script.js

document.addEventListener('DOMContentLoaded', () => {
  const BASE_PUZZLE = '530070000600195000098000060800060003400803001700020006060000280000419005000080079';
  const TECHNIQUE_LABELS = {
    'naked-single': '단일 후보',
    'hidden-single-row': '행 숨은 싱글',
    'hidden-single-col': '열 숨은 싱글',
    'hidden-single-box': '박스 숨은 싱글'
  };

  const dom = {
    board: document.getElementById('sudoku-board'),
    newGameBtn: document.getElementById('new-game-btn'),
    hintBtn: document.getElementById('hint-btn'),
    applyHintBtn: document.getElementById('apply-hint-btn'),
    checkBtn: document.getElementById('check-btn'),
    resetBtn: document.getElementById('reset-btn'),
    hintMessage: document.getElementById('hint-message'),
    gameStatus: document.getElementById('game-status'),
    puzzleMeta: document.getElementById('puzzle-meta'),
    difficultyBadge: document.getElementById('difficulty-badge'),
    filledCount: document.getElementById('filled-count'),
    remainingCount: document.getElementById('remaining-count'),
    nextTechnique: document.getElementById('next-technique'),
    analysisSummary: document.getElementById('analysis-summary'),
    logList: document.getElementById('log-list')
  };

  const state = {
    board: [],
    initial: [],
    solution: [],
    analysis: null,
    pendingHint: null,
    selected: null,
    showMistakes: false,
    hintMessage: '힌트 보기를 누르면 다음 논리 단계를 설명합니다.',
    gameCount: 0,
    learningLog: [],
    cells: []
  };

  createBoard();
  bindEvents();
  startNewGame();

  function bindEvents() {
    dom.newGameBtn.addEventListener('click', startNewGame);
    dom.hintBtn.addEventListener('click', requestHint);
    dom.applyHintBtn.addEventListener('click', applyHint);
    dom.checkBtn.addEventListener('click', toggleMistakes);
    dom.resetBtn.addEventListener('click', resetBoard);
  }

  function createBoard() {
    const fragment = document.createDocumentFragment();

    for (let row = 0; row < 9; row += 1) {
      const rowCells = [];
      for (let col = 0; col < 9; col += 1) {
        const input = document.createElement('input');
        input.type = 'text';
        input.className = 'cell';
        input.maxLength = 1;
        input.inputMode = 'numeric';
        input.autocomplete = 'off';
        input.pattern = '[1-9]';
        input.spellcheck = false;
        input.setAttribute('aria-describedby', 'sudoku-help');
        input.dataset.row = String(row);
        input.dataset.col = String(col);
        input.setAttribute('role', 'gridcell');
        input.setAttribute('aria-rowindex', String(row + 1));
        input.setAttribute('aria-colindex', String(col + 1));

        if (col === 2 || col === 5) {
          input.classList.add('edge-right');
        }
        if (row === 2 || row === 5) {
          input.classList.add('edge-bottom');
        }

        input.addEventListener('focus', onCellFocus);
        input.addEventListener('click', onCellFocus);
        input.addEventListener('input', onCellInput);
        input.addEventListener('keydown', onCellKeyDown);

        rowCells.push(input);
        fragment.appendChild(input);
      }
      state.cells.push(rowCells);
    }

    dom.board.appendChild(fragment);
  }

  function startNewGame() {
    const initial = generatePuzzle();
    const solution = solveBoard(initial);

    if (!solution) {
      setStatus('퍼즐 생성에 실패했습니다. 새로고침 후 다시 시도하세요.');
      return;
    }

    state.initial = cloneBoard(initial);
    state.board = cloneBoard(initial);
    state.solution = solution;
    state.analysis = analyzePuzzle(initial);
    state.pendingHint = null;
    state.selected = findFirstEmpty(initial);
    state.showMistakes = false;
    state.hintMessage = '힌트 보기를 누르면 다음 논리 단계를 설명합니다.';
    state.gameCount += 1;
    state.learningLog = [
      {
        kind: '분석',
        message: describeAnalysis(state.analysis)
      }
    ];

