diff --git a/labs/d5/README.md b/labs/d5/README.md new file mode 100644 index 0000000..21bc021 --- /dev/null +++ b/labs/d5/README.md @@ -0,0 +1,40 @@ +# D5 · 三转链式锁构造原型 + +目的:验证在现行规则(消除单调、旋转免费可逆)下,能否稳定构造出**最少需要三次旋转**、且**开局大部分棋子被锁住**的关卡。这是 v0.6 难度曲线里 D5 档的内容来源;v0.5 千关里该档为 0,`createStageSeed` 只能产出两转锁。 + +打开:`npm run dev` 后访问 `/labs/d5/index.html`。只读 `levels/prototypes/d5.json`,不写入主线存档。 + +## 构造方法 + +`src/deep-lock.js` + +1. **`createDeepLock(base)`** — 四子链式锁 A/B/C/D。朝向 0 全部被锁;+1 只有 B 能走;+2(B 走后)只有 C 能走,A 与 D 互锁;转回 +1 放 A,再放 D。网格路线只用来提议,每一阶段都用主游戏的扫掠碰撞 `trace()` 逐条认证,最后由 `solveRotations()` 证明不存在一转或两转的清盘方案。 +2. **`growDeepLevel(base, lock, { target, layerShares })`** — 反向插入更多棋子,按朝向 0 / 1 / 2 分层配额;优先选「在更早的朝向都被挡」的棋子,使它们真正等旋转;每插一枚重新求解,最少旋转数跌破 3 即拒绝。 +3. **`deepLevelStats(level)`** — 锁住占比(首转时剩余)、每次旋转释放数、首转是否只有一侧能开路、波次。 + +## 一次扫描的产出(6 形态 × r3/r4 × 8 种子) + +``` +找到锁 55/96 · 长成 R≥3 关 55 · 旋转次数 {3:47, 4:1, 5:7} +锁住占比中位 78%(v0.5 现状 22%)· 每转释放 ≥2 枚 38/55 · 首转单向 9/55 +随机玩家 动作÷棋子 中位 7.5(v0.5 全库 1.67,v0.4 手作 3.42) +switchback r3、crossing r3 产出 0:小盘上这两种形态找不到满足四子约束的候选 +``` + +重新生成:`node scripts/prototype-d5.mjs --seeds=8 --keep=18`(`--radii=3,4,5` 可含 91 格;默认不含)。 + +## 「无解」问题与可玩性门槛 + +第一批里的第 02 关(orbits r3 s3)被试玩者判为无解。穷举全部 324 个可达状态:0 个死局,参考解在真实界面里也能清盘。问题出在体感:**开局 100% 锁死 + 首转只有右边有效 + 最后一步要转回来**。先往左转的人连看 3 个空朝向,右右之后继续右转的人连看 4 个——两条路都读作"无解"。 + +对策分两层,都已落地: + +1. **结构门槛**(`scripts/prototype-d5.mjs`):`deadTurnAudit()` 穷举玩家可达的全部状态(任意点击顺序、任意旋转序列),证明没有死局,并统计「双向死转态」(卡住时左右各转一次都打不开的状态数)与「最长盲转」。入选关必须:首转两侧都能开路、开局锁住 ≤90%、无不可解可达态;按双向死转态升序排。现在前 4 关这两项都是 0,随机玩家动作÷棋子回到 3.6–6.5。 +2. **反馈**(`labs/d5/app.js`):卡住后闲置 3 秒,正确的旋转按钮开始脉冲并提示方向——即 §07 第 1 条的做法,方向永远不即时给出。任何输入都会清掉提示。 + +## 尚未解决 + +- 随机玩家的动作数仍高于手作版(v0.4 为 3.42);D5 放在第 501 关后是否合适,要真人试玩。 +- 现在的参考解是求解器给出的最短解,不是作者解;正式接入生产时应保留作者见证(同 `createStageSeed`)。 +- 「首转释放 ≥2 枚」只在扫描时排序,未在生长时强制。 +- 「双向死转态 = 0」目前只是排序偏好,不是硬门槛;D5 后段若需要单向关,应配合闲置提示一起上线,不能单独放。 diff --git a/labs/d5/app.js b/labs/d5/app.js new file mode 100644 index 0000000..7111409 --- /dev/null +++ b/labs/d5/app.js @@ -0,0 +1,159 @@ +import { Game, available, trace, solveRotations } from '../../src/core.js'; +import { TapQueue } from '../../src/tap-queue.js'; +import { layout, hitCell } from '../../src/geometry.js'; +import { CanvasPainter, drawScene } from '../../src/renderer.js'; +import { TILE_ATLAS } from '../../src/sprites.js'; +import { exitTiming } from '../../src/exit-animation.js'; +import { MOTION } from '../../src/design-tokens.js'; +import { unlockAudio, playSound } from '../../src/audio.js'; + +const $ = id => document.getElementById(id); +const canvas = $('board'), context = canvas.getContext('2d'), painter = new CanvasPainter(context); +const taps = new TapQueue(); +const reduced = matchMedia('(prefers-reduced-motion: reduce)').matches; +let levels = [], current = null, game = null, view, width, height, animation = null, turning = null, hint = null, path = null, frame = 0; + +const pct = value => `${Math.round(value * 100)}%`; +function describeWitness(actions, tiles) { + // Compress the solver reference into "+1 · 3 枚 · +1 · 2 枚 · −1 · 4 枚". + const parts = []; let taps = 0; + for (const action of actions) { + if (action.type === 'rotate') { if (taps) parts.push(`${taps} 枚`); taps = 0; parts.push(action.direction === 1 ? '右转' : '左转'); } + else taps++; + } + if (taps) parts.push(`${taps} 枚`); + return `参考解:${parts.join(' · ')}(共 ${tiles.length} 枚)`; +} +function showEvidence() { + const p = current.prototype, s = p.stats; + const rows = [ + ['底盘 / 棋子', `${current.cells.length} 格 · ${s.pieces} 枚 · ${p.family} r${p.radius} · seed ${p.seed}`], + ['最少旋转', `${s.rotations} 次`], + ['开局被锁住', `${s.lockedAtStart} / ${s.pieces} 枚(${pct(s.lockedShare)})`], + ['每次旋转释放', s.releasePerTurn.join(' / ') + ' 枚'], + ['首转方向', s.firstTurnDirections === 1 ? '只有一侧能开路' : '两侧都能开路'], + ['主角路线', `${p.lock.heroBends} 弯`], + ['随机玩家 动作 ÷ 棋子', p.monkeyActionsPerPiece.toFixed(2) + '(v0.5 全库 1.67)'], + ]; + $('evidence').innerHTML = rows.map(([k, v]) => `
${k}
${v}
`).join(''); + $('witness').textContent = describeWitness(current.experience.actions, current.tiles); +} +// Stuck-state idle hint: when nothing can leave, wait, then point at the turn +// that opens something. This is the §07 rule — the direction is never shown +// instantly, so "which way" stays the player's move first. +let idleTimer = null; +function clearIdleHint() { clearTimeout(idleTimer); idleTimer = null; for (const id of ['left', 'right']) $(id).classList.remove('hinted'); } +function scheduleIdleHint() { + clearIdleHint(); + if (!game || game.won || animation || turning || available(game.level, game.tiles).length) return; + idleTimer = setTimeout(() => { + const action = solveRotations({ ...game.level, tiles: game.tiles, moveLimit: game.moves }).actions[0]; + if (!action || action.type !== 'rotate') return; + $(action.direction === 1 ? 'right' : 'left').classList.add('hinted'); + $('message').textContent = `这个朝向没有出口。试试向${action.direction === 1 ? '右' : '左'}转。`; + }, 3000); +} +function stats() { + const busy = !!