef, Subquery from django.db.models.functions import Coalesce from django.utils import timezone BETA2 = 328.33 ** 2 RATING_INIT = 1200 # Newcomer's rating when applying the rating floor/ceiling MEAN_INIT = 1400. VAR_INIT = 250**2 * (BETA2 / 212**2) SD_INIT = sqrt(VAR_INIT) VALID_RANGE = MEAN_INIT - 20 * SD_INIT, MEAN_INIT + 20 * SD_INIT VAR_PER_CONTEST = 1219.047619 * (BETA2 / 212**2) VAR_LIM = (sqrt(VAR_PER_CONTEST**2 + 4 * BETA2 * VAR_PER_CONTEST) - VAR_PER_CONTEST) / 2 SD_LIM = sqrt(VAR_LIM) TANH_C = sqrt(3) / pi def tie_ranker(iterable, key=attrgetter('points')): rank = 0 delta = 1 last = None buf = [] for item in iterable: new = key(item) if new != last: for _ in buf: yield rank + (delta - 1) / 2.0 rank += delta delta = 0 buf = [] delta += 1 buf.append(item) last = key(item) for _ in buf: yield rank + (delta - 1) / 2.0 def eval_tanhs(tanh_terms, x): return sum((wt / sd) * tanh((x - mu) / (2 * sd)) for mu, sd, wt in tanh_terms) def solve(tanh_terms, y_tg, lin_factor=0, bounds=VALID_RANGE): L, R = bounds Ly, Ry = None, None while R - L > 2: x = (L + R) / 2 y = lin_factor * x + eval_tanhs(tanh_terms, x) if y > y_tg: R, Ry = x, y elif y < y_tg: L, Ly = x, y else: return x # Use linear interpolation to be slightly more accurate. if Ly is None: Ly = lin_factor * L + eval_tanhs(tanh_terms, L) if y_tg <= Ly: return L if Ry is None: Ry = lin_factor * R + eval_tanhs(tanh_terms, R) if y_tg >= Ry: return R ratio = (y_tg - Ly) / (Ry - Ly) return L * (1 - ratio) + R * ratio def get_var(times_ranked, cache=[VAR_INIT]): while times_ranked >= len(cache): next_var = 1. / (1. / (cache[-1] + VAR_PER_CONTEST) + 1. / BETA2) cache.append(next_var) return cache[times_ranked] def recalculate_ratings(ranking, old_mean, times_ranked, historical_p): n = len(ranking) new_p = [0.] * n new_mean = [0.] * n # Note: pre-multiply delta by TANH_C to improve efficiency. delta = [TANH_C * sqrt(get_var(t) + VAR_PER_CONTEST + BETA2) for t in times_ranked] p_tanh_terms = [(m, d, 1) for m, d in zip(old_mean, delta)] # Calculate performance at index i. def solve_idx(i, bounds=VALID_RANGE): r = ranking[i] y_tg = 0 for d, s in zip(delta, ranking): if s > r: # s loses to r y_tg += 1. / d elif s < r: # s beats r y_tg -= 1. / d # Otherwise, this is a tie that counts as half a win, as per Elo-MMR. new_p[i] = solve(p_tanh_terms, y_tg, bounds=bounds) # Fill all indices between i and j, inclusive. Use the fact that new_p is non-increasing. def divconq(i, j): if j - i > 1: k = (i + j) // 2 solve_idx(k, bounds=(new_p[j], new_p[i])) divconq(i, k) divconq(k, j) if n < 2: new_p = list(old_mean) new_mean = list(old_mean) else: # Calculate performance. solve_idx(0) solve_idx(n - 1) divconq(0, n - 1) # Calculate mean. for i, r in enumerate(ranking): tanh_terms = [] w_prev = 1. w_sum = 0. for j, h in enumerate([new_p[i]] + historical_p[i]): gamma2 = (VAR_PER_CONTEST if j > 0 else 0) h_var = get_var(times_ranked[i] + 1 - j) k = h_var / (h_var + gamma2) w = w_prev * k**2 # Future optimization: If j is around 20, then w < 1e-3 and it is possible to break early. tanh_terms.append((h, sqrt(BETA2) * TANH_C, w)) w_prev = w w_sum += w / BETA2 w0 = 1. / get_var(times_ranked[i] + 1) - w_sum p0 = eval_tanhs(tanh_terms[1:], old_mean[i]) / w0 + old_mean[i] new_mean[i] = solve(tanh_terms, w0 * p0, lin_factor=w0) # Display a slightly lower rating to incentivize participation. # As times_ranked increases, new_rating converges to new_mean. new_rating = [max(1, round(m - (sqrt(get_var(t + 1)) - SD_LIM))) for m, t in zip(new_mean, times_ranked)] return new_rating, new_mean, new_p def rate_contest(contest): from judge.models import Rating, Profile rating_subquery = Rating.objects.filter(user=OuterRef('user')) rating_sorted = rating_subquery.order_by('-contest__end_time') users = contest.users.order_by('is_disqualified', '-score', 'cumtime', 'tiebreaker') \ .annotate(submissions=Count('submission'), last_rating=Coalesce(Subquery(rating_sorted.values('rating')[:1]), RATING_INIT), last_mean=Coalesce(Subquery(rating_sorted.values('mean')[:1]), MEAN_INIT), times=Coalesce(Subquery(rating_subquery.order_by().values('user_id') .annotate(count=Count('id')).values('count')), 0)) \ .exclude(user_id__in=contest.rate_exclude.all()) \ .filter(virtual=0).values('id', 'user_id', 'score', 'cumtime', 'tiebreaker', 'last_rating', 'last_mean', 'times') if not contest.rate_all: users = users.filter(submissions__gt=0) if contest.rating_floor is not None: users = users.exclude(last_rating__lt=contest.rating_floor) if contest.rating_ceiling is not None: users = users.exclude(last_rating__gt=contest.rating_ceiling) users = list(users) participation_ids = list(map(itemgetter('id'), users)) user_ids = list(map(itemgetter('user_id'), users)) ranking = list(tie_ranker(users, key=itemgetter('score', 'cumtime', 'tiebreaker'))) old_mean = list(map(itemgetter('last_mean'), users)) times_ranked = list(map(itemgetter('times'), users)) historical_p = [[] for _ in users] user_id_to_idx = {uid: i for i, uid in enumerate(user_ids)} for h in Rating.objects.filter(user_id__in=user_ids) \ .order_by('-contest__end_time') \ .values('user_id', 'performance'): idx = user_id_to_idx[h['user_id']] historical_p[idx].append(h['performance']) rating, mean, performance = recalculate_ratings(ranking, old_mean, times_ranked, historical_p) now = timezone.now() ratings = [Rating(user_id=i, contest=contest, rating=r, mean=m, performance=perf, last_rated=now, participation_id=pid, rank=z) for i, pid, r, m, perf, z in zip(user_ids, participation_ids, rating, mean, performance, ranking)] with transaction.atomic(): Rating.objects.bulk_create(ratings) Profile.objects.filter(contest_history__contest=contest, contest_history__virtual=0).update( rating=Subquery(Rating.objects.filter(user=OuterRef('id')) .order_by('-contest__end_time').values('rating')[:1])) RATING_LEVELS = ['Newbie', 'Amateur', 'Expert', 'Candidate Master', 'Master', 'Grandmaster', 'Target'] RATING_VALUES = [1000, 1300, 1600, 1900, 2400, 3000] RATING_CLASS = ['rate-newbie', 'rate-amateur', 'rate-expert', 'rate-candidate-master', 'rate-master', 'rate-grandmaster', 'rate-target'] def rating_level(rating): return bisect(RATING_VALUES, rating) def rating_name(rating): return RATING_LEVELS[rating_level(rating)] def rating_class(rating): return RATING_CLASS[rating_level(rating)] def rating_progress(rating): level = bisect(RATING_VALUES, rating) if level == len(RATING_VALUES): return 1.0 prev = 0 if not level else RATING_VALUES[level - 1] next = RATING_VALUES[level] return (rating - prev + 0.0) / (next - prev)