    dom.checkBtn.textContent = '오답 확인';
    setStatus('새 퍼즐을 불러왔습니다.');
    render();
    focusSelectedCell();
  }

  function resetBoard() {
    state.board = cloneBoard(state.initial);
    state.pendingHint = null;
    state.showMistakes = false;
    state.selected = findFirstEmpty(state.initial);
    state.hintMessage = '퍼즐을 초기 상태로 되돌렸습니다. 다시 논리로 풀어보세요.';
    state.learningLog.unshift({ kind: '초기화', message: '입력한 값을 지우고 시작 상태로 돌아갔습니다.' });
    state.learningLog = state.learningLog.slice(0, 8);
    dom.checkBtn.textContent = '오답 확인';
    setStatus('퍼즐을 초기화했습니다.');
    render();
    focusSelectedCell();
  }

  function requestHint() {
    const conflicts = collectConflicts(state.board);
    const wrongCells = collectWrongCells(state.board, state.solution);

    if (conflicts.size > 0) {
      state.pendingHint = null;
      state.hintMessage = '같은 행, 열 또는 박스에 중복된 숫자가 있습니다. 충돌을 먼저 정리하세요.';
      setStatus('규칙 충돌이 있어 힌트를 중단했습니다.');
      render();
      return;
    }

    if (wrongCells.length > 0) {
      state.pendingHint = null;
      state.showMistakes = true;
      dom.checkBtn.textContent = '오답 숨기기';
      state.hintMessage = '정답과 다른 칸이 있어 힌트를 멈췄습니다. 붉은 표시를 먼저 고쳐보세요.';
      setStatus('오답이 있어 힌트를 중단했습니다.');
      render();
      return;
    }

    if (isSolved(state.board)) {
      state.pendingHint = null;
      state.hintMessage = '이미 퍼즐을 모두 해결했습니다. 새 퍼즐을 시작할 수 있습니다.';
      setStatus('퍼즐이 이미 완성되어 있습니다.');
      render();
      return;
    }

    const step = findNextLogicalStep(state.board);

    if (!step) {
      state.pendingHint = null;
      state.hintMessage = '현재 MVP 규칙(단일 후보, 숨은 싱글)로는 다음 단계를 찾지 못했습니다.';
      setStatus('추가 규칙이 필요한 구간입니다.');
      render();
      return;
    }

    state.pendingHint = step;
    state.selected = { row: step.row, col: step.col };
    state.hintMessage = `${TECHNIQUE_LABELS[step.type]}: ${step.detail}`;
    recordLog('힌트', `${cellRef(step.row, step.col)} = ${step.value} · ${TECHNIQUE_LABELS[step.type]}`);
    setStatus('다음 논리 단계를 찾았습니다.');
    render();
    focusSelectedCell();
  }

  function applyHint() {
    if (!state.pendingHint) {
      requestHint();
      return;
    }

    const { row, col, value, type } = state.pendingHint;
    state.board[row][col] = value;
    state.selected = { row, col };
    state.hintMessage = `${cellRef(row, col)}에 ${value}를 넣었습니다. 다음 단계가 필요하면 다시 힌트를 요청하세요.`;
    recordLog('적용', `${cellRef(row, col)} = ${value} · ${TECHNIQUE_LABELS[type]}`);
    state.pendingHint = null;

    if (boardsEqual(state.board, state.solution)) {
      state.hintMessage = '퍼즐을 해결했습니다. 새 퍼즐로 다시 시작할 수 있습니다.';
      setStatus('완성했습니다. 모든 칸이 맞습니다.');
      recordLog('완료', '모든 칸을 올바르게 채웠습니다.');
    } else {
      setStatus('힌트를 적용했습니다.');
    }

