1.8.0

package-lock.json

@@ -1,12 +1,12 @@
 {
   "name": "vue-nonograms-solid",
-  "version": "1.7.0",
+  "version": "1.8.0",
   "lockfileVersion": 3,
   "requires": true,
   "packages": {
     "": {
       "name": "vue-nonograms-solid",
-      "version": "1.7.0",
+      "version": "1.8.0",
       "dependencies": {
         "fireworks-js": "^2.10.8",
         "flag-icons": "^7.5.0",

package.json

@@ -1,6 +1,6 @@
 {
   "name": "vue-nonograms-solid",
-  "version": "1.7.0",
+  "version": "1.8.0",
   "type": "module",
   "scripts": {
     "dev": "vite",

scripts/simulate_difficulty.js

@@ -0,0 +1,75 @@
+
+import fs from 'fs';
+import path from 'path';
+import { generateRandomGrid, calculateHints } from '../src/utils/puzzleUtils.js';
+import { solvePuzzle } from '../src/utils/solver.js';
+
+const OUTPUT_FILE = 'difficulty_simulation_results.json';
+const CSV_FILE = 'difficulty_simulation_results.csv';
+
+// Configuration
+const SIZES = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80]; // Steps of 5 up to 50, then 10
+const DENSITIES = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9];
+const SAMPLES_PER_POINT = 20; // Adjust based on time/accuracy needs
+
+console.log('Starting Monte Carlo Simulation for Nonogram Difficulty...');
+console.log(`Config: Sizes=${SIZES.length}, Densities=${DENSITIES.length}, Samples=${SAMPLES_PER_POINT}`);
+
+const results = [];
+const csvRows = ['size,density,avg_solved_percent,min_solved_percent,max_solved_percent,avg_time_ms'];
+
+const startTime = Date.now();
+
+for (const size of SIZES) {
+    for (const density of DENSITIES) {
+        let totalSolved = 0;
+        let minSolved = 100;
+        let maxSolved = 0;
+        let totalTime = 0;
+
+        process.stdout.write(`Simulating Size: ${size}x${size}, Density: ${density} ... `);
+
+        for (let i = 0; i < SAMPLES_PER_POINT; i++) {
+            const t0 = performance.now();
+            
+            // 1. Generate
+            const grid = generateRandomGrid(size, density);
+            const { rowHints, colHints } = calculateHints(grid);
+            
+            // 2. Solve
+            const { percentSolved } = solvePuzzle(rowHints, colHints);
+            
+            const t1 = performance.now();
+            
+            totalSolved += percentSolved;
+            minSolved = Math.min(minSolved, percentSolved);
+            maxSolved = Math.max(maxSolved, percentSolved);
+            totalTime += (t1 - t0);
+        }
+
+        const avgSolved = totalSolved / SAMPLES_PER_POINT;
+        const avgTime = totalTime / SAMPLES_PER_POINT;
+
+        results.push({
+            size,
+            density,
+            avgSolved,
+            minSolved,
+            maxSolved,
+            avgTime
+        });
+
+        csvRows.push(`${size},${density},${avgSolved.toFixed(2)},${minSolved.toFixed(2)},${maxSolved.toFixed(2)},${avgTime.toFixed(2)}`);
+        
+        console.log(`Avg Solved: ${avgSolved.toFixed(1)}%`);
+    }
+}
+
+const totalDuration = (Date.now() - startTime) / 1000;
+console.log(`Simulation complete in ${totalDuration.toFixed(1)}s`);
+
+// Save results
+fs.writeFileSync(OUTPUT_FILE, JSON.stringify(results, null, 2));
+fs.writeFileSync(CSV_FILE, csvRows.join('\n'));
+
+console.log(`Results saved to ${OUTPUT_FILE} and ${CSV_FILE}`);

src/App.vue

@@ -8,6 +8,7 @@ import StatusPanel from './components/StatusPanel.vue';
 import GuidePanel from './components/GuidePanel.vue';
 import WinModal from './components/WinModal.vue';
 import CustomGameModal from './components/CustomGameModal.vue';
+import SimulationView from './components/SimulationView.vue';
 import FixedBar from './components/FixedBar.vue';
 import ReloadPrompt from './components/ReloadPrompt.vue';
 
