HolodoriCalc/src/lib/engine/score-probability.ts

import { effectiveActiveProbability } from './active-probability.ts';
import { passiveScoreSupportByCard } from './passive-support.ts';
import { effectiveCooldownSeconds } from './timeline.ts';
import type {
  CooldownReduction,
  ExactScoreOptions,
  ExactSongChart,
  OptimizerCard,
  ScoreAchievementProbabilities
} from './types.ts';

type Attempt = {
  key: string;
  probability: number;
};

type NoteCandidate = {
  attemptIndex: number;
  boost: number;
};

type ScoreGroup = {
  candidates: readonly NoteCandidate[];
  scores: readonly number[];
};

type PreparedProbabilityModel = {
  attempts: readonly Attempt[];
  groups: readonly ScoreGroup[];
  maximumScore: number;
  maximumClauses: readonly (readonly number[])[];
};

function specialActive(card: OptimizerCard, start: number | null | undefined, time: number): boolean {
  return start !== null && start !== undefined && start <= time && time < start + card.special.durationSeconds;
}

function specialRate(
  cards: readonly OptimizerCard[],
  chart: ExactSongChart,
  time: number,
  field: 'scoreUpPercent' | 'activationRateUpPercent'
): number {
  return cards.reduce((sum, card, slot) => sum +
    (specialActive(card, chart.specialStartSeconds[slot], time) ? card.special[field] ?? 0 : 0), 0);
}

function comboBonus(combo: number): number {
  return combo >= 1_000 ? 0.1 : combo >= 100 ? Math.floor(combo / 100) * 0.01 : 0;
}

function finalNoteScore(score: number, percent: number): number {
  const scaled = score * (1 + percent / 100);
  return Math.ceil(scaled - Number.EPSILON * Math.max(1, scaled) * 4);
}

function scoreNotes(chart: ExactSongChart): ExactSongChart['notes'] {
  return chart.notes;
}

function prepareModel(
  cards: readonly OptimizerCard[],
  reductions: Readonly<Record<string, CooldownReduction>>,
  chart: ExactSongChart,
  options: ExactScoreOptions,
  onNote?: (probability: number) => void
): PreparedProbabilityModel {
  const attempts: Attempt[] = [];
  const attemptIndexes = new Map<string, number>();
  const passiveSupport = passiveScoreSupportByCard(cards);
  const grouped = new Map<string, { candidates: NoteCandidate[]; scores: number[] }>();
  const clauses: number[][] = [];
  let maximumScore = 0;
  let prefixProbability = 1;
  let prefixClauses: number[][] = [];

  scoreNotes(chart).forEach((note, noteIndex) => {
    const candidates: NoteCandidate[] = [];
    const specialSupport = specialRate(cards, chart, note.timeSeconds, 'scoreUpPercent');
    cards.forEach((card, cardIndex) => {
      const reduction = reductions[card.id] ?? 0;
      const interval = effectiveCooldownSeconds(card.active.cooldownSeconds, reduction);
      const attemptNumber = Math.floor((note.timeSeconds + 1e-9) / interval);
      if (attemptNumber <= 0) return;
      const activationTime = attemptNumber * interval;
      if (options.excludedActiveWindows?.some((window) =>
        window.cardId === card.id && Math.abs(window.startSeconds - activationTime) < 1e-9)) return;
      if (note.timeSeconds >= activationTime + card.active.durationSeconds) return;
      const key = `${card.id}:${attemptNumber}`;
      let attemptIndex = attemptIndexes.get(key);
      if (attemptIndex === undefined) {
        const activationBonus = specialRate(cards, chart, activationTime, 'activationRateUpPercent');
        const probability = effectiveActiveProbability(card, activationBonus);
        attemptIndex = attempts.length;
        attemptIndexes.set(key, attemptIndex);
        attempts.push({ key, probability });
      }
      candidates.push({
        attemptIndex,
        boost: card.active.scoreUpPercent / 100 *
          (1 + (specialSupport + (card.scoreSupportPercent ?? 0) + passiveSupport[cardIndex]) / 100)
      });
    });
    candidates.sort((left, right) => right.boost - left.boost || left.attemptIndex - right.attemptIndex);

    const combo = noteIndex + 1;
    const baseNoteScore = note.type === 'mid'
      ? Math.ceil(options.perfectNoteScore * 0.1)
      : options.perfectNoteScore * (note.isFlick ? 1.05 : 1);
    const rawBaseline = baseNoteScore * (1 + comboBonus(combo));
    const directBonus = options.directSongScoreBonusPercent ?? 0;
    const scores = [
      ...candidates.map((candidate) => finalNoteScore(rawBaseline * (1 + candidate.boost), directBonus)),
      finalNoteScore(rawBaseline, directBonus)
    ];
    maximumScore += scores[0];

    // No activation is required when rounding gives the baseline the same score.
    if (scores[0] > scores[scores.length - 1]) {
      const clause = candidates
        .filter((_, index) => scores[index] === scores[0])
        .map((candidate) => candidate.attemptIndex);
      clauses.push(clause);
      if (onNote && !prefixClauses.some((existing) => existing.every((variable) => clause.includes(variable)))) {
        prefixClauses = simplifyClauses([...prefixClauses, clause]);
        prefixProbability = exactClauseProbability(prefixClauses, attempts);
      }
    }
    onNote?.(prefixProbability);

    const signature = candidates.map((candidate) => `${candidate.attemptIndex}:${candidate.boost.toPrecision(15)}`).join('|');
    const existing = grouped.get(signature);
    if (existing) scores.forEach((score, index) => { existing.scores[index] += score; });
    else grouped.set(signature, { candidates, scores });
  });

  return {
    attempts,
    groups: Array.from(grouped.values()),
    maximumScore,
    maximumClauses: simplifyClauses(clauses)
  };
}