    render();
    focusSelectedCell();
  }

  function toggleMistakes() {
    state.showMistakes = !state.showMistakes;
    dom.checkBtn.textContent = state.showMistakes ? '오답 숨기기' : '오답 확인';
    setStatus(state.showMistakes ? '오답 표시를 켰습니다.' : '오답 표시를 껐습니다.');
    render();
  }

  function onCellFocus(event) {
    const row = Number(event.target.dataset.row);
    const col = Number(event.target.dataset.col);
    state.selected = { row, col };
    renderBoard();
  }

  function onCellInput(event) {
    const input = event.target;
    const row = Number(input.dataset.row);
    const col = Number(input.dataset.col);
    const previousValue = state.board[row][col];

    if (state.initial[row][col] !== 0) {
      input.value = String(state.initial[row][col]);
      return;
    }

    const raw = input.value.replace(/[^1-9]/g, '').slice(-1);
    input.value = raw;
    state.board[row][col] = raw ? Number(raw) : 0;
    state.pendingHint = null;
    state.selected = { row, col };
    const conflicts = collectConflicts(state.board);
    const wrongCells = collectWrongCells(state.board, state.solution);

    if (boardsEqual(state.board, state.solution)) {
      state.hintMessage = '퍼즐을 해결했습니다. 새 퍼즐로 다시 시작할 수 있습니다.';
      setStatus('완성했습니다. 모든 칸이 맞습니다.');
      recordLog('완료', '모든 칸을 올바르게 채웠습니다.');
    } else if (!raw && previousValue !== 0) {
      setStatus('칸을 비웠습니다.');
    } else if (!raw) {
      setStatus('1부터 9까지의 숫자만 입력할 수 있습니다.');
    } else if (conflicts.size > 0) {
      setStatus('규칙 충돌이 있습니다.');
    } else if (wrongCells.length > 0 && countFilled(state.board) === 81) {
      setStatus('오답이 있습니다. 오답 확인으로 점검하세요.');
    } else {
      const filled = countFilled(state.board);
      setStatus(`${filled}칸을 채웠습니다.`);
    }

    render();
  }

  function onCellKeyDown(event) {
    const row = Number(event.target.dataset.row);
    const col = Number(event.target.dataset.col);
    let nextRow = row;
    let nextCol = col;

    if (event.key === 'ArrowUp') {
      nextRow = Math.max(0, row - 1);
    } else if (event.key === 'ArrowDown') {
      nextRow = Math.min(8, row + 1);
    } else if (event.key === 'ArrowLeft') {
      nextCol = Math.max(0, col - 1);
    } else if (event.key === 'ArrowRight') {
      nextCol = Math.min(8, col + 1);
    } else if (event.key === 'Backspace' || event.key === 'Delete' || event.key === 'Escape' || event.key === '0' || event.key === ' ') {
      if (state.initial[row][col] === 0) {
        state.board[row][col] = 0;
        state.pendingHint = null;
        state.selected = { row, col };
        setStatus('칸을 비웠습니다.');
        render();
      }
      event.preventDefault();
      return;
    } else {
      return;
    }

    event.preventDefault();
    state.selected = { row: nextRow, col: nextCol };
    focusSelectedCell();
    renderBoard();
  }

  function render() {
    renderBoard();
    renderSidebar();
    updateActionButtons();
  }

  function updateActionButtons() {
    const isComplete = boardsEqual(state.board, state.solution);

    dom.hintBtn.disabled = isComplete;
    dom.applyHintBtn.disabled = !state.pendingHint || isComplete;
    dom.resetBtn.disabled = boardsEqual(state.board, state.initial);
    dom.checkBtn.textContent = state.showMistakes ? '오답 숨기기' : '오답 확인';
    dom.checkBtn.setAttribute('aria-pressed', String(state.showMistakes));
  }