(animation || turning); + if (!busy) scheduleIdleHint(); + $('remaining').textContent = game.tiles.length; + $('progress').textContent = game.won ? '清盘 · 三转到位' : `已放行 ${current.tiles.length - game.tiles.length} / ${current.tiles.length} · 旋转 ${game.rotations}${taps.ids.length ? ` · 待出发 ${taps.ids.length}` : ''}`; + for (const id of ['left', 'right', 'hint']) $(id).disabled = busy || game.won; + $('undo').disabled = busy || !game.history.length; + if (game.won && !busy) $('message').textContent = `清盘。用了 ${game.rotations} 次旋转,参考解 ${current.prototype.stats.rotations} 次。`; +} +function draw(now = performance.now()) { + cancelAnimationFrame(frame); + if (!view || !game) return; + context.clearRect(0, 0, width, height); + const state = { hint, path, reduced, queued: taps.ids }; + if (animation) { + const progress = Math.min(1, (now - animation.start) / animation.duration); + state.animation = { route: animation.route, progress }; + if (progress >= 1) animation = null; + } + if (turning) { + const progress = Math.min(1, (now - turning.start) / turning.duration); + state.boardAngle = -turning.direction * Math.PI / 3 * Math.pow(1 - progress, 3); + if (progress >= 1) turning = null; + } + drawScene(painter, game.level, game.tiles, view, state); + if (!animation && !turning) { + const next = taps.take(game.tiles); + if (next) { tap(next); return; } + } + stats(); + if (animation || turning) frame = requestAnimationFrame(draw); +} +function resize() { + if (!game) return; + const rect = canvas.getBoundingClientRect(), dpr = Math.min(devicePixelRatio || 1, 3); + width = rect.width; height = rect.height; + canvas.width = Math.round(width * dpr); canvas.height = Math.round(height * dpr); + context.setTransform(dpr, 0, 0, dpr, 0, 0); + view = layout(game.level.cells, width, height); draw(); +} +function clearEffects() { taps.clear(); cancelAnimationFrame(frame); animation = null; turning = null; hint = null; path = null; clearIdleHint(); } +canvas.addEventListener('pointerdown', clearIdleHint, { passive: true }); +for (const id of ['left', 'right', 'undo', 'reset', 'hint']) $(id).addEventListener('pointerdown', clearIdleHint, { passive: true }); +function load(index) { + current = levels[index]; clearEffects(); game = new Game(current); + const free = available(game.level, game.tiles).length; + $('message').textContent = free ? `开局有 ${free} 枚能走,其余都在等旋转。` : '开局没有任何棋子能走。转一下,看哪一层松开了。'; + $('meta').textContent = `${current.cells.length} 格 · ${current.tiles.length} 枚 · 最少 ${current.prototype.stats.rotations} 转`; + showEvidence(); resize(); +} +function tap(tile) { + if (game.won) return; + if (animation || turning) { if (taps.add(tile.id, animation?.route.tile.id)) draw(); return; } + hint = null; path = null; + const before = new Set(available(game.level, game.tiles).map(t => t.id)); + const result = game.tap(tile.id); + if (result.status === 'exit') { + animation = { route: result, start: performance.now(), duration: reduced ? 100 : exitTiming(result).duration }; + const opened = available(game.level, game.tiles).filter(t => !before.has(t.id)).length; + $('message').textContent = opened ? `移开这一枚,${opened} 枚棋子的路通了。` : result.steps.length > 3 ? '沿着轨道绕出去了。' : '出去了。'; + playSound('exit'); + } else { + taps.clear(); + if (result.travelPoints) animation = { route: result, start: performance.now(), duration: reduced ? 150 : MOTION.collisionMs }; + $('message').textContent = result.status === 'loop' ? '这条路线绕回原处。转一下底盘换条路。' : '前方有棋子挡住。它在等另一个朝向。'; + playSound('hit'); + } + draw(); +} +function rotate(direction) { + if (animation || turning || game.won) return; + taps.clear(); + const before = new Set(available(game.level, game.tiles).map(t => t.id)); + game.rotate(direction); hint = null; path = null; + const opened = available(game.level, game.tiles).filter(t => !before.has(t.id)).length; + turning = { direction, start: performance.now(), duration: reduced ? 100 : MOTION.rotationMs }; + $('message').textContent = opened ? `这一转松开了 ${opened} 枚。` : '这个朝向什么都没松开。再转,或转回去。'; + playSound('rotate'); draw(); +} +canvas.addEventListener('pointerup', event => { + const rect = canvas.getBoundingClientRect(), cell = hitCell(game.level.cells, view, event.clientX - rect.left, event.clientY - rect.top); + const tile = cell && game.tiles.find(t => t.q === cell.q && t.r === cell.r); + if (tile) tap(tile); +}); +$('left').onclick = () => rotate(-1); +$('right').onclick = () => rotate(1); +$('undo').onclick = () => { if (!animation && !turning && game.undo()) { clearEffects(); $('message').textContent = '回到上一步。'; draw(); } }; +$('reset').onclick = () => load(Number($('level').value)); +$('hint').onclick = () => { + const action = solveRotations({ ...game.level, tiles: game.tiles, moveLimit: game.moves }).actions[0]; + if (!action) return; + if (action.type === 'rotate') { $('message').textContent = `向${action.direction === 1 ? '右' : '左'}转一次。`; } + else { hint = action.id; path = trace(game.level, game.tiles.find(t => t.id === hint), game.tiles); $('message').textContent = '这一枚现在可以走。'; } + draw(); +}; +$('level').onchange = () => load(Number($('level').value)); +document.addEventListener('pointerdown', unlockAudio, { passive: true }); +const atlas = new Image(); atlas.onload = () => { painter.atlas = atlas; draw(); }; atlas.src = '../../' + TILE_ATLAS; +new ResizeObserver(resize).observe(canvas); + +const response = await fetch('../../levels/prototypes/d5.json'); +levels = (await response.json()).levels; +$('level').innerHTML = levels.map((level, i) => ``).join(''); +load(0); diff --git a/labs/d5/index.html b/labs/d5/index.html new file mode 100644 index 0000000..5ffc0b4 --- /dev/null +++ b/labs/d5/index.html @@ -0,0 +1,46 @@ + + + + + + 三转锁 · D5 构造原型 + + + +