@@ -15,6 +16,7 @@ import ReloadPrompt from './components/ReloadPrompt.vue';
 const store = usePuzzleStore();
 const { t, locale, setLocale, locales } = useI18n();
 const showCustomModal = ref(false);
+const showSimulation = ref(false);
 const showGuide = ref(false);
 const deferredPrompt = ref(null);
 const canInstall = ref(false);
@@ -173,7 +175,8 @@ onUnmounted(() => {
     <!-- Modals Teleport -->
     <Teleport to="body">
       <WinModal v-if="store.isGameWon" />
-      <CustomGameModal v-if="showCustomModal" @close="showCustomModal = false" />
+      <CustomGameModal v-if="showCustomModal" @close="showCustomModal = false" @open-simulation="showSimulation = true" />
+      <SimulationView v-if="showSimulation" @close="showSimulation = false" />
       <ReloadPrompt />
     </Teleport>
   </main>

src/components/CustomGameModal.vue

@@ -3,8 +3,9 @@ import { ref, computed, onMounted, watch, nextTick } from 'vue';
 import { usePuzzleStore } from '@/stores/puzzle';
 import { useI18n } from '@/composables/useI18n';
 import { calculateDifficulty } from '@/utils/puzzleUtils';
+import { HelpCircle } from 'lucide-vue-next';
 
-const emit = defineEmits(['close']);
+const emit = defineEmits(['close', 'open-simulation']);
 const store = usePuzzleStore();
 const { t } = useI18n();
 
@@ -284,7 +285,12 @@ const confirm = () => {
       </div>
 
       <div class="difficulty-indicator">
-        <div class="label">{{ t('custom.difficulty') }}</div>
+        <div class="label-row">
+            <div class="label">{{ t('custom.difficulty') }}</div>
+            <button class="help-btn" @click="emit('open-simulation')" :title="t('custom.simulationHelp') || 'How is this calculated?'">
+                <HelpCircle class="icon-sm" />
+            </button>
+        </div>
         <div class="difficulty-row">
             <div class="level" :style="{ color: difficultyColor }">{{ t(`difficulty.${difficultyInfo.level}`) }}</div>
             <div class="percentage" :style="{ color: difficultyColor }">({{ difficultyInfo.value }}%)</div>
@@ -457,6 +463,34 @@ input[type="range"]::-moz-range-thumb {
     gap: 5px;
 }
 
+.label-row {
+    display: flex;
+    align-items: center;
+    gap: 8px;
+}
+
+.help-btn {
+    background: none;
+    border: none;
+    color: var(--text-muted);
+    cursor: pointer;
+    display: flex;
+    align-items: center;
+    padding: 4px;
+    border-radius: 50%;
+    transition: color 0.3s, background 0.3s;
+}
+
+.help-btn:hover {
+    color: var(--accent-cyan);
+    background: rgba(0, 242, 255, 0.1);
+}
+
+.icon-sm {
+    width: 16px;
+    height: 16px;
+}
+
 .difficulty-row {
     display: flex;
     flex-direction: row;

