refactor: optimize solver to use pure logic without guessing

src/utils/puzzleUtils.js

@@ -51,3 +51,25 @@ export function generateRandomGrid(size, density = 0.5) {
     }
     return grid;
 }
+
+export function calculateDifficulty(density) {
+    // 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)
+    
+    // Avoid log(0)
+    if (density <= 0 || density >= 1) return 'easy';
+    
+    const entropy = -density * Math.log2(density) - (1 - density) * Math.log2(1 - density);
+    
+    // Thresholds based on entropy
+    // 0.5 density -> entropy 1.0 (Extreme)
+    // 0.4/0.6 density -> entropy ~0.97 (Extreme)
+    // 0.3/0.7 density -> entropy ~0.88 (Hardest)
+    // 0.2/0.8 density -> entropy ~0.72 (Harder)
+    // <0.2/>0.8 density -> entropy <0.72 (Easy)
+
+    if (entropy >= 0.96) return 'extreme'; // approx 38% - 62%
+    if (entropy >= 0.85) return 'hardest'; // approx 28% - 38% & 62% - 72%
+    if (entropy >= 0.65) return 'harder';  // approx 17% - 28% & 72% - 83%
+    return 'easy';
+}