/**
 * Generate a fully valid Sudoku solution using a base pattern and structural shuffles.
 * Returns a string of 81 digits (row-major order).
 */
export function generateSolvedBoard(): string {
  const size = 9;
  const box = 3;

  // --- 1️⃣ Base pattern function ---
  const pattern = (r: number, c: number) =>
    (box * (r % box) + Math.floor(r / box) + c) % size;

  // --- 2️⃣ Create base board ---
  const baseBoard: number[][] = Array.from({ length: size }, (_, r) =>
    Array.from({ length: size }, (_, c) => pattern(r, c) + 1)
  );

  // --- 3️⃣ Helper to shuffle an array in place ---
  const shuffle = <T>(arr: T[]): T[] => {
    const copy = [...arr];
    for (let i = copy.length - 1; i > 0; i--) {
      const j = Math.floor(Math.random() * (i + 1));
      [copy[i], copy[j]] = [copy[j], copy[i]];
    }
    return copy;
  };

  // --- 4️⃣ Build shuffled row/col indices preserving 3×3 structure ---
  const rows = shuffle([0, 1, 2])
    .concat(shuffle([3, 4, 5]))
    .concat(shuffle([6, 7, 8]));
  const cols = shuffle([0, 1, 2])
    .concat(shuffle([3, 4, 5]))
    .concat(shuffle([6, 7, 8]));

  // --- 5️⃣ Shuffle entire bands and stacks (groups of 3) ---
  const rowBands = shuffle([0, 1, 2]);
  const colStacks = shuffle([0, 1, 2]);

  const shuffledRows = rowBands.flatMap(band => rows.slice(band * 3, band * 3 + 3));
  const shuffledCols = colStacks.flatMap(stack => cols.slice(stack * 3, stack * 3 + 3));

  // --- 6️⃣ Digit permutation (1–9) ---
  const digits = shuffle([1, 2, 3, 4, 5, 6, 7, 8, 9]);

  // --- 7️⃣ Build the final shuffled board ---
  const board: number[][] = shuffledRows.map(r =>
    shuffledCols.map(c => digits[baseBoard[r][c] - 1])
  );

  // --- 8️⃣ Flatten to 81-char string ---
  return board.flat().join('');
}