src/components/SimulationView.vue

@@ -0,0 +1,310 @@
+
+<script setup>
+import { ref, computed } from 'vue';
+import { generateRandomGrid, calculateHints } from '@/utils/puzzleUtils';
+import { solvePuzzle } from '@/utils/solver';
+import { X, Play, Square, RotateCcw } from 'lucide-vue-next';
+
+const emit = defineEmits(['close']);
+
+const SIZES = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]; 
+const DENSITIES = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9];
+const SAMPLES_PER_POINT = 10; // Reduced for web performance demo
+
+const isRunning = ref(false);
+const progress = ref(0);
+const currentStatus = ref('Ready');
+const results = ref([]);
+const simulationSpeed = ref(1); // 1 = Normal, 2 = Fast (less render updates)
+
+let stopRequested = false;
+
+const startSimulation = async () => {
+    if (isRunning.value) return;
+    isRunning.value = true;
+    stopRequested = false;
+    results.value = [];
+    progress.value = 0;
+
+    const totalSteps = SIZES.length * DENSITIES.length;
+    let stepCount = 0;
+
+    for (const size of SIZES) {
+        for (const density of DENSITIES) {
+            if (stopRequested) {
+                currentStatus.value = 'Stopped';
+                isRunning.value = false;
+                return;
+            }
+
+            currentStatus.value = `Simulating ${size}x${size} @ ${(density * 100).toFixed(0)}%`;
+            
+            let totalSolved = 0;
+            
+            // Run samples
+            for (let i = 0; i < SAMPLES_PER_POINT; i++) {
+                const grid = generateRandomGrid(size, density);
+                const { rowHints, colHints } = calculateHints(grid);
+                const { percentSolved } = solvePuzzle(rowHints, colHints);
+                totalSolved += percentSolved;
+                
+                // Yield to UI every few samples to keep it responsive
+                if (i % 2 === 0) await new Promise(r => setTimeout(r, 0));
+            }
+
+            const avgSolved = totalSolved / SAMPLES_PER_POINT;
+            
+            results.value.unshift({
+                size,
+                density,
+                avgSolved: avgSolved.toFixed(1)
+            });
+
+            stepCount++;
+            progress.value = (stepCount / totalSteps) * 100;
+        }
+    }
+
+    isRunning.value = false;
+    currentStatus.value = 'Completed';
+};
+
+const stopSimulation = () => {
+    stopRequested = true;
+};
+
+const getRowColor = (solved) => {
+    if (solved >= 90) return 'color-easy';
+    if (solved >= 60) return 'color-harder';
+    if (solved >= 30) return 'color-hardest';
+    return 'color-extreme';
+};
+
+</script>
+
+<template>
+  <div class="modal-overlay" @click.self="emit('close')">
+    <div class="modal glass-panel">
+      <div class="header">
+        <h2>Difficulty Simulation</h2>
+        <button class="close-btn" @click="emit('close')">
+            <X />
+        </button>
+      </div>
+      
+      <div class="content">
+        <div class="controls">
+            <div class="status-bar">
+                <div class="status-text">{{ currentStatus }}</div>
+                <div class="progress-track">
+                    <div class="progress-fill" :style="{ width: progress + '%' }"></div>
+                </div>
+            </div>
+            
+            <div class="actions">
+                <button v-if="!isRunning" class="btn-neon" @click="startSimulation">
+                    <Play class="icon" /> Start Simulation
+                </button>
+                <button v-else class="btn-neon secondary" @click="stopSimulation">
+                    <Square class="icon" /> Stop
+                </button>
+            </div>
+        </div>
+
+        <div class="results-container">
+            <table class="results-table">
+                <thead>
+                    <tr>