+
+ ← 返回主线 + D5 · 三转链式锁 · 原型 +
+
+

THREE TURNS TO CLEAR

+

三转锁 深旋转

+

开局几乎全锁。转一次放一层,转两次放一层,转回来放主角。

+
+
+ + + +
+
待离场 0已放行 0 / 0 · 旋转 0
+
+

先找找有没有能直接走的棋子——多半没有。转一下。

+ +
+

结构证据

+
+

+
+ +
+ + + diff --git a/labs/d5/style.css b/labs/d5/style.css new file mode 100644 index 0000000..25de62b --- /dev/null +++ b/labs/d5/style.css @@ -0,0 +1,41 @@ +:root{font-family:system-ui,-apple-system,"PingFang SC",sans-serif;color:#33414d;background:#e9edf0;font-synthesis:none} +*{box-sizing:border-box} +body{margin:0} +main{max-width:900px;margin:auto;padding:16px 28px 24px} +header{display:flex;align-items:center;justify-content:space-between;gap:12px} +.back{color:#526575;text-decoration:none;font-size:13px} +.badge{font-size:11px;letter-spacing:.08em;color:#4d6478;border:1px solid #b9c7d2;border-radius:20px;padding:7px 12px} +.intro{text-align:center;margin:10px 0 12px} +.eyebrow{font-size:10px;letter-spacing:.24em;color:#6b7f90} +h1{font-size:28px;letter-spacing:.15em;margin:7px 0 10px;font-weight:650} +h1 small{font-size:13px;letter-spacing:.1em;font-weight:500;vertical-align:middle;border-left:1px solid #b9c7d2;margin-left:5px;padding-left:12px;color:#6b7f90} +.intro>p:last-child{font-size:13px;margin:0;color:#65717b} +.picker{display:flex;align-items:center;justify-content:center;gap:10px;flex-wrap:wrap;margin:6px auto 10px;font-size:12px;color:#526575} +.picker select{font:13px system-ui;padding:7px 10px;border:1px solid #b9c7d2;border-radius:10px;background:#fff;color:#33414d;max-width:100%} +.picker .meta{font-variant-numeric:tabular-nums;color:#6b7f90} +.status{display:flex;align-items:center;justify-content:space-between;gap:12px;max-width:620px;margin:auto;font-size:12px;color:#65717b} +.status strong{font-size:24px;color:#33414d;margin-left:6px} +#progress{font-size:11px;font-variant-numeric:tabular-nums} +.board-wrap{width:100%;height:clamp(400px,calc(100svh - 360px),700px);min-height:380px} +canvas{width:100%;height:100%;display:block;touch-action:manipulation} +.message{margin:4px 0 16px;text-align:center;font-size:13px;min-height:36px;line-height:1.6} +.controls{display:flex;justify-content:center;gap:14px} +button{font:24px 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+.evidence dl>div{display:flex;justify-content:space-between;gap:10px;border-bottom:1px dashed #d8e0e6;padding-bottom:6px} +.evidence dt{color:#6b7f90} +.evidence dd{margin:0;font-variant-numeric:tabular-nums;text-align:right;color:#33414d} +.witness{margin:12px 0 0;font-size:12px;color:#526575;font-variant-numeric:tabular-nums;text-align:center} +footer{text-align:center;margin:18px auto 0;max-width:560px;font-size:11px;color:#6b757e;line-height:1.7} +footer code{font-family:ui-monospace,Menlo,monospace;font-size:10.5px;background:#dfe6ec;padding:1px 4px;border-radius:3px} +@media(max-width:540px){main{padding:16px 14px 20px}.board-wrap{height:380px;min-height:0}.controls{gap:9px}button{min-width:57px;min-height:60px;padding:5px 9px}.message{font-size:12px;margin-bottom:12px}.evidence dl{grid-template-columns:1fr}} +@media(prefers-reduced-motion:reduce){button:active{transform:none}} diff --git a/levels/prototypes/d5.json b/levels/prototypes/d5.json new file mode 100644 index 0000000..2345eef --- /dev/null +++ b/levels/prototypes/d5.json @@ -0,0 +1,26766 @@ +{ + "generated": "prototype-d5", + "version": 1, + "options": { + "seeds": 8, + "target": 12, + "radii": [ + 3, + 4 + ] + }, + "summary": { + "candidates": 55, + "kept": 18, + "yieldTable": { + "petals/r3": { + "locks": 6, + "grown": 6, + "seeds": 8 + }, + "petals/r4": { + "locks": 3, + "grown": 3, + "seeds": 8 + }, + "orbits/r3": { + "locks": 8, + "grown": 8, + "seeds": 8 + }, + "orbits/r4": { + "locks": 8, + "grown": 8, + "seeds": 8 + }, + "spiral/r3": { + "locks": 4, + "grown": 4, + "seeds": 8 + }, + "spiral/r4": { + "locks": 7, + "grown": 7, + "seeds": 8 + }, + "switchback/r3": { + "locks": 0, + "grown": 0, + "seeds": 8 + }, + "switchback/r4": { + "locks": 6, + "grown": 6, + "seeds": 8 + }, + "weave/r3": { + "locks": 4, + "grown": 4, + "seeds": 8 + }, + "weave/r4": { + "locks": 8, + "grown": 8, + "seeds": 8 + }, + "crossing/r3": { + "locks": 0, + "grown": 0, + "seeds": 8 + }, + "crossing/r4": { + 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"bends": 27, + "featuredPairs": 61 + }, + { + "q": -1, + "r": 0, + "dir": 2, + "steps": 62, + "bends": 27, + "featuredPairs": 61 + }, + { + "q": -4, + "r": 4, + "dir": 0, + "steps": 61, + "bends": 26, + "featuredPairs": 60 + }, + { + "q": 0, + "r": 0, + "dir": 1, + "steps": 61, + "bends": 26, + "featuredPairs": 60 + }, + { + "q": -4, + "r": 3, + "dir": 0, + "steps": 60, + "bends": 26, + "featuredPairs": 59 + }, + { + "q": 1, + "r": -1, + "dir": 5, + "steps": 60, + "bends": 25, + "featuredPairs": 59 + }, + { + "q": -4, + "r": 2, + "dir": 0, + "steps": 59, + "bends": 26, + "featuredPairs": 58 + }, + { + "q": 0, + "r": -1, + "dir": 4, + "steps": 59, + "bends": 24, + "featuredPairs": 58 + }, + { + "q": -4, + "r": 1, + "dir": 0, + "steps": 58, + "bends": 26, + "featuredPairs": 57 + }, + { + "q": -1, + "r": 0, + "dir": 3, + "steps": 58, + "bends": 23, + "featuredPairs": 57 + }, + { + "q": -4, + "r": 0, + "dir": 1, + "steps": 57, + "bends": 25, + "featuredPairs": 56 + }, + { + "q": -1, + "r": 1, + "dir": 2, + "steps": 57, + "bends": 22, + "featuredPairs": 56 + }, + { + "q": -3, + "r": -1, + "dir": 1, + "steps": 56, + "bends": 25, + "featuredPairs": 55 + }, + { + "q": 0, + "r": 1, + "dir": 1, + "steps": 56, + "bends": 21, + "featuredPairs": 55 + }, + { + "q": -2, + "r": -2, + "dir": 1, + "steps": 55, + "bends": 25, + "featuredPairs": 54 + }, + { + "q": 1, + "r": 0, + "dir": 2, + "steps": 55, + "bends": 20, + "featuredPairs": 54 + }, + { + "q": -1, + "r": -3, + "dir": 1, + "steps": 54, + "bends": 25, + "featuredPairs": 53 + }, + { + "q": 2, + "r": 0, + "dir": 0, + "steps": 54, + "bends": 19, + "featuredPairs": 53 + }, + { + "q": 0, + "r": -4, + "dir": 2, + "steps": 53, + "bends": 24, + "featuredPairs": 52 + }, + { + "q": 2, + "r": -1, + "dir": 0, + "steps": 53, + "bends": 19, + "featuredPairs": 52 + }, + { + "q": 1, + "r": -4, + "dir": 2, + "steps": 52, + "bends": 24, + "featuredPairs": 51 + }, + { + "q": 2, + "r": -2, + "dir": 5, + "steps": 52, + "bends": 18, + "featuredPairs": 51 + }, + { + "q": 2, + "r": -4, + "dir": 2, + "steps": 51, + "bends": 24, + "featuredPairs": 50 + }, + { + "q": 1, + "r": -2, + "dir": 5, + "steps": 51, + "bends": 18, + "featuredPairs": 50 + }, + { + "q": 3, + "r": -4, + "dir": 2, + "steps": 50, + "bends": 24, + "featuredPairs": 49 + }, + { + "q": 0, + "r": -2, + "dir": 4, + "steps": 50, + "bends": 17, + "featuredPairs": 49 + }, + { + "q": 4, + "r": -4, + "dir": 3, + "steps": 49, + "bends": 23, + "featuredPairs": 48 + }, + { + "q": -1, + "r": -1, + "dir": 4, + "steps": 49, + "bends": 17, + "featuredPairs": 48 + }, + { + "q": 4, + "r": -3, + "dir": 3, + "steps": 48, + "bends": 23, + "featuredPairs": 47 + }, + { + "q": -2, + "r": 0, + "dir": 3, + "steps": 48, + "bends": 16, + "featuredPairs": 47 + } + ] + }, + "experience": { + "kind": "deep", + "feature": { + "id": "t0" + }, + "actions": [ + { + "type": "tap", + "id": "t6" + }, + { + "type": "tap", + "id": "t8" + }, + { + "type": "tap", + "id": "t11" + }, + { + "type": "tap", + "id": "t10" + }, + { + "type": "tap", + "id": "t9" + }, + { + "type": "rotate", + "direction": 1 + }, + { + "type": "tap", + "id": "t5" + }, + { + "type": "tap", + "id": "t7" + }, + { + "type": "tap", + "id": "t1" + }, + { + "type": "tap", + "id": "t4" + }, + { + "type": "rotate", + "direction": 1 + }, + { + "type": "tap", + "id": "t2" + }, + { + "type": "rotate", + "direction": -1 + }, + { + "type": "tap", + "id": "t0" + }, + { + "type": "tap", + "id": "t3" + } + ] + }, + "prototype": { + "family": "spiral", + "radius": 4, + "seed": 1, + "target": 12, + "lock": { + "hero": "t0", + "heroBends": 9, + "search": { + "checks": 41798, + "formalChecks": 41798, + "heroCandidates": 100, + "poolSize": 366 + } + }, + "placements": [ + 1, + 1, + 2, + 1, + 2, + 1, + 0, + 1, + 0, + 2, + 1, + 0 + ], + "rejected": { + "orientationless": 450, + "shortcut": 0 + }, + "stats": { + "pieces": 12, + "rotations": 3, + "lockedShare": 0.5833333333333334, + "lockedAtStart": 7, + "firstTurnDirections": 2, + "releasePerTurn": [ + 4, + 1, + 2 + ], + "minRelease": 1, + "waves": [ + 3, + 1, + 1, + 2, + 1, + 1, + 1, + 1, + 1 + ], + "states": 9 + }, + "audit": { + "states": 2094, + "stuckStates": 30, + "doubleDead": 6, + "maxDeadTurns": 2, + "unsolvable": 0, + "exhausted": false + }, + "monkeyActionsPerPiece": 6.739583333333333 + } + } + ] +} \ No newline at end of file diff --git a/scripts/prototype-d5.mjs b/scripts/prototype-d5.mjs new file mode 100644 index 0000000..11f21f3 --- /dev/null +++ b/scripts/prototype-d5.mjs @@ -0,0 +1,100 @@ +#!/usr/bin/env node +// D5 (three-turn) construction prototype. Sweeps route families and seeds, +// grows each chain lock into a full level, and writes a small playable set. +// Usage: node scripts/prototype-d5.mjs [--seeds=8] [--target=12] [--keep=18] [--out=levels/prototypes/d5.json] +import { mkdirSync, writeFileSync } from 'node:fs'; +import { dirname, resolve } from 'node:path'; +import { Game, random } from '../src/core.js'; +import { createRouteBoard, ROUTE_FAMILIES } from '../src/route-grammar.js'; +import { createDeepLock, growDeepLevel, deepLevelStats, deepLevelKey, deadTurnAudit } from '../src/deep-lock.js'; + +const args = Object.fromEntries(process.argv.slice(2).map(a => { const [k, v] = a.replace(/^--/, '').split('='); return [k, v ?? true]; })); +const SEEDS = Number(args.seeds ?? 8), TARGET = Number(args.target ?? 12), KEEP = Number(args.keep ?? 18); +const OUT = resolve(args.out ?? 'levels/prototypes/d5.json'); +// 91-cell boards stay out by default: they are a readability problem, not a difficulty band. +const RADII = String(args.radii ?? '3,4').split(',').map(Number); +const MIN_PIECES = Number(args.minPieces ?? 