  function renderBoard() {
    const conflicts = collectConflicts(state.board);
    const wrongCells = state.showMistakes ? new Set(collectWrongCells(state.board, state.solution)) : new Set();

    for (let row = 0; row < 9; row += 1) {
      for (let col = 0; col < 9; col += 1) {
        const input = state.cells[row][col];
        const value = state.board[row][col];
        const key = toKey(row, col);
        const isGiven = state.initial[row][col] !== 0;
        const isSelected = Boolean(state.selected && state.selected.row === row && state.selected.col === col);
        const isHint = Boolean(state.pendingHint && state.pendingHint.row === row && state.pendingHint.col === col);
        const hasConflict = conflicts.has(key);
        const hasMistake = wrongCells.has(key);

        input.value = value === 0 ? '' : String(value);
        input.readOnly = isGiven;
        input.classList.toggle('is-given', isGiven);
        input.classList.toggle('is-selected', isSelected);
        input.classList.toggle('is-hint', isHint);
        input.classList.toggle('is-conflict', hasConflict);
        input.classList.toggle('is-mistake', hasMistake);
        input.setAttribute('aria-label', buildCellLabel(row, col, value, isGiven));
        input.setAttribute('aria-selected', String(isSelected));
        input.setAttribute('aria-invalid', String(hasConflict || hasMistake));
        input.setAttribute('aria-readonly', String(isGiven));
      }
    }
  }

  function renderSidebar() {
    const filled = countFilled(state.board);
    const conflicts = collectConflicts(state.board);
    const wrongCells = collectWrongCells(state.board, state.solution);
    const isComplete = boardsEqual(state.board, state.solution);
    let nextTechniqueLabel = '대기 중';

    if (isComplete) {
      nextTechniqueLabel = '완료';
    } else if (conflicts.size > 0) {
      nextTechniqueLabel = '충돌 정리 필요';
    } else if (wrongCells.length > 0) {
      nextTechniqueLabel = '오답 수정 필요';
    } else {
      const nextStep = findNextLogicalStep(state.board);
      nextTechniqueLabel = nextStep ? TECHNIQUE_LABELS[nextStep.type] : '현재 규칙으로 찾지 못함';
    }

    dom.puzzleMeta.textContent = `${state.gameCount}번째 퍼즐 · 랜덤 변형 학습 퍼즐`;
    dom.difficultyBadge.textContent = state.analysis.difficulty;
    dom.hintMessage.textContent = state.hintMessage;
    dom.filledCount.textContent = String(filled);
    dom.remainingCount.textContent = String(81 - filled);
    dom.nextTechnique.textContent = nextTechniqueLabel;
    dom.analysisSummary.textContent = describeAnalysis(state.analysis);

    dom.logList.innerHTML = '';
    const items = state.learningLog.length > 0 ? state.learningLog : [{ kind: '안내', message: '힌트 로그가 여기에 표시됩니다.' }];
    items.slice(0, 8).forEach((item) => {
      const li = document.createElement('li');
      li.textContent = `${item.kind} · ${item.message}`;
      dom.logList.appendChild(li);
    });
  }

  function setStatus(message) {
    dom.gameStatus.textContent = message;
  }

  function recordLog(kind, message) {
    const latest = `${kind}:${message}`;
    const exists = state.learningLog.some((entry) => `${entry.kind}:${entry.message}` === latest);
    if (!exists) {
      state.learningLog.unshift({ kind, message });
      state.learningLog = state.learningLog.slice(0, 8);
    }
  }

  function buildCellLabel(row, col, value, isGiven) {
    if (isGiven) {
      return `${row + 1}행 ${col + 1}열, 고정 숫자 ${value}`;
    }
    if (value === 0) {
      return `${row + 1}행 ${col + 1}열, 빈칸`;
    }
    return `${row + 1}행 ${col + 1}열, 입력값 ${value}`;
  }

  function focusSelectedCell() {
    if (!state.selected) {
      return;
    }
    const cell = state.cells[state.selected.row][state.selected.col];
    if (cell) {
      cell.focus();
    }
  }