+                        <th>Size</th>
+                        <th>Density</th>
+                        <th>Solved (Logic)</th>
+                    </tr>
+                </thead>
+                <tbody>
+                    <tr v-for="(row, idx) in results" :key="idx" :class="getRowColor(row.avgSolved)">
+                        <td>{{ row.size }}x{{ row.size }}</td>
+                        <td>{{ (row.density * 100).toFixed(0) }}%</td>
+                        <td>{{ row.avgSolved }}%</td>
+                    </tr>
+                </tbody>
+            </table>
+            <div v-if="results.length === 0" class="empty-state">
+                Press Start to run Monte Carlo simulation
+            </div>
+        </div>
+      </div>
+    </div>
+  </div>
+</template>
+
+<style scoped>
+.modal-overlay {
+  position: fixed;
+  top: 0;
+  left: 0;
+  width: 100vw;
+  height: 100vh;
+  background: var(--modal-overlay);
+  backdrop-filter: blur(5px);
+  display: flex;
+  justify-content: center;
+  align-items: center;
+  z-index: 3000;
+  animation: fadeIn 0.3s ease;
+}
+
+.modal {
+  padding: 30px;
+  width: 90%;
+  max-width: 600px;
+  height: 80vh;
+  display: flex;
+  flex-direction: column;
+  border: 1px solid var(--accent-cyan);
+  box-shadow: 0 0 50px rgba(0, 242, 255, 0.2);
+}
+
+.header {
+    display: flex;
+    justify-content: space-between;
+    align-items: center;
+    margin-bottom: 20px;
+}
+
+h2 {
+    color: var(--accent-cyan);
+    margin: 0;
+    font-size: 1.5rem;
+}
+
+.close-btn {
+    background: none;
+    border: none;
+    color: var(--text-muted);
+    cursor: pointer;
+    padding: 5px;
+}
+
+.close-btn:hover {
+    color: var(--text-color);
+}
+
+.content {
+    flex: 1;
+    display: flex;
+    flex-direction: column;
+    gap: 20px;
+    overflow: hidden;
+}
+
+.controls {
+    display: flex;
+    flex-direction: column;
+    gap: 15px;
+    padding-bottom: 15px;
+    border-bottom: 1px solid var(--panel-border);
+}
+
+.status-bar {
+    display: flex;
+    flex-direction: column;
+    gap: 5px;
+}
+
+.status-text {
+    font-size: 0.9rem;
+    color: var(--text-muted);
+}
+
+.progress-track {
+    width: 100%;
+    height: 4px;
+    background: var(--panel-bg-strong);
+    border-radius: 2px;
+    overflow: hidden;
+}
+
+.progress-fill {
+    height: 100%;
+    background: var(--accent-cyan);
+    transition: width 0.3s ease;
+}
+
+.actions {
+    display: flex;
+    justify-content: flex-end;
+}
+
+.btn-neon {
+    display: flex;
+    align-items: center;
+    gap: 8px;
+    padding: 8px 16px;
+    font-size: 0.9rem;
+}
+
+.icon {
+    width: 16px;
+    height: 16px;
+}
+
+.results-container {
+    flex: 1;
+    overflow-y: auto;
+    background: rgba(0, 0, 0, 0.2);
+    border-radius: 8px;
+    padding: 10px;
+}
+
+.results-table {
+    width: 100%;
+    border-collapse: collapse;
+    font-size: 0.9rem;
+}
+
+.results-table th {
+    text-align: left;
+    padding: 8px;
+    color: var(--text-muted);
+    border-bottom: 1px solid var(--panel-border);
+    position: sticky;
+    top: 0;
+    background: var(--panel-bg);
+}
+
+.results-table td {
+    padding: 8px;
+    border-bottom: 1px solid rgba(255, 255, 255, 0.05);
+}
+
+.color-easy { color: #33ff33; }
+.color-harder { color: #ffff33; }
+.color-hardest { color: #ff9933; }
+.color-extreme { color: #ff3333; }
+
+.empty-state {
+    padding: 40px;
+    text-align: center;
+    color: var(--text-muted);
+    font-style: italic;
+}
+
+/* Scrollbar styling */
+.results-container::-webkit-scrollbar {
+  width: 8px;
+}
+
+.results-container::-webkit-scrollbar-track {
+  background: rgba(0, 0, 0, 0.1);
+}
+
+.results-container::-webkit-scrollbar-thumb {
+  background: var(--panel-border);
+  border-radius: 4px;
+}
+
+@keyframes fadeIn {
+  from { opacity: 0; }
+  to { opacity: 1; }
+}
+</style>

