feat: expand sudoku analysis and interoperability

src/solver/exact.ts

@@ -111,6 +111,13 @@ export function solveExact(
     "timeoutMs",
   );
   const compiled = compilePuzzle(normalized);
+  const preferredSolution =
+    normalized.solution !== undefined &&
+    board.every(
+      (value, cell) => value === 0 || value === normalized.solution?.[cell],
+    )
+      ? normalized.solution
+      : undefined;
   const random: RandomSource | undefined =
     options.seed === undefined ? undefined : seededRandom(options.seed);
   const solutions: number[][] = [];
@@ -157,6 +164,15 @@ export function solveExact(
     const chosen = selection[0];
     let choices = selection[1];
     if (random !== undefined) choices = shuffled(choices, random);
+    else {
+      const preferred = preferredSolution?.[chosen];
+      if (preferred !== undefined && choices.includes(preferred)) {
+        choices = [
+          preferred,
+          ...choices.filter((value) => value !== preferred),
+        ];
+      }
+    }
     for (const value of choices) {
       board[chosen] = value;
       search();