  function analyzePuzzle(board) {
    const solverResult = buildSolverLog(board);
    const counts = solverResult.steps.reduce((acc, step) => {
      acc[step.type] = (acc[step.type] || 0) + 1;
      return acc;
    }, {});

    return {
      steps: solverResult.steps,
      solved: solverResult.solved,
      counts,
      difficulty: classifyDifficulty(solverResult.solved, counts)
    };
  }

  function describeAnalysis(analysis) {
    const countSummary = formatTechniqueCounts(analysis.counts);
    if (analysis.solved) {
      return `${analysis.steps.length}단계 논리 풀이 · ${countSummary}`;
    }
    return `일부만 논리 풀이 가능 · ${countSummary}`;
  }

  function formatTechniqueCounts(counts) {
    const parts = [];
    if (counts['naked-single']) {
      parts.push(`단일 후보 ${counts['naked-single']}회`);
    }
    if (counts['hidden-single-row']) {
      parts.push(`행 숨은 싱글 ${counts['hidden-single-row']}회`);
    }
    if (counts['hidden-single-col']) {
      parts.push(`열 숨은 싱글 ${counts['hidden-single-col']}회`);
    }
    if (counts['hidden-single-box']) {
      parts.push(`박스 숨은 싱글 ${counts['hidden-single-box']}회`);
    }
    return parts.length > 0 ? parts.join(', ') : '기본 규칙 분석 없음';
  }

  function classifyDifficulty(solved, counts) {
    const hiddenCount = (counts['hidden-single-row'] || 0) + (counts['hidden-single-col'] || 0) + (counts['hidden-single-box'] || 0);
    if (!solved) {
      return '연습';
    }
    if (hiddenCount === 0) {
      return '입문';
    }
    if (hiddenCount <= 8) {
      return '초급';
    }
    return '중급';
  }

  function buildSolverLog(board) {
    const working = cloneBoard(board);
    const steps = [];
    let guard = 0;

    while (guard < 100) {
      if (isSolved(working)) {
        return { solved: true, steps };
      }

      const next = findNextLogicalStep(working);
      if (!next) {
        break;
      }

      working[next.row][next.col] = next.value;
      steps.push(next);
      guard += 1;
    }

    return { solved: isSolved(working), steps };
  }

  function findNextLogicalStep(board) {
    const candidates = [];

    for (let row = 0; row < 9; row += 1) {
      candidates[row] = [];
      for (let col = 0; col < 9; col += 1) {
        candidates[row][col] = board[row][col] === 0 ? getCandidates(board, row, col) : [];
      }
    }

    for (let row = 0; row < 9; row += 1) {
      for (let col = 0; col < 9; col += 1) {
        if (board[row][col] !== 0) {
          continue;
        }
        if (candidates[row][col].length === 1) {
          const value = candidates[row][col][0];
          return {
            type: 'naked-single',
            row,
            col,
            value,
            detail: `${cellRef(row, col)}의 후보는 ${value} 하나뿐입니다. 행, 열, 박스에서 다른 숫자가 모두 제외됩니다.`
          };
        }
      }
    }

    for (let row = 0; row < 9; row += 1) {
      for (let value = 1; value <= 9; value += 1) {
        const spots = [];
        for (let col = 0; col < 9; col += 1) {
          if (candidates[row][col].includes(value)) {
            spots.push({ row, col });
          }
        }
        if (spots.length === 1) {
          return {
            type: 'hidden-single-row',
            row: spots[0].row,
            col: spots[0].col,
            value,
            detail: `${row + 1}행에서 숫자 ${value}가 들어갈 수 있는 칸은 ${cellRef(spots[0].row, spots[0].col)} 하나뿐입니다.`
          };
        }
      }
    }