src/utils/puzzleUtils.js

@@ -53,35 +53,78 @@ export function generateRandomGrid(size, density = 0.5) {
 }
 
 export function calculateDifficulty(density, size = 10) {
-    // Shannon Entropy: H(x) = -x*log2(x) - (1-x)*log2(1-x)
-    // Normalized to 0-1 range (since max entropy at 0.5 is 1)
+    // Data derived from Monte Carlo Simulation (Logical Solver)
+    // Format: { size: [solved_pct_at_0.1, ..., solved_pct_at_0.9] }
+    // Densities: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9
+    const SIM_DATA = {
+        5:  [89, 74, 74, 81, 97, 98, 99, 100, 100],
+        10: [57, 20, 16, 54, 92, 100, 100, 100, 100],
+        15: [37, 10, 2, 12, 68, 100, 100, 100, 100],
+        20: [23, 3, 1, 2, 37, 100, 100, 100, 100],
+        25: [16, 0, 0, 1, 19, 99, 100, 100, 100],
+        30: [8, 0, 0, 0, 5, 99, 100, 100, 100],
+        35: [6, 0, 0, 0, 4, 91, 100, 100, 100],
+        40: [3, 0, 0, 0, 2, 91, 100, 100, 100],
+        45: [2, 0, 0, 0, 1, 82, 100, 100, 100],
+        50: [2, 0, 0, 0, 1, 73, 100, 100, 100],
+        60: [0, 0, 0, 0, 0, 35, 100, 100, 100],
+        70: [0, 0, 0, 0, 0, 16, 100, 100, 100],
+        80: [0, 0, 0, 0, 0, 1, 100, 100, 100]
+    };
+
+    // Helper to get interpolated value from array
+    const getSimulatedSolvedPct = (s, d) => {
+        // Find closest sizes
+        const sizes = Object.keys(SIM_DATA).map(Number).sort((a, b) => a - b);
+        let sLower = sizes[0];
+        let sUpper = sizes[sizes.length - 1];
+        
+        for (let i = 0; i < sizes.length - 1; i++) {
+            if (s >= sizes[i] && s <= sizes[i+1]) {
+                sLower = sizes[i];
+                sUpper = sizes[i+1];
+                break;
+            }
+        }
+        
+        // Clamp density to 0.1 - 0.9
+        const dClamped = Math.max(0.1, Math.min(0.9, d));
+        // Index in array: 0.1 -> 0, 0.9 -> 8
+        const dIndex = (dClamped - 0.1) * 10;
+        const dLowerIdx = Math.floor(dIndex);
+        const dUpperIdx = Math.ceil(dIndex);
+        const dFraction = dIndex - dLowerIdx;
+
+        // Bilinear Interpolation
+        
+        // 1. Interpolate Density for Lower Size
+        const rowLower = SIM_DATA[sLower];
+        const valLower = rowLower[dLowerIdx] * (1 - dFraction) + (rowLower[dUpperIdx] || rowLower[dLowerIdx]) * dFraction;
+        
+        // 2. Interpolate Density for Upper Size
+        const rowUpper = SIM_DATA[sUpper];
+        const valUpper = rowUpper[dLowerIdx] * (1 - dFraction) + (rowUpper[dUpperIdx] || rowUpper[dLowerIdx]) * dFraction;
+        
+        // 3. Interpolate Size
+        if (sLower === sUpper) return valLower;
+        const sFraction = (s - sLower) / (sUpper - sLower);
+        
+        return valLower * (1 - sFraction) + valUpper * sFraction;
+    };
+
+    const solvedPct = getSimulatedSolvedPct(size, density);
     
-    // Avoid log(0)
-    if (density <= 0 || density >= 1) return { level: 'easy', value: 0 };
-    
-    const entropy = -density * Math.log2(density) - (1 - density) * Math.log2(1 - density);
-    
-    // Difficulty score combines entropy (complexity) and size (scale)
-    // We use sqrt(size) to dampen the effect of very large grids, 
-    // ensuring that density still plays a major role.
-    // Normalized against max size (80)
-    const sizeFactor = Math.sqrt(size / 80);
-    const score = entropy * sizeFactor * 100;
-    const value = Math.round(score);
+    // Difficulty Score: Inverse of Solved Percent
+    // 100% Solved -> 0 Difficulty
+    // 0% Solved -> 100 Difficulty
+    const value = Math.round(100 - solvedPct);
     
