feat: compare top five cooldown combinations in analysis

UPDATES.md

@@ -1,9 +1,13 @@
 ---
-updatedAt: 2026-09-25T11:16:00Z
+updatedAt: 2026-09-25T14:08:52Z
 ---
 
 ## 2026년 9월 25일
 
+### 배치 분석 빈도 조합 비교
+
+`IMPROVED` 서로 다른 빈도 감소 조합을 최고점 내림차순으로 최대 5개 표시합니다. 각 조합의 예상 점수와 고점 달성 확률을 비교하고, 원하는 결과를 선택해 상세 점수와 그래프를 확인할 수 있습니다. 점수·확률 열의 최댓값은 공동 최댓값을 포함해 굵게 표시합니다.
+
 ### 64. 악곡과 이벤트 과제곡 선택
 
 `DATA` 아냐 멜핏사의 솔로곡 64.를 추가했습니다. Easy·Normal·Hard·Expert의 정확한 채보와 곡별 점수 계산을 지원합니다.

src/lib/engine/exact-optimizer.test.ts

@@ -1,6 +1,6 @@
 import test from 'node:test';
 import assert from 'node:assert/strict';
-import { optimizeExactOrderAndCooldowns } from './exact-optimizer.ts';
+import { optimizeExactOrderAndCooldowns, rankExactCooldownCombinations } from './exact-optimizer.ts';
 import { passiveScoreSupportByCard } from './passive-support.ts';
 import type { ExactSongChart, OptimizerCard } from './types.ts';
 
@@ -21,6 +21,27 @@ const chart: ExactSongChart = {
   specialStartSeconds: [1, 2, 3, 4, 5]
 };
 
+test('빈도 조합별 최적 순서를 최고점 순으로 최대 5개 반환한다', () => {
+  const flexible = cards.map((card, index) => ({ ...card, allowedCooldownReductions: index < 3 ? [0, 4] as const : [0] as const }));
+  const exhaustive = [0, 4].flatMap((a) => [0, 4].flatMap((b) => [0, 4].map((c) =>
+    optimizeExactOrderAndCooldowns(cards.map((card, index) => ({
+      ...card, allowedCooldownReductions: [[a, b, c, 0, 0][index] as 0 | 4]
+    })), chart, { perfectNoteScore: 100 })
+  ))).sort((left, right) => right.theoreticalMaxScore - left.theoreticalMaxScore ||
+    right.expectedScore - left.expectedScore ||
+    Object.values(left.cooldownReductions).reduce<number>((a, b) => a + b, 0) - Object.values(right.cooldownReductions).reduce<number>((a, b) => a + b, 0));
+  const ranked = rankExactCooldownCombinations(flexible, chart, { perfectNoteScore: 100 });
+  assert.equal(ranked.length, 5);
+  assert.equal(new Set(ranked.map((result) => JSON.stringify(result.cooldownReductions))).size, 5);
+  ranked.forEach((result, index) => {
+    assert.equal(result.theoreticalMaxScore, exhaustive[index].theoreticalMaxScore);
+    assert.deepEqual(result.cooldownReductions, exhaustive[index].cooldownReductions);
+    assert.deepEqual(result.order, exhaustive[index].order);
+    assert.equal(result.evaluatedCandidates, 120 * 8);
+  });
+  assert.equal(rankExactCooldownCombinations(cards, chart, { perfectNoteScore: 100 }).length, 1);
+});
+
 test('정확 분석 결과에 최적 조합의 액티브와 스페셜 지속 구간을 포함한다', () => {
   const result = optimizeExactOrderAndCooldowns(cards, chart, { perfectNoteScore: 100 });
 

