NDOJ/judge/ratings.py

import math
from bisect import bisect
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


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 rational_approximation(t):
    # Abramowitz and Stegun formula 26.2.23.
    # The absolute value of the error should be less than 4.5 e-4.
    c = [2.515517, 0.802853, 0.010328]
    d = [1.432788, 0.189269, 0.001308]
    numerator = (c[2] * t + c[1]) * t + c[0]
    denominator = ((d[2] * t + d[1]) * t + d[0]) * t + 1.0
    return t - numerator / denominator


def normal_CDF_inverse(p):
    assert 0.0 < p < 1

    # See article above for explanation of this section.
    if p < 0.5:
        # F^-1(p) = - G^-1(p)
        return -rational_approximation(math.sqrt(-2.0 * math.log(p)))
    else:
        # F^-1(p) = G^-1(1-p)
        return rational_approximation(math.sqrt(-2.0 * math.log(1.0 - p)))


def WP(RA, RB, VA, VB):
    return (math.erf((RB - RA) / math.sqrt(2 * (VA * VA + VB * VB))) + 1) / 2.0


def recalculate_ratings(old_rating, old_volatility, actual_rank, times_rated, is_disqualified):
    # actual_rank: 1 is first place, N is last place
    # if there are ties, use the average of places (if places 2, 3, 4, 5 tie, use 3.5 for all of them)

    N = len(old_rating)
    new_rating = old_rating[:]
    new_volatility = old_volatility[:]
    if N <= 1:
        return new_rating, new_volatility

    ranking = list(range(N))
    ranking.sort(key=old_rating.__getitem__, reverse=True)

    ave_rating = float(sum(old_rating)) / N
    sum1 = sum(i * i for i in old_volatility) / N
    sum2 = sum((i - ave_rating) ** 2 for i in old_rating) / (N - 1)
    CF = math.sqrt(sum1 + sum2)

    for i in range(N):
        ERank = 0.5
        for j in range(N):
            ERank += WP(old_rating[i], old_rating[j], old_volatility[i], old_volatility[j])

        EPerf = -normal_CDF_inverse((ERank - 0.5) / N)
        APerf = -normal_CDF_inverse((actual_rank[i] - 0.5) / N)
        PerfAs = old_rating[i] + CF * (APerf - EPerf)
        Weight = 1.0 / (1 - (0.42 / (times_rated[i] + 1) + 0.18)) - 1.0
        if old_rating[i] > 2500:
            Weight *= 0.8
        elif old_rating[i] >= 2000:
            Weight *= 0.9

        Cap = 150.0 + 1500.0 / (times_rated[i] + 2)

        new_rating[i] = (old_rating[i] + Weight * PerfAs) / (1.0 + Weight)

        if times_rated[i] == 0:
            new_volatility[i] = 385
        else:
            new_volatility[i] = math.sqrt(((new_rating[i] - old_rating[i]) ** 2) / Weight +
                                          (old_volatility[i] ** 2) / (Weight + 1))

        if is_disqualified[i]:
            # DQed users can manipulate TopCoder ratings to get higher volatility in order to increase their rating
            # later on, prohibit this by ensuring their volatility never increases in this situation
            new_volatility[i] = min(new_volatility[i], old_volatility[i])

        if abs(old_rating[i] - new_rating[i]) > Cap:
            if old_rating[i] < new_rating[i]:
                new_rating[i] = old_rating[i] + Cap
            else:
                new_rating[i] = old_rating[i] - Cap

    # try to keep the sum of ratings constant
    adjust = float(sum(old_rating) - sum(new_rating)) / N
    new_rating = list(map(adjust.__add__, new_rating))
    # inflate a little if we have to so people who placed first don't lose rating
    best_rank = min(actual_rank)
    for i in range(N):
        if abs(actual_rank[i] - best_rank) <= 1e-3 and new_rating[i] < old_rating[i] + 1:
            new_rating[i] = old_rating[i] + 1
    return list(map(int, map(round, new_rating))), list(map(int, map(round, new_volatility)))


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]), 1200),
                  volatility=Coalesce(Subquery(rating_sorted.values('volatility')[:1]), 535),
                  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', 'is_disqualified',
                                  'last_rating', 'volatility', '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))
    is_disqualified = list(map(itemgetter('is_disqualified'), users))
    ranking = list(tie_ranker(users, key=itemgetter('score', 'cumtime', 'tiebreaker')))
    old_rating = list(map(itemgetter('last_rating'), users))
    old_volatility = list(map(itemgetter('volatility'), users))
    times_ranked = list(map(itemgetter('times'), users))
    rating, volatility = recalculate_ratings(old_rating, old_volatility, ranking, times_ranked, is_disqualified)

    now = timezone.now()
    ratings = [Rating(user_id=i, contest=contest, rating=r, volatility=v, last_rated=now, participation_id=p, rank=z)
               for i, p, r, v, z in zip(user_ids, participation_ids, rating, volatility, ranking)]
    with transaction.atomic():
        Rating.objects.filter(contest=contest).delete()
        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]))
    return old_rating, old_volatility, ranking, times_ranked, rating, volatility


RATING_LEVELS = ['Newbie', 'Amateur', 'Expert', 'Candidate Master', 'Master', 'Grandmaster', 'Target']
RATING_VALUES = [1000, 1200, 1500, 1800, 2200, 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)