using QuestionsApi.Models;

namespace QuestionsApi.Services;

public static class ExamSimulationScoring
{
    public const string ModelVersion = "provisional-1";
    private const double PriorMean = 1000.0;
    private const double PriorSd = 400.0;

    public static ExamSimulationScore Calculate(
        IReadOnlyList<ExamSimulationItem> items,
        IReadOnlyDictionary<string, ExamSimulationResponse> responses,
        IReadOnlyDictionary<string, Question> questions)
    {
        var ability = EstimateAbility(items, responses, questions);
        var predicted = Math.Clamp((int)Math.Round(227.0 + (ability - 1000.0) * 15.0 / 200.0), 1, 300);
        var information = 1.0 / (PriorSd * PriorSd);
        var correct = 0;
        var seen = 0;
        var categories = new Dictionary<string, ExamSimulationCategoryScore>();

        foreach (var item in items)
        {
            if (!questions.TryGetValue(item.QuestionExternalId, out var question))
                continue;
            responses.TryGetValue(item.QuestionExternalId, out var response);
            var isCorrect = response?.ChoiceId == question.CorrectChoiceId;
            if (isCorrect) correct++;
            if (item.WasSeen) seen++;
            var weight = item.WasSeen ? 0.5 : 1.0;
            var probability = Expected(ability, item.QuestionElo);
            information += weight * probability * (1.0 - probability) * Math.Pow(Math.Log(10.0) / 400.0, 2);
            if (!categories.TryGetValue(item.BlueprintCategory, out var category))
            {
                category = new ExamSimulationCategoryScore();
                categories[item.BlueprintCategory] = category;
            }
            category.Total++;
            if (isCorrect) category.Correct++;
        }

        var abilitySe = Math.Sqrt(1.0 / information);
        var scoreSe = abilitySe * 15.0 / 200.0;
        var combinedSe = Math.Sqrt(7.0 * 7.0 + 15.0 * 15.0 + scoreSe * scoreSe);
        var range = (int)Math.Ceiling(combinedSe);
        var passProbability = NormalCdf((predicted - 200.0) / combinedSe);
        return new ExamSimulationScore
        {
            PredictedScore = predicted,
            RangeLow = Math.Clamp(predicted - range, 1, 300),
            RangeHigh = Math.Clamp(predicted + range, 1, 300),
            PassProbability = Math.Round(passProbability, 4),
            Correct = correct,
            Total = items.Count,
            SeenCount = seen,
            AbilityElo = Math.Round(ability, 1),
            Categories = categories
        };
    }

    private static double EstimateAbility(
        IReadOnlyList<ExamSimulationItem> items,
        IReadOnlyDictionary<string, ExamSimulationResponse> responses,
        IReadOnlyDictionary<string, Question> questions)
    {
        var low = 100.0;
        var high = 1900.0;
        for (var iteration = 0; iteration < 80; iteration++)
        {
            var ability = (low + high) / 2.0;
            var derivative = -(ability - PriorMean) / (PriorSd * PriorSd);
            foreach (var item in items)
            {
                if (!questions.TryGetValue(item.QuestionExternalId, out var question)) continue;
                responses.TryGetValue(item.QuestionExternalId, out var response);
                var actual = response?.ChoiceId == question.CorrectChoiceId ? 1.0 : 0.0;
                var weight = item.WasSeen ? 0.5 : 1.0;
                derivative += weight * (actual - Expected(ability, item.QuestionElo)) * Math.Log(10.0) / 400.0;
            }
            if (derivative > 0) low = ability; else high = ability;
        }
        return (low + high) / 2.0;
    }

    private static double Expected(double ability, int difficulty) =>
        1.0 / (1.0 + Math.Pow(10.0, (difficulty - ability) / 400.0));

    private static double NormalCdf(double value) => 0.5 * (1.0 + Erf(value / Math.Sqrt(2.0)));

    private static double Erf(double value)
    {
        var sign = value < 0 ? -1.0 : 1.0;
        value = Math.Abs(value);
        const double p = 0.3275911;
        var t = 1.0 / (1.0 + p * value);
        var y = 1.0 - (((((1.061405429 * t - 1.453152027) * t) + 1.421413741) * t - 0.284496736) * t + 0.254829592) * t * Math.Exp(-value * value);
        return sign * y;
    }
}