src/lib/engine/exact-optimizer.ts

@@ -226,6 +226,16 @@ export function optimizeExactOrderAndCooldowns(
   chart: ExactSongChart,
   options: ExactOptimizeOptions
 ): ExactOptimizationResult {
+  return rankExactCooldownCombinations(cards, chart, options, 1)[0];
+}
+
+/** Keep the best special order for each distinct per-card cooldown assignment. */
+export function rankExactCooldownCombinations(
+  cards: readonly OptimizerCard[],
+  chart: ExactSongChart,
+  options: ExactOptimizeOptions,
+  limit = 5
+): ExactOptimizationResult[] {
   if (cards.length !== 5 || new Set(cards.map((card) => card.id)).size !== 5) {
     throw new Error('서로 다른 카드 5장이 필요합니다.');
   }
@@ -234,46 +244,39 @@ export function optimizeExactOrderAndCooldowns(
   const orderCount = cards.reduce((value, _, index) => value * (index + 1), 1);
   const totalCandidates = orderCount * reductionAssignments.length;
   let evaluatedCandidates = 0;
-  let bestTheoreticalMaxScore = Number.NEGATIVE_INFINITY;
-  let bestExpectedScore = Number.NEGATIVE_INFINITY;
-  let bestOrder: OptimizerCard[] | null = null;
-  let bestReductions: Record<string, CooldownReduction> | null = null;
-  let bestReductionTotal = Number.POSITIVE_INFINITY;
+  type Candidate = {
+    order: OptimizerCard[];
+    reductions: Record<string, CooldownReduction>;
+    theoreticalMaxScore: number;
+    expectedScore: number;
+    reductionTotal: number;
+  };
+  const bestByAssignment = new Map<Record<string, CooldownReduction>, Candidate>();
+  const compare = (left: Candidate, right: Candidate): number =>
+    (options.objective === 'expected'
+      ? right.expectedScore - left.expectedScore || right.theoreticalMaxScore - left.theoreticalMaxScore
+      : right.theoreticalMaxScore - left.theoreticalMaxScore || right.expectedScore - left.expectedScore) ||
+    left.reductionTotal - right.reductionTotal;
 
   for (const order of permutations(cards)) {
     const profiles = makeProfiles(order, chart);
     for (const reductions of reductionAssignments) {
       const score = scoreAssignment(order, reductions, profiles, base, options.directSongScoreBonusPercent ?? 0);
       const reductionTotal = Object.values(reductions).reduce<number>((sum, value) => sum + value, 0);
-      const expectedFirst = options.objective === 'expected';
-      const isBetterPrimary = expectedFirst
-        ? score.expectedScore > bestExpectedScore
-        : score.theoreticalMaxScore > bestTheoreticalMaxScore;
-      const isBetterSecondary = expectedFirst
-        ? score.expectedScore === bestExpectedScore && score.theoreticalMaxScore > bestTheoreticalMaxScore
-        : score.theoreticalMaxScore === bestTheoreticalMaxScore && score.expectedScore > bestExpectedScore;
-      const isCheaperTie = score.theoreticalMaxScore === bestTheoreticalMaxScore &&
-        score.expectedScore === bestExpectedScore && reductionTotal < bestReductionTotal;
-      if (isBetterPrimary || isBetterSecondary || isCheaperTie) {
-        bestTheoreticalMaxScore = score.theoreticalMaxScore;
-        bestExpectedScore = score.expectedScore;
-        bestOrder = order;
-        bestReductions = reductions;
-        bestReductionTotal = reductionTotal;
-      }
+      const candidate = { ...score, order, reductions, reductionTotal };
+      const previous = bestByAssignment.get(reductions);
+      if (!previous || compare(candidate, previous) < 0) bestByAssignment.set(reductions, candidate);
       evaluatedCandidates += 1;
     }
     options.onProgress?.({ evaluatedCandidates, totalCandidates });
   }
 
