joke-app/packages/games/src/rummikub/rules.ts

/**
 * 숫자 타일 (docs/games/rummikub.md §3, §5.1, §5.5): tile ids, set validation / joker interpretation,
 * scoring helpers and simple "what can I play from my rack" search (hint button + random playouts).
 * Pure functions without zod so the screen can import them cheaply.
 */

export type TileColor = 'K' | 'R' | 'B' | 'O';
export type Tile = { id: string; kind: 'num'; color: TileColor; n: number } | { id: string; kind: 'joker' };
export type NumTile = Extract<Tile, { kind: 'num' }>;

export const COLORS: TileColor[] = ['K', 'R', 'B', 'O'];
export const COLOR_KO: Record<TileColor, string> = { K: '검정', R: '빨강', B: '파랑', O: '주황' };

/** 106 ids: `R7a`, `R7b`, ... and `JK1`, `JK2` (§3). */
export const ALL_TILE_IDS: string[] = (() => {
  const out: string[] = [];
  for (const c of COLORS) for (let n = 1; n <= 13; n++) for (const copy of ['a', 'b']) out.push(`${c}${n}${copy}`);
  out.push('JK1', 'JK2');
  return out;
})();

const TILES = new Map<string, Tile>(
  ALL_TILE_IDS.map((id): [string, Tile] =>
    id.startsWith('JK') ? [id, { id, kind: 'joker' }] : [id, { id, kind: 'num', color: id[0] as TileColor, n: Number(id.slice(1, -1)) }],
  ),
);

export const isTileId = (id: string): boolean => TILES.has(id);
export function tileOf(id: string): Tile {
  const t = TILES.get(id);
  if (!t) throw new Error(`unknown tile ${id}`);
  return t;
}
export const isJoker = (id: string): boolean => id === 'JK1' || id === 'JK2';

export interface DraftSet {
  tileIds: string[];
  /** Hint for sets that could be read both ways, e.g. [빨강5, 조커, 조커] (§5.5). */
  as?: 'run' | 'group';
}

export interface JokerAs {
  /** null = one of the missing colours of a group (not fixed). */
  color: TileColor | null;
  n: number;
}

export interface NormalSet {
  /** Display order (runs ascending). */
  tileIds: string[];
  kind: 'run' | 'group';
  jokerAs: Record<string, JokerAs>;
  points: number;
}

function asGroup(ts: Tile[]): NormalSet | null {
  if (ts.length < 3 || ts.length > 4) return null;
  const nums = ts.filter((t): t is NumTile => t.kind === 'num');
  if (nums.length === 0) return null;
  const n = nums[0]!.n;
  if (nums.some((t) => t.n !== n)) return null;
  if (new Set(nums.map((t) => t.color)).size !== nums.length) return null;
  const jokerAs: Record<string, JokerAs> = {};
  for (const t of ts) if (t.kind === 'joker') jokerAs[t.id] = { color: null, n };
  // Numbers first in colour order, jokers last.
  const order = [...nums].sort((a, b) => COLORS.indexOf(a.color) - COLORS.indexOf(b.color)).map((t) => t.id);
  for (const t of ts) if (t.kind === 'joker') order.push(t.id);
  return { tileIds: order, kind: 'group', jokerAs, points: n * ts.length };
}

function runFrom(ts: Tile[], start: number, color: TileColor): NormalSet {
  const jokerAs: Record<string, JokerAs> = {};
  let points = 0;
  ts.forEach((t, k) => {
    points += start + k;
    if (t.kind === 'joker') jokerAs[t.id] = { color, n: start + k };
  });
  return { tileIds: ts.map((t) => t.id), kind: 'run', jokerAs, points };
}

