radomirregular region

2026-05-15 21:53:08 +08:00
parent 0e87d5546d
commit e54b9a0b7a
3 changed files with 330 additions and 37 deletions
--- a/src/components/SudokuGame.tsx
+++ b/src/components/SudokuGame.tsx
@@ -4,14 +4,25 @@ import {
  GameBoard,
  Difficulty,
  GameMode,
-  STANDARD_REGION_MAP,
-  generatePuzzle,
+  RegionMap,
+  generatePuzzleForMode,
  getRegionId,
  getRegionNeighbors,
-  getRegionMapByMode,
 } from './sudokuEngine';

 type HighlightType = 'none' | 'row' | 'col' | 'box' | 'sameNumber';
+type SudokuRound = {
+  board: GameBoard;
+  regionMap: RegionMap;
+};
+
+const createSudokuRound = (difficulty: Difficulty, mode: GameMode): SudokuRound => {
+  const { puzzle, regionMap } = generatePuzzleForMode(difficulty, mode);
+  return {
+    board: puzzle,
+    regionMap,
+  };
+};

 const SudokuGame: React.FC = () => {
  // 游戏难度
@@ -20,10 +31,15 @@ const SudokuGame: React.FC = () => {
  // 游戏模式：标准或不规则
  const [gameMode, setGameMode] = useState<GameMode>('standard');
  
-  // 使用 useMemo 确保 regionMap 随 gameMode 变化
-  const regionMap = useMemo(() => getRegionMapByMode(gameMode), [gameMode]);
+  const [round, setRound] = useState<SudokuRound>(() => createSudokuRound('hard', 'standard'));
+  const { board, regionMap } = round;

-  const [board, setBoard] = useState<GameBoard>(() => generatePuzzle('hard', STANDARD_REGION_MAP));
+  const setBoard = (nextBoard: GameBoard) => {
+    setRound((currentRound) => ({
+      ...currentRound,
+      board: nextBoard,
+    }));
+  };

  const [fixedCells, setFixedCells] = useState<boolean[][]>(() =>
    board.map(row => row.map(cell => cell !== 0))
@@ -181,10 +197,9 @@ const SudokuGame: React.FC = () => {
  };

  const createNewGame = (level: Difficulty, mode: GameMode = gameMode) => {
-    const nextRegionMap = getRegionMapByMode(mode);
-    const newPuzzle = generatePuzzle(level, nextRegionMap);
-    setBoard(newPuzzle);
-    setFixedCells(newPuzzle.map(row => row.map(cell => cell !== 0)));
+    const nextRound = createSudokuRound(level, mode);
+    setRound(nextRound);
+    setFixedCells(nextRound.board.map(row => row.map(cell => cell !== 0)));
    setSelectedCell(null);
    setIsGameComplete(false);
    setShowCompleteDialog(false);
@@ -306,7 +321,7 @@ const SudokuGame: React.FC = () => {
      }
    }
    return highlighted;
-  }, [board, selectedCell, config]);
+  }, [board, selectedCell, config, regionMap]);

  // 计算剩余未填写的数字数量
  const remainingCount = useMemo(() => {
--- a/src/components/sudokuEngine.test.ts
+++ b/src/components/sudokuEngine.test.ts
@@ -1,7 +1,9 @@
 import {
  createEmptyBoard,
  generateFullBoard,
+  generateIrregularRegionMap,
  generatePuzzle,
+  generatePuzzleForMode,
  getRegionId,
  getRegionNeighbors,
  IRREGULAR_REGION_MAP,
@@ -35,6 +37,17 @@ describe('sudokuEngine', () => {
    expect(isValidRegionMap(IRREGULAR_REGION_MAP)).toBe(true);
  });

+  test('generateIrregularRegionMap creates a non-standard connected region map', () => {
+    const regionMap = generateIrregularRegionMap();
+    const differentCells = regionMap.reduce(
+      (count, row, rowIndex) => count + row.filter((regionId, colIndex) => regionId !== STANDARD_REGION_MAP[rowIndex][colIndex]).length,
+      0
+    );
+
+    expect(isValidRegionMap(regionMap)).toBe(true);
+    expect(differentCells).toBeGreaterThan(0);
+  });
+
  test('isPlacementValid uses irregular regions instead of 3x3 boxes', () => {
    const board = createEmptyBoard();
    board[0][0] = 5;
@@ -56,6 +69,17 @@ describe('sudokuEngine', () => {
    expect(puzzle.flat().some((cell) => cell === 0)).toBe(true);
  });