    for (let col = 0; col < 9; col += 1) {
      for (let value = 1; value <= 9; value += 1) {
        const spots = [];
        for (let row = 0; row < 9; row += 1) {
          if (candidates[row][col].includes(value)) {
            spots.push({ row, col });
          }
        }
        if (spots.length === 1) {
          return {
            type: 'hidden-single-col',
            row: spots[0].row,
            col: spots[0].col,
            value,
            detail: `${col + 1}열에서 숫자 ${value}가 들어갈 수 있는 칸은 ${cellRef(spots[0].row, spots[0].col)} 하나뿐입니다.`
          };
        }
      }
    }

    for (let box = 0; box < 9; box += 1) {
      const startRow = Math.floor(box / 3) * 3;
      const startCol = (box % 3) * 3;
      for (let value = 1; value <= 9; value += 1) {
        const spots = [];
        for (let row = startRow; row < startRow + 3; row += 1) {
          for (let col = startCol; col < startCol + 3; col += 1) {
            if (candidates[row][col].includes(value)) {
              spots.push({ row, col });
            }
          }
        }
        if (spots.length === 1) {
          return {
            type: 'hidden-single-box',
            row: spots[0].row,
            col: spots[0].col,
            value,
            detail: `${box + 1}번 박스에서 숫자 ${value}가 들어갈 수 있는 칸은 ${cellRef(spots[0].row, spots[0].col)} 하나뿐입니다.`
          };
        }
      }
    }

    return null;
  }

  function generatePuzzle() {
    let board = parseBoard(BASE_PUZZLE);
    board = remapDigits(board);
    board = shuffleRows(board);
    board = shuffleCols(board);
    if (Math.random() > 0.5) {
      board = transpose(board);
    }
    return board;
  }

  function remapDigits(board) {
    const digits = shuffle([1, 2, 3, 4, 5, 6, 7, 8, 9]);
    const map = new Map();
    for (let i = 1; i <= 9; i += 1) {
      map.set(i, digits[i - 1]);
    }
    return board.map((row) => row.map((value) => (value === 0 ? 0 : map.get(value))));
  }

  function shuffleRows(board) {
    const bands = shuffle([0, 1, 2]);
    const order = [];
    bands.forEach((band) => {
      shuffle([0, 1, 2]).forEach((offset) => order.push(band * 3 + offset));
    });
    return order.map((rowIndex) => board[rowIndex].slice());
  }

  function shuffleCols(board) {
    const stacks = shuffle([0, 1, 2]);
    const order = [];
    stacks.forEach((stack) => {
      shuffle([0, 1, 2]).forEach((offset) => order.push(stack * 3 + offset));
    });
    return board.map((row) => order.map((colIndex) => row[colIndex]));
  }

  function transpose(board) {
    return board[0].map((_, col) => board.map((row) => row[col]));
  }

  function shuffle(values) {
    const copy = values.slice();
    for (let i = copy.length - 1; i > 0; i -= 1) {
      const j = Math.floor(Math.random() * (i + 1));
      [copy[i], copy[j]] = [copy[j], copy[i]];
    }
    return copy;
  }

  function solveBoard(board) {
    const working = cloneBoard(board);
    return solveRecursive(working) ? working : null;
  }

  function solveRecursive(board) {
    let bestCell = null;
    let bestCandidates = null;

    for (let row = 0; row < 9; row += 1) {
      for (let col = 0; col < 9; col += 1) {
        if (board[row][col] !== 0) {
          continue;
        }
        const candidates = getCandidates(board, row, col);
        if (candidates.length === 0) {
          return false;
        }
        if (!bestCandidates || candidates.length < bestCandidates.length) {
          bestCell = { row, col };
          bestCandidates = candidates;
        }
      }
    }

    if (!bestCell) {
      return true;
    }

    for (const value of bestCandidates) {
      board[bestCell.row][bestCell.col] = value;
      if (solveRecursive(board)) {
        return true;
      }
    }

