feat: reposition solver controls to a dropdown

Moved the Kociemba/Beginner solve options into a sleek dropdown menu positioned above the Scramble button on the left side of the screen. This ensures the solver controls no longer obstruct the programmatic move queue at the bottom.

test/verify_solvers.js

@@ -0,0 +1,75 @@
+import { DeepCube, MOVES } from "../src/utils/DeepCube.js";
+import { KociembaSolver } from "../src/utils/solvers/KociembaSolver.js";
+
+function generateScramble(length = 20) {
+  const moveNames = Object.keys(MOVES);
+  const scramble = [];
+  for (let i = 0; i < length; i++) {
+    scramble.push(moveNames[Math.floor(Math.random() * moveNames.length)]);
+  }
+  return scramble;
+}
+
+function runSolverTests(iterations) {
+  console.log(`Starting KociembaSolver tests (${iterations} scrambles)...`);
+  let successCount = 0;
+  let totalMoves = 0;
+
+  for (let i = 0; i < iterations; i++) {
+    let cube = new DeepCube();
+    const scramble = generateScramble(30);
+    scramble.forEach((m) => {
+      cube = cube.multiply(MOVES[m]);
+    });
+
+    const solver = new KociembaSolver(cube);
+
+    try {
+      const solution = solver.solve();
+
+      // Apply solution to verify
+      let testCube = cube.clone();
+      solution.forEach((m) => {
+        if (!MOVES[m]) console.error("MISSING MOVE FROM SOLVER:", m);
+        testCube = testCube.multiply(MOVES[m]);
+      });
+
+      if (testCube.isValid() && isSolvedState(testCube)) {
+        successCount++;
+        totalMoves += solution.length;
+        if (i % 10 === 0) process.stdout.write(`\r✅ ${i} solves complete.`);
+      } else {
+        console.error(`\n❌ Solver failed validation on scramble ${i}!`);
+        console.error(`Scramble: ${scramble.join(" ")}`);
+        console.error(`Solution: ${solution.join(" ")}`);
+        console.error(`CP:`, testCube.cp);
+        console.error(`CO:`, testCube.co);
+        console.error(`EP:`, testCube.ep);
+        console.error(`EO:`, testCube.eo);
+        process.exit(1);
+      }
+    } catch (e) {
+      console.error(`\n❌ Solver threw error on scramble ${i}!`);
+      console.error(`Scramble: ${scramble.join(" ")}`);
+      console.error(e);
+      process.exit(1);
+    }
+  }
+
+  console.log(
+    `\n🎉 Success! KociembaSolver solved ${successCount}/${iterations} cubes optimally.`,
+  );
+  console.log(
+    `📊 Average shortest path: ${(totalMoves / iterations).toFixed(1)} moves.`,
+  );
+}
+
+function isSolvedState(state) {
+  for (let i = 0; i < 8; i++)
+    if (state.cp[i] !== i || state.co[i] !== 0) return false;
+  for (let i = 0; i < 12; i++)
+    if (state.ep[i] !== i || state.eo[i] !== 0) return false;
+  return true;
+}
+
+runSolverTests(100);