-  if (!bestOrder || !bestReductions) throw new Error('분석 결과를 만들지 못했습니다.');
-  const windows = buildExactSkillWindows(bestOrder, bestReductions, chart);
-  return {
-    ...calculateExactScore(bestOrder, bestReductions, chart, options),
-    order: bestOrder.map((card) => card.id),
+  return [...bestByAssignment.values()].sort(compare).slice(0, Math.max(1, Math.floor(limit))).map((candidate) => ({
+    ...calculateExactScore(candidate.order, candidate.reductions, chart, options),
+    order: candidate.order.map((card) => card.id),
     formationOrder: cards.map((card) => card.id),
-    cooldownReductions: { ...bestReductions },
-    ...windows,
+    cooldownReductions: { ...candidate.reductions },
+    ...buildExactSkillWindows(candidate.order, candidate.reductions, chart),
     evaluatedCandidates
-  };
+  }));
 }

src/lib/workers/score-optimizer.worker.ts

@@ -1,6 +1,7 @@
 /// <reference lib="webworker" />
 
 import { countOptimizationCandidates, estimateScoreAchievementProbabilities, optimizeExactOrderAndCooldowns } from '../engine/index.ts';
+import { rankExactCooldownCombinations } from '../engine/exact-optimizer.ts';
 import type { ExactOptimizationResult, ExactOptimizeOptions, ExactSongChart, OptimizerCard, ScoreAchievementProbabilities } from '../engine/index.ts';
 
 type OptimizeRequest = {
@@ -10,6 +11,7 @@ type OptimizeRequest = {
   perfectNoteScore: number;
   directSongScoreBonusPercent?: number;
   includeAchievementProbabilities?: boolean;
+  cooldownResultLimit?: number;
 };
 
 type CombinationCandidate = {
@@ -77,19 +79,19 @@ self.onmessage = (event: MessageEvent<OptimizeRequest | CombinationRequest | Ach
         directSongScoreBonusPercent: event.data.directSongScoreBonusPercent,
         onProgress: (progress) => self.postMessage({ type: 'progress', progress })
       };
-      const result = optimizeExactOrderAndCooldowns(event.data.cards, event.data.chart, options);
-      let achievementProbabilities: ScoreAchievementProbabilities | undefined;
-      if (event.data.includeAchievementProbabilities) {
-        self.postMessage({ type: 'probability-start' });
-        const orderedCards = cardsForResult(event.data.cards, result);
-        achievementProbabilities = estimateScoreAchievementProbabilities(
-          orderedCards,
+      const request = event.data;
+      const results = rankExactCooldownCombinations(request.cards, request.chart, options, request.cooldownResultLimit === 5 ? 5 : 1);
+      if (request.includeAchievementProbabilities) self.postMessage({ type: 'probability-start' });
+      const cooldownRankings = results.map((result) => {
+        const achievementProbabilities = request.includeAchievementProbabilities ? estimateScoreAchievementProbabilities(
+          cardsForResult(request.cards, result),
           result.cooldownReductions,
-          event.data.chart,
+          request.chart,
           { ...options, sampleCount: 25_000 }
-        );
-      }
-      self.postMessage({ type: 'result', result, achievementProbabilities });
+        ) : undefined;
+        return { result, achievementProbabilities };
+      });
+      self.postMessage({ type: 'result', ...cooldownRankings[0], cooldownRankings });
       return;
     }
 