function asRun(ts: Tile[]): NormalSet | null {
  const len = ts.length;
  if (len < 3 || len > 13) return null;
  const nums = ts.filter((t): t is NumTile => t.kind === 'num');
  if (nums.length === 0) return null;
  const color = nums[0]!.color;
  if (nums.some((t) => t.color !== color)) return null;
  // (a) the order the client sent, if it is a valid run as it stands.
  const first = ts.findIndex((t) => t.kind === 'num');
  const start = nums[0]!.n - first;
  if (start >= 1 && start + len - 1 <= 13 && ts.every((t, k) => t.kind === 'joker' || t.n === start + k)) return runFrom(ts, start, color);
  // (b) sort, fill gaps with jokers, extra jokers go up (towards 13) first, then down.
  const sorted = [...nums].sort((a, b) => a.n - b.n);
  for (let i = 1; i < sorted.length; i++) if (sorted[i]!.n === sorted[i - 1]!.n) return null;
  const min = sorted[0]!.n;
  const max = sorted[sorted.length - 1]!.n;
  const jokers = ts.filter((t) => t.kind === 'joker');
  const gaps = max - min + 1 - sorted.length;
  if (gaps > jokers.length) return null;
  const extra = jokers.length - gaps;
  const up = Math.min(extra, 13 - max);
  const down = extra - up;
  if (min - down < 1) return null;
  const lo = min - down;
  const hi = max + up;
  const out: Tile[] = [];
  let j = 0;
  let k = 0;
  for (let n = lo; n <= hi; n++) {
    if (sorted[k]?.n === n) out.push(sorted[k++]!);
    else out.push(jokers[j++]!);
  }
  return runFrom(out, lo, color);
}

/** Validates one set and decides what its jokers stand for (§5.5, §8.2). null = not a valid set. */
export function normalizeSet(d: DraftSet): NormalSet | null {
  const ids = d.tileIds;
  if (ids.length < 3 || ids.length > 13) return null;
  const ts: Tile[] = [];
  for (const id of ids) {
    const t = TILES.get(id);
    if (!t || ts.includes(t)) return null;
    ts.push(t);
  }
  const g = asGroup(ts);
  const r = asRun(ts);
  if (g && r) return d.as === 'group' ? g : r;
  return g ?? r;
}

/** Short Korean reason why a set is not valid (null when valid) — live red/green feedback (§9). */
export function setProblem(d: DraftSet): string | null {
  const ids = d.tileIds;
  if (ids.length === 0) return null;
  if (ids.length < 3) return '3장 이상이어야 해요';
  if (normalizeSet(d)) return null;
  const ts = ids.filter(isTileId).map(tileOf);
  const nums = ts.filter((t): t is NumTile => t.kind === 'num');
  if (nums.length === 0) return '숫자 타일이 1장 이상 있어야 해요';
  const sameN = nums.every((t) => t.n === nums[0]!.n);
  const sameC = nums.every((t) => t.color === nums[0]!.color);
  if (sameN && nums.length > 1) {
    if (new Set(nums.map((t) => t.color)).size !== nums.length) return '같은 색이 두 개예요';
    if (ids.length > 4) return '같은 숫자 묶음은 4장까지예요';
  }
  if (sameC) {
    if (new Set(nums.map((t) => t.n)).size !== nums.length) return '같은 숫자가 두 번 있어요';
    if (ids.length > 13) return '13장보다 길 수 없어요';
    if (nums.some((t) => t.n === 13) && nums.some((t) => t.n === 1)) return '13 다음에 1은 올 수 없어요';
    return '숫자가 이어지지 않아요';
  }
  return '같은 색 연속 숫자나, 같은 숫자 다른 색이어야 해요';
}

/** Score of a tile left on the rack at the end (§6). */
export const tileValue = (id: string, jokerPenalty: number): number => {
  const t = tileOf(id);
  return t.kind === 'joker' ? jokerPenalty : t.n;
};
export const rackValue = (ids: readonly string[], jokerPenalty: number): number => ids.reduce((a, id) => a + tileValue(id, jokerPenalty), 0);

/** Order-insensitive key of an arrangement (each set as a tile set). */
export function arrangementKey(sets: readonly { tileIds: readonly string[] }[]): string {
  return sets
    .filter((s) => s.tileIds.length > 0)
    .map((s) => [...s.tileIds].sort().join(','))
    .sort()
    .join('|');
}

/** Rack sort orders (§9): by colour then number, or number then colour; jokers last. */
export function sortTiles(ids: readonly string[], by: 'color' | 'number'): string[] {
  const key = (id: string): number => {
    const t = tileOf(id);
    if (t.kind === 'joker') return 10_000 + Number(id.slice(2));
    const c = COLORS.indexOf(t.color);
    return by === 'color' ? c * 100 + t.n * 2 + (id.endsWith('b') ? 1 : 0) : t.n * 10 + c + (id.endsWith('b') ? 0.5 : 0);
  };
  return [...ids].sort((a, b) => key(a) - key(b));
}

/** Korean label of a tile for screen readers, e.g. "빨강 7", "조커". */
export function tileLabel(id: string, as?: JokerAs): string {
  const t = tileOf(id);
  if (t.kind === 'joker') return as ? `조커(${as.color ? `${COLOR_KO[as.color]} ` : ''}${as.n})` : '조커';
  return `${COLOR_KO[t.color]} ${t.n}`;
}

