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

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 };
 }