     // Thresholds
     let level = 'easy';
-    if (value >= 80) level = 'extreme';
-    else if (value >= 60) level = 'hardest';
-    else if (value >= 40) level = 'harder';
-    else if (value >= 20) level = 'medium'; // Using 'medium' key if available, or we need to add it?
-    // Wait, useI18n only has: easy, harder, hardest, extreme.
-    // Let's stick to those keys but adjust ranges.
-    
-    if (value >= 75) level = 'extreme';
-    else if (value >= 50) level = 'hardest';
-    else if (value >= 25) level = 'harder';
-    else level = 'easy';
+    if (value >= 90) level = 'extreme';     // < 10% Solved
+    else if (value >= 60) level = 'hardest'; // < 40% Solved
+    else if (value >= 30) level = 'harder';  // < 70% Solved
+    else level = 'easy';                     // > 70% Solved
 
     return { level, value };
 }

src/utils/solver.js

@@ -0,0 +1,278 @@
+
+/**
+ * Represents the state of a cell in the solver.
+ * -1: Unknown
+ *  0: Empty
+ *  1: Filled
+ */
+
+/**
+ * Solves a single line (row or column) based on hints and current knowledge.
+ * Uses the "Left-Right Overlap" algorithm to find common filled cells.
+ * Also identifies definitely empty cells (reachable by no block).
+ * 
+ * @param {number[]} currentLine - Array of -1, 0, 1
+ * @param {number[]} hints - Array of block lengths
+ * @returns {number[]} - Updated line (or null if contradiction/impossible - though shouldn't happen for valid puzzles)
+ */
+function solveLine(currentLine, hints) {
+    const length = currentLine.length;
+    
+    // If no hints, all must be empty
+    if (hints.length === 0 || (hints.length === 1 && hints[0] === 0)) {
+        return Array(length).fill(0);
+    }
+
+    // Helper to check if a block can be placed at start index
+    const canPlace = (line, start, blockSize) => {
+        if (start + blockSize > line.length) return false;
+        // Check if any cell in block is 0 (Empty) -> Invalid
+        for (let i = start; i < start + blockSize; i++) {
+            if (line[i] === 0) return false;
+        }
+        // Check boundaries (must be separated by empty or edge)
+        if (start > 0 && line[start - 1] === 1) return false;
+        if (start + blockSize < line.length && line[start + blockSize] === 1) return false;
+        return true;
+    };
+
+    // 1. Calculate Left-Most Positions
+    const leftPositions = [];
+    let currentIdx = 0;
+    for (let hIndex = 0; hIndex < hints.length; hIndex++) {
+        const block = hints[hIndex];
+        // Find first valid position
+        while (currentIdx <= length - block) {
+            if (canPlace(currentLine, currentIdx, block)) {
+                // Verify we can fit remaining blocks
+                // Simple heuristic: do we have enough space? 
+                // A full recursive check is better but slower. 
+                // For "Logical Solver" we assume valid placement is possible if we respect current constraints.
+                // However, strictly, we need to know if there is *any* valid arrangement starting here.
+                // Let's use a recursive check with memoization for "can fit rest".
+                if (canFitRest(currentLine, currentIdx + block + 1, hints, hIndex + 1)) {
+                    leftPositions.push(currentIdx);
+                    currentIdx += block + 1; // Move past this block + 1 space
+                    break;
+                }
+            }
+            currentIdx++;
+        }
+        if (leftPositions.length <= hIndex) return null; // Impossible
+    }
+
+    // 2. Calculate Right-Most Positions (by reversing line and hints)
+    // This is symmetrical to Left-Most.
+    // Instead of implementing reverse logic, we can just reverse inputs, run left-most, and reverse back.
+    // But we need to respect the "currentLine" constraints which might be asymmetric.