8); + +// Random player: taps a random piece; after three blocked taps in a row, turns randomly. +function monkeyActionsPerPiece(level, runs = 8) { + let total = 0; + for (let run = 0; run < runs; run++) { + const rng = random(4242 + run * 31), game = new Game(level); + let actions = 0, streak = 0; + while (!game.won && !game.lost && actions < 800) { + if (streak >= 3) { game.rotate(rng() < .5 ? 1 : -1); actions++; streak = 0; continue; } + const tile = game.tiles[Math.floor(rng() * game.tiles.length)]; + const result = game.tap(tile.id); actions++; + if (result.status === 'exit') streak = 0; else streak++; + } + total += game.won ? actions / level.tiles.length : 999; + } + return total / runs; +} + +const started = Date.now(); +const rows = [], seen = new Set(); +const yieldTable = {}; +for (const { id: family } of ROUTE_FAMILIES) for (const radius of RADII) { + const cellKey = `${family}/r${radius}`; + yieldTable[cellKey] = { locks: 0, grown: 0, seeds: SEEDS }; + for (let seed = 0; seed < SEEDS; seed++) { + const base = createRouteBoard(seed, { family, radius }); + const lock = createDeepLock(base, { seed, maxChecks: 600000 }); + if (!lock) continue; + yieldTable[cellKey].locks++; + const target = Math.min(TARGET, { 3: 9, 4: 12, 5: 14 }[radius]); + const grown = growDeepLevel(base, lock, { seed, target }); + const level = grown.level; + if (grown.solution.rotations < 3) continue; + const signature = deepLevelKey(level); + if (seen.has(signature)) continue; + seen.add(signature); + yieldTable[cellKey].grown++; + const stats = deepLevelStats(level); + const audit = deadTurnAudit(level); + const apt = monkeyActionsPerPiece(level); + level.id = `proto-d5-${family}-r${radius}-s${seed}`; + level.prototype = { family, radius, seed, target, lock: { hero: lock.hero.id, heroBends: lock.heroRoute.bends, search: lock.search }, placements: grown.placements, rejected: grown.rejected, stats, audit, monkeyActionsPerPiece: apt }; + rows.push({ level, stats, audit, apt, family, radius, seed }); + } +} + +// A bare four-piece lock is 100% locked by definition; only fully grown levels +// count. The playable set also refuses what reads as "unsolvable": a fully +// locked opening, a first turn that only works one way, or any stuck state +// where neither adjacent orientation opens anything. +const grownEnough = rows.filter(r => r.stats.pieces >= MIN_PIECES); +const playable = grownEnough.filter(r => r.audit.unsolvable === 0 && r.stats.firstTurnDirections === 2 && r.stats.lockedShare <= .9); +playable.sort((a, b) => (a.audit.doubleDead - b.audit.doubleDead) || (b.stats.minRelease - a.stats.minRelease) || (b.stats.lockedShare - a.stats.lockedShare) || (a.apt - b.apt)); +console.log(`\n【可玩性门槛】长成 ${grownEnough.length} 关 → 首转双向 ${grownEnough.filter(r => r.stats.firstTurnDirections === 2).length} → 开局锁住 ≤90% ${grownEnough.filter(r => r.stats.firstTurnDirections === 2 && r.stats.lockedShare <= .9).length} → 无不可解可达态 ${playable.length}`); +const kept = []; +const perFamily = {}; +for (const row of playable) { + perFamily[row.family] = (perFamily[row.family] || 0); + if (perFamily[row.family] >= Math.ceil(KEEP / ROUTE_FAMILIES.length) + 1) continue; + perFamily[row.family]++; + kept.push(row); + if (kept.length >= KEEP) break; +} + +const pad = (v, w) => String(v).padStart(w); +console.log(`D5 三转构造原型 · ${ROUTE_FAMILIES.length} 形态 × ${RADII.length} 尺寸 × ${SEEDS} 种子 · ${((Date.now() - started) / 1000).toFixed(1)} s`); +console.log('\n【产出率】形态/尺寸 找到锁 长成 R=3 关'); +for (const [k, v] of Object.entries(yieldTable)) console.log(' ' + k.padEnd(18) + pad(v.locks, 5) + '/' + v.seeds + pad(v.grown, 9) + '/' + v.seeds); +const all = rows.map(r => r.stats); +const med = arr => { const s = [...arr].sort((a, b) => a - b); return s.length ? s[Math.floor(s.length / 2)] : NaN; }; +console.log(`\n【全部 ${rows.length} 个 R≥3 关卡】`); +console.log(` 旋转次数分布: ${JSON.stringify(all.reduce((m, s) => (m[s.rotations] = (m[s.rotations] || 0) + 1, m), {}))}`); +console.log(` 锁住占比(首转时剩余)中位 ${(med(all.map(s => s.lockedShare)) * 100).toFixed(0)}% (v0.5 现状中位 22%)`); +console.log(` 每次旋转最少释放 ≥2 枚的关: ${all.filter(s => s.minRelease >= 2).length}/${all.length}`); +console.log(` 首转只有一侧能开路的关: ${all.filter(s => s.firstTurnDirections === 1).length}/${all.length}`); +console.log(` 猴子 动作/棋子 中位 ${med(rows.map(r => r.apt)).toFixed(2)} (v0.5 全库 1.67 · v0.4 手作 3.42)`); +console.log(`\n【写入 ${kept.length} 关】`); +console.log(' id 格 枚 R 锁住% 每转释放 首转方向 双向死转态 最长盲转 猴子APT hero弯'); +for (const { level, stats, audit, apt } of kept) console.log(' ' + level.id.padEnd(36) + pad(level.cells.length, 3) + pad(stats.pieces, 4) + pad(stats.rotations, 3) + pad((stats.lockedShare * 100).toFixed(0) + '%', 7) + ' ' + stats.releasePerTurn.join('/').padEnd(12) + pad(stats.firstTurnDirections === 1 ? '单向' : '双向', 6) + pad(audit.doubleDead, 10) + pad(audit.maxDeadTurns, 9) + pad(apt.toFixed(2), 9) + pad(level.prototype.lock.heroBends, 7)); +console.log('\n 「双向死转态」= 可达的卡住状态里,左右各转一次都打不开任何棋子的状态数;「最长盲转」= 从某个可达卡住态朝错误方向连转、遇到第一个有效朝向前经过的空朝向数。'); + +mkdirSync(dirname(OUT), { recursive: true }); +writeFileSync(OUT, JSON.stringify({ generated: 'prototype-d5', version: 1, options: { seeds: SEEDS, target: TARGET, radii: RADII }, summary: { candidates: rows.length, kept: kept.length, yieldTable }, levels: kept.map(r => r.level) }, null, 1)); +console.log(`\n已写入 ${OUT}`); diff --git a/src/deep-lock.js b/src/deep-lock.js new file mode 100644 index 0000000..a82bcd3 --- /dev/null +++ b/src/deep-lock.js @@ -0,0 +1,213 @@ +import { available, key, opposite, random, rotateBoard, solveRotations, trace, validateLevel } from './core.js'; + +const positionKey = tile => `${tile.q},${tile.r}`; +const countBends = route => route.steps.filter(step => step.enter !