src/routes/analysis/+page.svelte

@@ -118,6 +118,23 @@
   let running = false;
   let progress: OptimizationProgress = { evaluatedCandidates: 0, totalCandidates: 0 };
   let result: ExactOptimizationResult | null = null;
+  let cooldownRankings: { result: ExactOptimizationResult; achievementProbabilities?: ScoreAchievementProbabilities }[] = [];
+  $: cooldownColumnMaxima = {
+    score: Math.max(...cooldownRankings.map(({ result }) => result.theoreticalMaxScore)),
+    expected: Math.max(...cooldownRankings.map(({ result }) => result.expectedScore)),
+    maximum: Math.max(...cooldownRankings.map(({ achievementProbabilities: p }) => p?.maximum ?? -Infinity)),
+    atLeast995Percent: Math.max(...cooldownRankings.map(({ achievementProbabilities: p }) => p?.atLeast995Percent ?? -Infinity)),
+    atLeast99Percent: Math.max(...cooldownRankings.map(({ achievementProbabilities: p }) => p?.atLeast99Percent ?? -Infinity)),
+    atLeast95Percent: Math.max(...cooldownRankings.map(({ achievementProbabilities: p }) => p?.atLeast95Percent ?? -Infinity))
+  };
+
+  function selectCooldownRanking(index: number): void {
+    const ranking = cooldownRankings[index];
+    if (!ranking || running) return;
+    result = ranking.result;
+    achievementProbabilities = ranking.achievementProbabilities;
+    clearConnectionOptimizationProposal();
+  }
   type SimulationContext = { cards: OptimizerCard[]; chart: ExactSongChart; options: ExactScoreOptions };
   let simulationContext: SimulationContext | null = null;
   let pendingSimulationContext: SimulationContext | null = null;
@@ -393,6 +410,7 @@
       if (event.data.type === 'progress') progress = event.data.progress;
       if (event.data.type === 'result') {
         result = event.data.result;
+        cooldownRankings = event.data.cooldownRankings ?? [];
         transferredResult = false;
         resultCapture = pendingCapture;
         resultInputKey = pendingInputKey;
@@ -864,7 +882,8 @@
         chart,
         perfectNoteScore: noteScore,
         directSongScoreBonusPercent: songBonus,
-        includeAchievementProbabilities: true
+        includeAchievementProbabilities: true,
+        cooldownResultLimit: mode === 'analysis' ? 5 : 1
       });
     } catch (error) {
       running = false;
@@ -1142,6 +1161,31 @@
     {#if mode === 'analysis' && resultCapture}<p class="board-guide"><strong>{resultCapture.title} · {difficultyLabel(resultCapture.settings.difficulty)}</strong> · 분석 당시 종합력 {resultCapture.overallPower.toLocaleString('ko-KR')}</p>{/if}
     {#if mode === 'rating' && result}<p class="board-guide"><strong>{selectedChart?.title} · {difficultyLabel(difficulty)}</strong> · 종합력 {overallPower.toLocaleString('ko-KR')} · 가창 보너스 10%</p>{/if}
     {#if result}
+      {#if mode === 'analysis' && cooldownRankings.length > 0}
+        <section class="cooldown-rankings" aria-labelledby="cooldown-rankings-title">
+          <h3 id="cooldown-rankings-title">빈도 조합 상위 {cooldownRankings.length}개</h3>
+          <p class="probability-guide">빈도 감소 조합마다 최적의 스페셜 순서를 구해 최고점 내림차순으로 표시합니다. 확률은 각 조합의 최고점 기준이며, 결과를 선택하면 아래 상세 점수와 그래프에 반영됩니다.</p>
+          <div class="cooldown-table-scroll">
+            <table>
+              <thead><tr><th>순위</th><th>카드별 빈도 감소</th><th>최고점</th><th>예상 점수</th><th>100% 달성</th><th>99.5% 이상</th><th>99% 이상</th><th>95% 이상</th></tr></thead>
+              <tbody>
+                {#each cooldownRankings as ranking, index}
+                  <tr class:selected={result === ranking.result}>
+                    <td><button class="cooldown-select" type="button" aria-label={`${index + 1}위 빈도 조합 선택`} aria-pressed={result === ranking.result} disabled={running} on:click={() => selectCooldownRanking(index)}><span class="cooldown-rank">{index + 1}위</span><span class="cooldown-selection"><span class="cooldown-selection-dot" aria-hidden="true"></span>{result === ranking.result ? '선택됨' : '선택'}</span></button></td>
+                    <td>{#each ranking.result.formationOrder as cardId}<div>{resultCardName(cardId)} <strong>{ranking.result.cooldownReductions[cardId]}%</strong></div>{/each}</td>
+                    <td><span class:column-maximum={ranking.result.theoreticalMaxScore === cooldownColumnMaxima.score}>{ranking.result.theoreticalMaxScore.toLocaleString('ko-KR')}</span></td>
+                    <td><span class:column-maximum={ranking.result.expectedScore === cooldownColumnMaxima.expected}>{ranking.result.expectedScore.toLocaleString('ko-KR')}</span></td>
+                    <td><span class:column-maximum={ranking.achievementProbabilities?.maximum === cooldownColumnMaxima.maximum}>{probabilityLabel(ranking.achievementProbabilities?.maximum)}</span></td>
+                    <td><span class:column-maximum={ranking.achievementProbabilities?.atLeast995Percent === cooldownColumnMaxima.atLeast995Percent}>{probabilityLabel(ranking.achievementProbabilities?.atLeast995Percent)}</span><small>{scoreThreshold(ranking.result.theoreticalMaxScore, 0.995)}점 이상</small></td>
+                    <td><span class:column-maximum={ranking.achievementProbabilities?.atLeast99Percent === cooldownColumnMaxima.atLeast99Percent}>{probabilityLabel(ranking.achievementProbabilities?.atLeast99Percent)}</span><small>{scoreThreshold(ranking.result.theoreticalMaxScore, 0.99)}점 이상</small></td>
+                    <td><span class:column-maximum={ranking.achievementProbabilities?.atLeast95Percent === cooldownColumnMaxima.atLeast95Percent}>{probabilityLabel(ranking.achievementProbabilities?.atLeast95Percent)}</span><small>{scoreThreshold(ranking.result.theoreticalMaxScore, 0.95)}점 이상</small></td>
+                  </tr>
+                {/each}
+              </tbody>
+            </table>
+          </div>
+        </section>
+      {/if}
       <div class="order-sections">
         <section class="order-section">
           <h3>추천 스페셜 발동 순서</h3>
@@ -1333,6 +1377,22 @@
 </main>
 
