feat(difficulty): implement Monte Carlo simulation for accurate difficulty calculation

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}`);