== null && opposite(step.enter) !== step.exit).length; + +function shuffled(items, rng) { + const result = [...items]; + for (let i = result.length - 1; i > 0; i--) { + const j = Math.floor(rng() * (i + 1)); + [result[i], result[j]] = [result[j], result[i]]; + } + return result; +} + +// Every candidate carries its independent route at orientations 0, 1 and 2. +// Grid membership only proposes a lock; the swept tracer certifies it below. +function candidatePool(base, boards, maxBends) { + const pool = []; + for (const cell of base.cells) for (let dir = 0; dir < 6; dir++) { + const tile = { q: cell.q, r: cell.r, dir }; + const routes = [0, 1, 2].map(turn => trace(boards[turn], tile, [], true)); + if (routes.some(route => route.status !== 'exit')) continue; + const bends = routes.map(countBends); + if (bends[1] > maxBends) continue; + pool.push({ + tile, position: positionKey(tile), bends, cells: routes.map(route => route.steps.length), + at: routes.map(route => new Set(route.steps.slice(1).map(positionKey))), + }); + } + return pool; +} + +// A/B/C/D is a three-turn chain, not three independent long routes. +// At 0 all four are locked. At +1 only B can leave. At +2 only C can leave; +// A and D still hold each other. Turning back to +1 frees A, then D. +// The solver certifies that no one- or two-turn plan clears the board. +export function createDeepLock(base, { + seed = 0, minHeroBends = 6, maxHeroBends = 70, maxChecks = 2000000, +} = {}) { + const rng = random(seed); + const boards = [0, 1, 2].map(turn => rotateBoard(base, turn)); + const pool = candidatePool(base, boards, maxHeroBends); + const candidates = shuffled(pool, rng); + const heroes = candidates.filter(c => c.bends[1] >= minHeroBends); + let checks = 0, formalChecks = 0; + for (const a of heroes) { + // D holds A at 0 and at +2, and never stands on A's +1 departure. + const tails = candidates.filter(d => d.position !== a.position + && a.at[0].has(d.position) && d.at[0].has(a.position) + && a.at[2].has(d.position) && d.at[2].has(a.position) + && !a.at[1].has(d.position)); + for (const d of tails) { + // C holds A at +1 and leaves alone at +2 once B is gone. + const seconds = candidates.filter(c => c.position !== a.position && c.position !== d.position + && a.at[1].has(c.position) && !c.at[2].has(a.position) && !c.at[2].has(d.position)); + for (const c of seconds) { + // B is A's blocker at 0 and is the only piece that leaves at +1. + const gates = candidates.filter(b => b.position !== a.position && b.position !== c.position && b.position !== d.position + && a.at[0].has(b.position) && !b.at[1].has(a.position) && !b.at[1].has(c.position) && !b.at[1].has(d.position) + && (c.at[1].has(a.position) || c.at[1].has(d.position) || c.at[1].has(b.position))); + for (const b of gates) { + if (++checks > maxChecks) return null; + const tiles = [a, b, c, d].map((candidate, i) => ({ ...candidate.tile, id: `t${i}`, color: i })); + const [hero, gate, second, tail] = tiles; + formalChecks++; + // Formal certification of every stage with the production swept tracer. + if (tiles.some(tile => trace(boards[0], tile, tiles).status === 'exit')) continue; + if (trace(boards[1], gate, tiles).status !== 'exit') continue; + const afterGate = [hero, second, tail]; + if (afterGate.some(tile => trace(boards[1], tile, afterGate).status === 'exit')) continue; + if (trace(boards[2], second, afterGate).status !== 'exit') continue; + const afterSecond = [hero, tail]; + if (afterSecond.some(tile => trace(boards[2], tile, afterSecond).status === 'exit')) continue; + if (trace(boards[1], hero, afterSecond).status !== 'exit') continue; + if (trace(boards[1], tail, [tail]).status !== 'exit') continue; + const level = { ...base, tiles, moveLimit: tiles.length }; + const solution = solveRotations(level); + if (!solution.solvable || solution.exhausted || solution.rotations !== 3) continue; + return { + tiles, placements: [1, 1, 2, 1], hero, + heroRoute: { bends: a.bends[1], cells: a.cells[1] }, + actions: [ + { type: 'rotate', direction: 1 }, { type: 'tap', id: gate.id }, + { type: 'rotate', direction: 1 }, { type: 'tap', id: second.id }, + { type: 'rotate', direction: -1 }, { type: 'tap', id: hero.id }, { type: 'tap', id: tail.id }, + ], + minimumRotations: solution.rotations, solution, + search: { checks, formalChecks, heroCandidates: heroes.length, poolSize: pool.length }, + }; + } + } + } + } + return null; +} + +// Reverse insertion keeps the chain intact while raising how much of the +// board depends on turning. Each inserted piece must leave at its scheduled +// orientation, and the solver must still need exactly three turns afterwards. +export function growDeepLevel(base, lock, { + seed = 0, target = 12, layerShares = { 0: .35, 1: .35, 2: .3 }, maxHeroBends = 