 <style>
+  .cooldown-rankings { margin-bottom: 24px; min-width: 0; }
+  .cooldown-rankings .column-maximum { font-weight: 800; }
+  .cooldown-table-scroll { overflow-x: auto; margin-top: 12px; }
+  .cooldown-rankings table { width: 100%; border-collapse: collapse; font-size: 13px; }
+  .cooldown-rankings th, .cooldown-rankings td { padding: 12px; text-align: left; border-bottom: 1px solid #334155; white-space: nowrap; }
+  .cooldown-rankings tr.selected { background: #2d2530; }
+  .cooldown-rankings small { display: block; color: #9caaba; margin-top: 4px; }
+  .cooldown-select { display: grid; justify-items: center; gap: 6px; min-width: 76px; min-height: 64px; padding: 10px 12px; border: 1px solid #414b5b; border-radius: 8px; background: #202630; color: #c1c8d3; font: inherit; cursor: pointer; }
+  .cooldown-rank { font-size: 15px; font-weight: 800; }
+  .cooldown-selection { display: flex; align-items: center; gap: 5px; font-size: 11px; }
+  .cooldown-selection-dot { width: 10px; height: 10px; border: 1px solid currentColor; border-radius: 50%; box-sizing: border-box; }
+  .cooldown-select:hover:not(:disabled) { border-color: #df74a2; color: #f5afcc; background: #2d2530; }
+  .cooldown-select[aria-pressed='true'] { border-color: #ed8bb5; color: #f5afcc; background: #37232e; }
+  .cooldown-select[aria-pressed='true'] .cooldown-selection-dot { background: #ed8bb5; border-color: #ed8bb5; box-shadow: inset 0 0 0 2px #37232e; }
+  .cooldown-select:focus-visible { outline: 2px solid #f1a0c2; outline-offset: 3px; }
+  .cooldown-select:disabled { opacity: .55; cursor: default; }
   .mobile-field-label, .selected-card-name { display: none; }
   .active-window-list { margin: 12px 0; padding: 12px; border: 1px solid #343c49; border-radius: 10px; }
   .active-window-list summary { min-height: 44px; align-content: center; cursor: pointer; font-size: 14px; }