import { mad, median } from '@rareindex/shared';

export interface PricePoint {
  id: string;
  priceUsd: number;
  date: Date;
  quantity?: number;
  isBundle?: boolean;
}

export interface OutlierFlag {
  id: string;
  reason: string;
  score: number;
}

/**
 * Robust outlier detection on log prices within a variant (§116): modified z-score
 * 0.6745·(x − median)/MAD > threshold. Needs ≥ 5 points; with a MAD of 0 (identical prices) any
 * different price beyond 3× is flagged. Never deletes — returns flags for audit.
 */
export function detectOutliers(points: PricePoint[], threshold = 3.5): OutlierFlag[] {
  const valid = points.filter((p) => p.priceUsd > 0 && !p.isBundle && (p.quantity ?? 1) === 1);
  if (valid.length < 5) return [];
  const logs = valid.map((p) => Math.log(p.priceUsd));
  const med = median(logs)!;
  const m = mad(logs)!;
  const out: OutlierFlag[] = [];
  for (let i = 0; i < valid.length; i++) {
    const p = valid[i]!;
    const dev = logs[i]! - med;
    let score: number;
    if (m > 0) score = (0.6745 * dev) / m;
    else score = Math.abs(dev) > Math.log(3) ? Math.sign(dev) * threshold * 2 : 0;
    if (Math.abs(score) > threshold) out.push({ id: p.id, reason: score > 0 ? 'abnormally_high_price' : 'abnormally_low_price', score: Math.round(score * 100) / 100 });
  }
  return out;
}