70, minRotations = 3, +} = {}) { + const rng = random(seed + 7919); + const boards = [0, 1, 2].map(turn => rotateBoard(base, turn)); + // A layer piece only needs a departure at its own orientation. Requiring + // exits at every orientation would leave almost nothing to insert. + const layerPool = boards.map(board => { + const pool = []; + for (const cell of base.cells) for (let dir = 0; dir < 6; dir++) { + const tile = { q: cell.q, r: cell.r, dir }, route = trace(board, tile, [], true); + if (route.status === 'exit' && countBends(route) <= maxHeroBends) pool.push({ tile, position: positionKey(tile), bends: countBends(route) }); + } + return pool; + }); + const tiles = [...lock.tiles], placements = [...lock.placements]; + const extras = Math.max(0, target - tiles.length); + const schedule = []; + for (const [turn, share] of Object.entries(layerShares)) for (let i = 0; i < Math.round(extras * share); i++) schedule.push(Number(turn)); + while (schedule.length < extras) schedule.push(0); + schedule.length = extras; + let rejected = { orientationless: 0, shortcut: 0 }; + for (const orientation of shuffled(schedule, rng)) { + const occupied = new Set(tiles.map(positionKey)); + const choices = shuffled(layerPool[orientation].filter(c => !occupied.has(c.position)), rng); + let chosen = null, fallback = null; + for (const c of choices) { + const tile = { ...c.tile, id: `t${tiles.length}`, color: tiles.length % 7 }, proposed = [...tiles, tile]; + if (trace(boards[orientation], tile, proposed).status !== 'exit') { rejected.orientationless++; continue; } + // Prefer pieces that genuinely wait for this turn: blocked at every earlier orientation. + const waits = [...Array(orientation).keys()].every(earlier => trace(boards[earlier], tile, proposed).status !== 'exit'); + if (!waits && fallback) continue; + const solution = solveRotations({ ...base, tiles: proposed, moveLimit: proposed.length }); + if (!solution.solvable || solution.exhausted || solution.rotations < minRotations) { rejected.shortcut++; continue; } + if (waits) { chosen = tile; break; } + fallback = tile; + } + chosen = chosen || fallback; + if (!chosen) break; + tiles.push(chosen); placements.push(orientation); + } + const level = { + ...base, tiles, moveLimit: tiles.length, + name: `${(base.name || 'route').replace(' · 路线草图', '')} · 深旋转`, + experience: { kind: 'deep', feature: { id: lock.hero.id } }, + }; + const solution = solveRotations(level); + level.experience.actions = solution.actions; + const errors = validateLevel(level); + if (errors.length) throw new Error(errors.join('; ')); + return { level, placements, solution, rejected }; +} + +// Structural evidence for the difficulty bands: how much of the board waits +// for a turn, how many pieces each turn releases, and whether the direction +// of the first turn is a real choice. +export function deepLevelStats(level) { + const n = level.tiles.length, solution = solveRotations(level); + let board = level, remaining = [...level.tiles]; + const drain = () => { for (;;) { const free = available(board, remaining); if (!free.length) return; const ids = new Set(free.map(t => t.id)); remaining = remaining.filter(t => !ids.has(t.id)); } }; + drain(); + const lockedAtStart = remaining.length; + const openings = [1, -1].filter(direction => available(rotateBoard(board, direction), remaining).length > 0).length; + const releases = []; + for (const action of solution.actions) { + if (action.type !== 'rotate') continue; + const before = remaining.length; + board = rotateBoard(board, action.direction); + drain(); + releases.push(before - remaining.length); + } + return { + pieces: n, rotations: solution.rotations, lockedShare: lockedAtStart / n, lockedAtStart, + firstTurnDirections: openings, releasePerTurn: releases, minRelease: releases.length ? Math.min(...releases) : 0, + waves: solution.waves.map(wave => wave.length), states: solution.states, + }; +} + +// Player-side audit over every reachable state (any tap order, any turn +// sequence). Removal only reduces occupancy and turns are reversible, so no +// reachable state can be unsolvable — the audit proves it rather than assuming +// it — and it measures how many blind turns a player can run into. +export function deadTurnAudit(level, maxStates = 20000) { + const boards = Array.from({ length: 6 }, (_, i) => rotateBoard(level, i)); + const keyOf = (o, rem) => o + ':' + [...rem].sort().join(','); + const start = { o: 0, rem: new Set(level.tiles.map(t => t.id)) }; + const seen = new Map([[keyOf(0, start.rem), start]]), queue = [start]; + let stuckStates = 0, doubleDead = 0, maxDeadTurns = 0, unsolvable = 0; + while (queue.length && seen.size < maxStates) { + const state = queue.shift(); + if (!state.rem.size) continue; + const tiles = level.tiles.filter(t => state.rem.has(t.id)), free = available(boards[state.o], tiles); + if (!free.length) { + stuckStates++; + if (![1, -1].some(d => available(boards[(state.o + d + 6) % 6], tiles).length)) doubleDead++; + let nearest = 6; + for (const d of [1, -1]) for (let k = 1; k < 6; k++) if (available(boards[(state.o + d * k + 6) % 6], tiles).length) { nearest = Math.min(nearest, k); break; } + if (nearest === 6) unsolvable++; else