/**
 * Candidate sets made only from rack tiles (not disjoint): groups of 3–4 colours, maximal runs, and a few
 * joker completions. No table rearrangement search (§9 hint: bounded work).
 */
export function findRackSets(rack: readonly string[]): NormalSet[] {
  const nums = rack.map(tileOf).filter((t): t is NumTile => t.kind === 'num');
  const jokers = rack.filter(isJoker);
  const out: NormalSet[] = [];
  const push = (ids: string[]) => {
    const n = normalizeSet({ tileIds: ids });
    if (n) out.push(n);
  };
  // Groups
  for (let n = 1; n <= 13; n++) {
    const byColor = new Map<TileColor, string>();
    for (const t of nums) if (t.n === n && !byColor.has(t.color)) byColor.set(t.color, t.id);
    const ids = [...byColor.values()];
    if (ids.length >= 3) push(ids);
    else if (ids.length === 2 && jokers.length > 0) push([...ids, jokers[0]!]);
  }
  // Runs: from every start that has no tile right below it, extend upwards, filling holes with jokers.
  for (const c of COLORS) {
    const at = new Map<number, string>();
    for (const t of nums) if (t.color === c && !at.has(t.n)) at.set(t.n, t.id);
    for (const [start] of [...at].sort((a, b) => a[0] - b[0])) {
      if (at.has(start - 1)) continue;
      const ids: string[] = [];
      let jUsed = 0;
      let best: string[] | null = null;
      for (let n = start; n <= 13; n++) {
        const id = at.get(n);
        if (id) ids.push(id);
        else if (jUsed < jokers.length) ids.push(jokers[jUsed++]!);
        else break;
        if (ids.length >= 3 && !isJoker(ids[ids.length - 1]!)) best = [...ids];
      }
      if (best) push(best);
      else if (jokers.length > 0 && at.has(start + 1) && start + 2 <= 13) push([at.get(start)!, at.get(start + 1)!, jokers[0]!]);
    }
  }
  return out;
}

/** Disjoint rack-only sets, greedy by points; stops as soon as `minPoints` is reached. */
export function pickDisjoint(rack: readonly string[], minPoints = Infinity): { sets: NormalSet[]; points: number } {
  const cands = findRackSets(rack).sort((a, b) => b.points - a.points);
  const used = new Set<string>();
  const sets: NormalSet[] = [];
  let points = 0;
  for (const c of cands) {
    if (c.tileIds.some((id) => used.has(id))) continue;
    sets.push(c);
    for (const id of c.tileIds) used.add(id);
    points += c.points;
    if (points >= minPoints) break;
  }
  return { sets, points };
}

/** Disjoint rack-only sets reaching `minPoints` (first meld), or null. */
export function findMeld(rack: readonly string[], minPoints: number): NormalSet[] | null {
  const r = pickDisjoint(rack, minPoints);
  return r.sets.length && r.points >= minPoints ? r.sets : null;
}

/** Adds one tile to a valid set at the matching end (run) or as a missing colour (group); null if it does not fit. */
export function extendSet(set: Pick<NormalSet, 'tileIds' | 'kind' | 'jokerAs'>, id: string): NormalSet | null {
  const t = tileOf(id);
  const ids = set.tileIds;
  const ts = ids.map(tileOf);
  let cand: string[] | null = null;
  if (set.kind === 'group') {
    if (ids.length >= 4) return null;
    if (t.kind === 'num') {
      const n = ts.find((x): x is NumTile => x.kind === 'num')?.n;
      if (n !== t.n || ts.some((x) => x.kind === 'num' && x.color === t.color)) return null;
    }
    cand = [...ids, id];
  } else {
    if (ids.length >= 13) return null;
    const val = (x: Tile) => (x.kind === 'num' ? x.n : (set.jokerAs[x.id]?.n ?? 0));
    const lo = val(ts[0]!);
    const hi = val(ts[ts.length - 1]!);
    if (t.kind === 'joker') cand = hi < 13 ? [...ids, id] : lo > 1 ? [id, ...ids] : null;
    else if (!ts.some((x) => x.kind === 'num' && x.color === t.color)) return null;
    else if (t.n === hi + 1) cand = [...ids, id];
    else if (t.n === lo - 1) cand = [id, ...ids];
  }
  return cand ? normalizeSet({ tileIds: cand, as: set.kind }) : null;
}