/** Exact cumulative maximum-score probability after each chart note, in note order. */
export function calculateMaximumScoreProbabilityTimeline(
  cards: readonly OptimizerCard[],
  reductions: Readonly<Record<string, CooldownReduction>>,
  chart: ExactSongChart,
  options: ExactScoreOptions
): number[] {
  const probabilities: number[] = [];
  prepareModel(cards, reductions, chart, options, (probability) => probabilities.push(probability));
  return probabilities;
}

function simplifyClauses(clauses: readonly (readonly number[])[]): number[][] {
  const unique = new Map<string, number[]>();
  for (const clause of clauses) {
    const normalized = Array.from(new Set(clause)).sort((left, right) => left - right);
    unique.set(normalized.join(','), normalized);
  }
  const sorted = Array.from(unique.values()).sort((left, right) => left.length - right.length);
  return sorted.filter((clause, index) => !sorted.slice(0, index).some((candidate) =>
    candidate.length <= clause.length && candidate.every((variable) => clause.includes(variable))));
}

function exactClauseProbability(clauses: readonly (readonly number[])[], attempts: readonly Attempt[]): number {
  const memo = new Map<string, number>();
  const solve = (current: readonly (readonly number[])[]): number => {
    if (current.length === 0) return 1;
    if (current.some((clause) => clause.length === 0)) return 0;
    const simplified = simplifyClauses(current);
    const key = simplified.map((clause) => clause.join(',')).join(';');
    const cached = memo.get(key);
    if (cached !== undefined) return cached;

    const required = new Set(simplified.filter((clause) => clause.length === 1).map((clause) => clause[0]));
    if (required.size > 0) {
      let requiredProbability = 1;
      for (const variable of required) requiredProbability *= attempts[variable]?.probability ?? 0;
      const remaining = simplified.filter((clause) => !clause.some((variable) => required.has(variable)));
      const result = requiredProbability * solve(remaining);
      memo.set(key, result);
      return result;
    }

    const occurrences = new Map<number, number>();
    simplified.forEach((clause) => clause.forEach((variable) =>
      occurrences.set(variable, (occurrences.get(variable) ?? 0) + 1)));
    const variable = Array.from(occurrences).sort((left, right) => right[1] - left[1])[0][0];
    const probability = attempts[variable]?.probability ?? 0;
    const whenTrue = simplified.filter((clause) => !clause.includes(variable));
    const whenFalse = simplified.map((clause) => clause.filter((candidate) => candidate !== variable));
    const result = probability * solve(whenTrue) + (1 - probability) * solve(whenFalse);
    memo.set(key, result);
    return result;
  };
  return solve(clauses);
}

function hashSeed(cards: readonly OptimizerCard[], reductions: Readonly<Record<string, CooldownReduction>>): number {
  const value = cards.map((card) => `${card.id}:${reductions[card.id] ?? 0}`).join('|');
  let hash = 2166136261;
  for (let index = 0; index < value.length; index += 1) {
    hash ^= value.charCodeAt(index);
    hash = Math.imul(hash, 16777619);
  }
  return hash >>> 0;
}

function randomGenerator(seed: number): () => number {
  let state = seed || 0x9e3779b9;
  return () => {
    state += 0x6d2b79f5;
    let value = state;
    value = Math.imul(value ^ value >>> 15, value | 1);
    value ^= value + Math.imul(value ^ value >>> 7, value | 61);
    return ((value ^ value >>> 14) >>> 0) / 4294967296;
  };
}

export function estimateScoreAchievementProbabilities(
  cards: readonly OptimizerCard[],
  reductions: Readonly<Record<string, CooldownReduction>>,
  chart: ExactSongChart,
  options: ExactScoreOptions & { sampleCount?: number; seed?: number }
): ScoreAchievementProbabilities {
  const model = prepareModel(cards, reductions, chart, options);
  const samples = Math.max(1, Math.round(options.sampleCount ?? 25_000));
  const random = randomGenerator(options.seed ?? hashSeed(cards, reductions));
  const active = new Uint8Array(model.attempts.length);
  let atLeast99 = 0;
  let atLeast95 = 0;
  const threshold99 = model.maximumScore * 0.99;
  const threshold95 = model.maximumScore * 0.95;

  for (let sample = 0; sample < samples; sample += 1) {
    model.attempts.forEach((attempt, index) => { active[index] = random() < attempt.probability ? 1 : 0; });
    let score = 0;
    for (const group of model.groups) {
      let scoreIndex = group.candidates.length;
      for (let index = 0; index < group.candidates.length; index += 1) {
        if (active[group.candidates[index].attemptIndex]) {
          scoreIndex = index;
          break;
        }
      }
      score += group.scores[scoreIndex];
    }
    if (score >= threshold99) atLeast99 += 1;
    if (score >= threshold95) atLeast95 += 1;
  }

  return {
    maximum: exactClauseProbability(model.maximumClauses, model.attempts),
    atLeast99Percent: atLeast99 / samples,
    atLeast95Percent: atLeast95 / samples,
    samples
  };
}