maxDeadTurns = Math.max(maxDeadTurns, nearest - 1); + } + for (const t of free) { + const rem = new Set(state.rem); rem.delete(t.id); + const k = keyOf(state.o, rem); + if (!seen.has(k)) { const next = { o: state.o, rem }; seen.set(k, next); queue.push(next); } + } + for (const d of [1, -1]) { + const o = (state.o + d + 6) % 6, k = keyOf(o, state.rem); + if (!seen.has(k)) { const next = { o, rem: state.rem }; seen.set(k, next); queue.push(next); } + } + } + return { states: seen.size, stuckStates, doubleDead, maxDeadTurns, unsolvable, exhausted: seen.size >= maxStates }; +} + +export const deepLevelKey = level => level.tiles.map(t => `${t.q},${t.r},${t.dir}`).sort().join('|'); +export { key as cellKey }; diff --git a/tests/deep-lock.test.js b/tests/deep-lock.test.js new file mode 100644 index 0000000..a6399e1 --- /dev/null +++ b/tests/deep-lock.test.js @@ -0,0 +1,78 @@ +import test from 'node:test'; +import assert from 'node:assert/strict'; +import { Game, rotateBoard, solveRotations, trace, validateLevel } from '../src/core.js'; +import { createRouteBoard } from '../src/route-grammar.js'; +import { createDeepLock, growDeepLevel, deepLevelStats, deadTurnAudit } from '../src/deep-lock.js'; + +// Seeds known to yield a chain lock; the sweep script records the full yield table. +const WITNESSES = [ + { family: 'orbits', radius: 3, seed: 0 }, + { family: 'weave', radius: 4, seed: 0 }, + { family: 'spiral', radius: 4, seed: 1 }, + { family: 'switchback', radius: 4, seed: 0 }, +]; + +for (const { family, radius, seed } of WITNESSES) { + test(`${family} r${radius}: three-turn chain is certified stage by stage and by the solver`, () => { + const base = createRouteBoard(seed, { family, radius }); + const snapshot = JSON.stringify(base); + const lock = createDeepLock(base, { seed }); + assert.ok(lock, `${family}, radius ${radius}, seed ${seed}`); + assert.equal(JSON.stringify(base), snapshot, 'The helper must not alter its input route'); + assert.equal(lock.minimumRotations, 3); + assert.ok(lock.heroRoute.bends >= 6); + + const level = { ...base, tiles: lock.tiles, moveLimit: lock.tiles.length }; + assert.deepEqual(validateLevel(level), []); + assert.equal(solveRotations(level).rotations, 3, 'No one- or two-turn plan may clear the chain'); + const [hero, gate, second, tail] = lock.tiles; + const at = turn => rotateBoard(level, turn); + assert.ok(lock.tiles.every(tile => trace(level, tile).status === 'blocked'), 'Everything is locked at the opening'); + assert.equal(trace(at(1), gate).status, 'exit', 'Only the gate leaves at +1'); + assert.ok([hero, second, tail].every(tile => trace(at(1), tile, [hero, second, tail]).status === 'blocked')); + assert.equal(trace(at(2), second, [hero, second, tail]).status, 'exit', 'The second gate leaves at +2'); + assert.equal(trace(at(2), hero, [hero, tail]).status, 'blocked', 'Hero and tail hold each other at +2'); + assert.equal(trace(at(2), tail, [hero, tail]).status, 'blocked'); + assert.equal(trace(at(1), hero, [hero, tail]).status, 'exit', 'Turning back frees the hero'); + + const game = new Game(level); + for (const action of lock.actions) { + if (action.type === 'rotate') game.rotate(action.direction); + else assert.equal(game.tap(action.id).status, 'exit'); + } + assert.equal(game.tiles.length, 0, 'The authored three-turn witness must fully clear the board'); + assert.equal(game.rotations, 3); + }); + + test(`${family} r${radius}: growth keeps three turns and locks most of the board`, () => { + const base = createRouteBoard(seed, { family, radius }); + const lock = createDeepLock(base, { seed }); + const target = radius === 3 ? 9 : 12; + const { level, solution, placements } = growDeepLevel(base, lock, { seed, target }); + assert.deepEqual(validateLevel(level), []); + assert.ok(level.tiles.length >= target - 2, `grew to ${level.tiles.length} of ${target}`); + assert.equal(placements.length, level.tiles.length); + assert.ok(solution.solvable && !solution.exhausted); + assert.ok(solution.rotations >= 3, 'Inserted pieces must not open a shorter plan'); + const stats = deepLevelStats(level); + assert.ok(stats.lockedShare >= .5, `locked share ${stats.lockedShare}`); + assert.equal(stats.releasePerTurn.length, stats.rotations); + // Every state a player can reach — any tap order, any turn sequence — must still clear. + const audit = deadTurnAudit(level); + assert.ok(!audit.exhausted, 'audit must enumerate every reachable state'); + assert.equal(audit.unsolvable, 0, 'no reachable state may be a dead end'); + const game = new Game(level); + for (const action of level.experience.actions) { + if (action.type === 'rotate') game.rotate(action.direction); + else assert.equal(game.tap(action.id).status, 'exit'); + } + assert.ok(game.won, 'The solver reference must clear the grown level'); + }); +} + +test('deep lock search is deterministic and an unmet constraint returns no lock', () => { + const base = createRouteBoard(0, { family: 'orbits', radius: 3 }); + assert.deepEqual(createDeepLock(base, { seed: 5 }), createDeepLock(base, { seed: 5 })); + assert.equal(createDeepLock(base, { minHeroBends: 999 }), null); + assert.equal(createDeepLock(base, { maxChecks: 0 }), null); +});