feat: add combination search workflow

src/lib/engine/combination-search.ts

@@ -0,0 +1,55 @@
+export type CombinationSearchCard = {
+  id: string;
+  characterId: string;
+};
+
+type BeamState<T extends CombinationSearchCard> = {
+  cards: T[];
+  score: number;
+};
+
+export function generateCombinationCandidates<T extends CombinationSearchCard>(
+  fixedCards: readonly T[],
+  candidateCards: readonly T[],
+  targetSize: number,
+  scoreCard: (card: T) => number,
+  beamWidth = 800
+): T[][] {
+  if (targetSize < fixedCards.length) throw new Error('목표 카드 수가 고정 카드 수보다 작습니다.');
+  if (new Set(fixedCards.map((card) => card.characterId)).size !== fixedCards.length) {
+    throw new Error('같은 멤버를 두 번 고정할 수 없습니다.');
+  }
+  const fixedIds = new Set(fixedCards.map((card) => card.id));
+  const fixedCharacters = new Set(fixedCards.map((card) => card.characterId));
+  const pool = candidateCards.filter((card) => !fixedIds.has(card.id) && !fixedCharacters.has(card.characterId));
+  let beam: BeamState<T>[] = [{
+    cards: Array.from(fixedCards),
+    score: fixedCards.reduce((sum, card) => sum + scoreCard(card), 0)
+  }];
+
+  for (let size = fixedCards.length; size < targetSize; size += 1) {
+    const expanded = new Map<string, BeamState<T>>();
+    for (const state of beam) {
+      const usedCharacters = new Set(state.cards.map((card) => card.characterId));
+      const usedIds = new Set(state.cards.map((card) => card.id));
+      for (const card of pool) {
+        if (usedIds.has(card.id)) continue;
+        if (usedCharacters.has(card.characterId)) continue;
+        const nextState = {
+          cards: [...state.cards, card],
+          score: state.score + scoreCard(card)
+        };
+        const key = nextState.cards.map((entry) => entry.id).sort().join('|');
+        if (!expanded.has(key)) expanded.set(key, nextState);
+      }
+    }
+    beam = Array.from(expanded.values())
+      .sort((left, right) => right.score - left.score || left.cards.map((card) => card.id).join().localeCompare(right.cards.map((card) => card.id).join()))
+      .slice(0, Math.max(1, beamWidth));
+    if (beam.length === 0) break;
+  }
+  return beam
+    .filter((state) => state.cards.length === targetSize)
+    .sort((left, right) => right.score - left.score)
+    .map((state) => state.cards);
+}