+    
+    // Actually, "Right-Most" is just "Left-Most" on the reversed grid.
+    const reversedLine = [...currentLine].reverse();
+    const reversedHints = [...hints].reverse();
+    const rightPositionsReversed = [];
+    
+    currentIdx = 0;
+    for (let hIndex = 0; hIndex < reversedHints.length; hIndex++) {
+        const block = reversedHints[hIndex];
+        while (currentIdx <= length - block) {
+            if (canPlace(reversedLine, currentIdx, block)) {
+                if (canFitRest(reversedLine, currentIdx + block + 1, reversedHints, hIndex + 1)) {
+                    rightPositionsReversed.push(currentIdx);
+                    currentIdx += block + 1;
+                    break;
+                }
+            }
+            currentIdx++;
+        }
+        if (rightPositionsReversed.length <= hIndex) return null;
+    }
+    
+    // Convert reversed positions to actual indices
+    // index in reversed = length - 1 - (original_index + block_size - 1)
+    // original_start = length - 1 - (reversed_start + block_size - 1) = length - reversed_start - block_size
+    const rightPositions = rightPositionsReversed.map((rStart, i) => {
+        const block = reversedHints[i];
+        return length - rStart - block;
+    }).reverse();
+
+
+    // 3. Intersect
+    const newLine = [...currentLine];
+    
+    // Fill intersection
+    for (let i = 0; i < hints.length; i++) {
+        const l = leftPositions[i];
+        const r = rightPositions[i];
+        const block = hints[i];
+        
+        // If overlap exists: [r, l + block - 1]
+        // Example: Block 5. Left: 2, Right: 4.
+        // Left:  ..XXXXX...
+        // Right: ....XXXXX.
+        // Overlap:   ..XXX...
+        // Indices: max(l, r) to min(l+block, r+block) - 1 ?
+        // Range is [r, l + block - 1] (inclusive)
+        
+        if (r < l + block) {
+            for (let k = r; k < l + block; k++) {
+                newLine[k] = 1;
+            }
+        }
+    }
+
+    // Determine Empty cells?
+    // A cell is empty if it is not covered by ANY block in ANY valid configuration.
+    // This is harder with just L/R limits.
+    // However, we can use the "Simple Glue" logic:
+    // If a cell is outside the range [LeftLimit[i], RightLimit[i] + block] for ALL i, it's empty.
+    // Wait, indices are not strictly partitioned. Block 1 could be at 0 or 10.
+    // But logic dictates order.
+    // Range of block i is [LeftPositions[i], RightPositions[i] + hints[i]].
+    // If a cell k is not in ANY of these ranges, it is 0.
+    
+    // Mask of possible filled cells
+    const possibleFilled = Array(length).fill(false);
+    for (let i = 0; i < hints.length; i++) {
+        for (let k = leftPositions[i]; k < rightPositions[i] + hints[i]; k++) {
+            possibleFilled[k] = true;
+        }
+    }
+    
+    for (let k = 0; k < length; k++) {
+        if (!possibleFilled[k]) {
+            newLine[k] = 0;
+        }
+    }
+
+    return newLine;
+}
+
+// Memoized helper for checking if hints fit
+const memo = new Map();
+function canFitRest(line, startIndex, hints, hintIndex) {
+    // Optimization: If hints are empty, we just need to check if remaining line has no '1's
+    if (hintIndex >= hints.length) {
+        for (let i = startIndex; i < line.length; i++) {
+            if (line[i] === 1) return false;
+        }
+        return true;
+    }
+
+    // Key for memoization (primitive approach)
+    // In a full solver, we'd pass a cache. For single line, maybe overkill, but safe.
+    // let key = `${startIndex}-${hintIndex}`; 
+    // Skipping memo for now as line lengths are small (<80) and recursion depth is low.
+    
+    const remainingLen = line.length - startIndex;