    board[bestCell.row][bestCell.col] = 0;
    return false;
  }

  function getCandidates(board, row, col) {
    if (board[row][col] !== 0) {
      return [];
    }
    const candidates = [];
    for (let value = 1; value <= 9; value += 1) {
      if (isValidPlacement(board, row, col, value)) {
        candidates.push(value);
      }
    }
    return candidates;
  }

  function isValidPlacement(board, row, col, value) {
    for (let index = 0; index < 9; index += 1) {
      if (board[row][index] === value) {
        return false;
      }
      if (board[index][col] === value) {
        return false;
      }
    }

    const startRow = Math.floor(row / 3) * 3;
    const startCol = Math.floor(col / 3) * 3;
    for (let r = startRow; r < startRow + 3; r += 1) {
      for (let c = startCol; c < startCol + 3; c += 1) {
        if (board[r][c] === value) {
          return false;
        }
      }
    }
    return true;
  }

  function collectConflicts(board) {
    const conflicts = new Set();

    for (let row = 0; row < 9; row += 1) {
      markHouseConflicts(conflicts, Array.from({ length: 9 }, (_, col) => ({ row, col, value: board[row][col] })));
    }
    for (let col = 0; col < 9; col += 1) {
      markHouseConflicts(conflicts, Array.from({ length: 9 }, (_, row) => ({ row, col, value: board[row][col] })));
    }
    for (let box = 0; box < 9; box += 1) {
      const startRow = Math.floor(box / 3) * 3;
      const startCol = (box % 3) * 3;
      const cells = [];
      for (let row = startRow; row < startRow + 3; row += 1) {
        for (let col = startCol; col < startCol + 3; col += 1) {
          cells.push({ row, col, value: board[row][col] });
        }
      }
      markHouseConflicts(conflicts, cells);
    }

    return conflicts;
  }

  function markHouseConflicts(conflicts, cells) {
    const buckets = new Map();
    cells.forEach((cell) => {
      if (cell.value === 0) {
        return;
      }
      if (!buckets.has(cell.value)) {
        buckets.set(cell.value, []);
      }
      buckets.get(cell.value).push(cell);
    });

    buckets.forEach((items) => {
      if (items.length > 1) {
        items.forEach((cell) => conflicts.add(toKey(cell.row, cell.col)));
      }
    });
  }

  function collectWrongCells(board, solution) {
    const wrong = [];
    for (let row = 0; row < 9; row += 1) {
      for (let col = 0; col < 9; col += 1) {
        if (board[row][col] !== 0 && board[row][col] !== solution[row][col]) {
          wrong.push(toKey(row, col));
        }
      }
    }
    return wrong;
  }

  function findFirstEmpty(board) {
    for (let row = 0; row < 9; row += 1) {
      for (let col = 0; col < 9; col += 1) {
        if (board[row][col] === 0) {
          return { row, col };
        }
      }
    }
    return { row: 0, col: 0 };
  }

  function isSolved(board) {
    return board.every((row) => row.every((value) => value !== 0));
  }

  function countFilled(board) {
    return board.flat().filter((value) => value !== 0).length;
  }

  function boardsEqual(a, b) {
    for (let row = 0; row < 9; row += 1) {
      for (let col = 0; col < 9; col += 1) {
        if (a[row][col] !== b[row][col]) {
          return false;
        }
      }
    }
    return true;
  }

  function cloneBoard(board) {
    return board.map((row) => row.slice());
  }

  function parseBoard(serialized) {
    const board = [];
    for (let row = 0; row < 9; row += 1) {
      const currentRow = [];
      for (let col = 0; col < 9; col += 1) {
        currentRow.push(Number(serialized[row * 9 + col]));
      }
      board.push(currentRow);
    }
    return board;
  }

  function toKey(row, col) {
    return `${row}-${col}`;
  }

  function cellRef(row, col) {
    return `${row + 1}행 ${col + 1}열`;
  }
});