+    // Min space needed: sum of hints + (hints.length - 1) spaces
+    // Calculate lazily or precalc?
+    let minSpace = 0;
+    for(let i=hintIndex; i<hints.length; i++) minSpace += hints[i] + (i < hints.length - 1 ? 1 : 0);
+    
+    if (remainingLen < minSpace) return false;
+
+    const block = hints[hintIndex];
+    // Try to find *any* valid placement for this block
+    // We only need ONE valid path to return true.
+    for (let i = startIndex; i <= line.length - minSpace; i++) { // Optimization on upper bound?
+         // Check placement
+         let valid = true;
+         // Block
+         for (let k = 0; k < block; k++) {
+             if (line[i+k] === 0) { valid = false; break; }
+         }
+         if (!valid) continue;
+         
+         // Boundary before (checked by loop start usually, but strictly:
+         if (i > 0 && line[i-1] === 1) valid = false; // Should have been handled by caller or skip
+         // Wait, the caller (loop) iterates i. 
+         // If i > startIndex, we implied space at i-1.
+         // If line[i-1] is 1, we can't place here if we skipped it.
+         // Actually, if we skip a '1', that's invalid.
+         // So we can't just skip '1's.
+         
+         // Correct logic:
+         // We iterate i. If we pass a '1' at index < i, that 1 is orphaned -> Invalid path.
+         // So we can only scan forward as long as we don't skip a '1'.
+         
+         let skippedOne = false;
+         for (let x = startIndex; x < i; x++) {
+             if (line[x] === 1) { skippedOne = true; break; }
+         }
+         if (skippedOne) break; // Cannot go further right, we left a 1 behind.
+         
+         // Boundary after
+         if (i + block < line.length && line[i+block] === 1) valid = false;
+         
+         if (valid) {
+             // Recurse
+             if (canFitRest(line, i + block + 1, hints, hintIndex + 1)) return true;
+         }
+    }
+    
+    return false;
+}
+
+
+/**
+ * Solves the puzzle using logical iteration.
+ * @param {number[][]} rowHints 
+ * @param {number[][]} colHints 
+ * @returns {object} { solvedGrid: number[][], percentSolved: number }
+ */
+export function solvePuzzle(rowHints, colHints) {
+    const rows = rowHints.length;
+    const cols = colHints.length;
+    
+    // Initialize grid with -1
+    let grid = Array(rows).fill(null).map(() => Array(cols).fill(-1));
+    
+    let changed = true;
+    let iterations = 0;
+    const MAX_ITER = 100; // Safety break
+    
+    while (changed && iterations < MAX_ITER) {
+        changed = false;
+        iterations++;
+        
+        // Rows
+        for (let r = 0; r < rows; r++) {
+            const newLine = solveLine(grid[r], rowHints[r]);
+            if (newLine) {
+                for (let c = 0; c < cols; c++) {
+                    if (grid[r][c] !== newLine[c]) {
+                        grid[r][c] = newLine[c];
+                        changed = true;
+                    }
+                }
+            }
+        }
+        
+        // Cols
+        for (let c = 0; c < cols; c++) {
+            const currentCol = grid.map(row => row[c]);
+            const newCol = solveLine(currentCol, colHints[c]);
+            if (newCol) {
+                for (let r = 0; r < rows; r++) {
+                    if (grid[r][c] !== newCol[r]) {
+                        grid[r][c] = newCol[r];
+                        changed = true;
+                    }
+                }
+            }
+        }
+    }
+    
+    // Calculate solved %
+    let solvedCount = 0;
+    for (let r = 0; r < rows; r++) {
+        for (let c = 0; c < cols; c++) {
+            if (grid[r][c] !== -1) solvedCount++;
+        }
+    }
+    
+    return {
+        solvedGrid: grid,
+        percentSolved: (solvedCount / (rows * cols)) * 100
+    };
+}