+  test('generatePuzzleForMode pairs irregular puzzles with their generated region map', () => {
+    const { puzzle, regionMap } = generatePuzzleForMode('medium', 'irregular');
+    const fullBoard = generateFullBoard(regionMap);
+
+    expect(isValidRegionMap(regionMap)).toBe(true);
+    expect(puzzle).toHaveLength(9);
+    expect(puzzle.every((row) => row.length === 9)).toBe(true);
+    expect(puzzle.flat().some((cell) => cell === 0)).toBe(true);
+    expectSolvedBoard(fullBoard, regionMap);
+  });
+
  test('generateFullBoard creates a solved irregular board', () => {
    const board = generateFullBoard(IRREGULAR_REGION_MAP);

--- a/src/components/sudokuEngine.ts
+++ b/src/components/sudokuEngine.ts
@@ -2,10 +2,35 @@ export type GameBoard = number[][];
 export type Difficulty = 'easy' | 'medium' | 'hard';
 export type GameMode = 'standard' | 'irregular';
 export type RegionMap = number[][];
+export type GeneratedPuzzle = {
+  puzzle: GameBoard;
+  regionMap: RegionMap;
+};
+
+type SolvedSudoku = {
+  fullBoard: GameBoard;
+  regionMap: RegionMap;
+};
+
+type CellPosition = [number, number];
+
+const DIGITS = [1, 2, 3, 4, 5, 6, 7, 8, 9];
+const DIRECTIONS: CellPosition[] = [
+  [-1, 0],
+  [1, 0],
+  [0, -1],
+  [0, 1],
+];
+
+const MIN_IRREGULAR_CELL_DIFFERENCE = 16;
+const MAX_IRREGULAR_RESTARTS = 24;
+const MAX_IRREGULAR_GREEDY_STEPS = 28;
+
+const generatedFullBoards = new WeakMap<RegionMap, GameBoard>();

 export const createEmptyBoard = (): GameBoard => Array.from({ length: 9 }, () => Array(9).fill(0));

-const shuffleArray = (arr: number[]) => {
+const shuffleArray = <T>(arr: T[]): T[] => {
  const result = [...arr];
  for (let i = result.length - 1; i > 0; i--) {
    const j = Math.floor(Math.random() * (i + 1));
@@ -14,6 +39,10 @@ const shuffleArray = (arr: number[]) => {
  return result;
 };

+const cloneBoard = (board: GameBoard): GameBoard => board.map((row) => [...row]);
+
+const cloneRegionMap = (regionMap: RegionMap): RegionMap => regionMap.map((row) => [...row]);
+
 export const STANDARD_REGION_MAP: RegionMap = Array.from({ length: 9 }, (_, row) =>
  Array.from({ length: 9 }, (_, col) => Math.floor(row / 3) * 3 + Math.floor(col / 3))
 );
@@ -44,6 +73,8 @@ const IRREGULAR_FULL_BOARD: GameBoard = [

 export const getRegionId = (regionMap: RegionMap, row: number, col: number): number => regionMap[row][col];

+const isInBounds = (row: number, col: number): boolean => row >= 0 && row < 9 && col >= 0 && col < 9;
+
 export const isValidRegionMap = (regionMap: RegionMap): boolean => {
  if (regionMap.length !== 9 || regionMap.some((row) => row.length !== 9)) {
    return false;
@@ -69,19 +100,14 @@ const isConnectedRegion = (cells: Array<[number, number]>): boolean => {

  const cellSet = new Set(cells.map(([row, col]) => `${row}-${col}`));
  const seen = new Set<string>();
-  const queue: Array<[number, number]> = [cells[0]];
+  const queue: CellPosition[] = [cells[0]];
  seen.add(`${cells[0][0]}-${cells[0][1]}`);

  for (let index = 0; index < queue.length; index++) {
    const [row, col] = queue[index];
-    const neighbors: Array<[number, number]> = [
-      [row - 1, col],
-      [row + 1, col],
-      [row, col - 1],
-      [row, col + 1],
-    ];
-
-    for (const [nextRow, nextCol] of neighbors) {
+    for (const [rowOffset, colOffset] of DIRECTIONS) {
+      const nextRow = row + rowOffset;
+      const nextCol = col + colOffset;
      const key = `${nextRow}-${nextCol}`;
      if (cellSet.has(key) && !seen.has(key)) {
        seen.add(key);
@@ -98,12 +124,203 @@ const isSameRegionMap = (left: RegionMap, right: RegionMap): boolean =>
  left.every((row, rowIndex) => row.length === right[rowIndex].length && row.every((cell, colIndex) => cell === right[rowIndex][colIndex]));

 const randomizeDigits = (board: GameBoard): GameBoard => {
-  const shuffledDigits = shuffleArray([1, 2, 3, 4, 5, 6, 7, 8, 9]);
+  const shuffledDigits = shuffleArray(DIGITS);
  const digitMap = new Map(shuffledDigits.map((digit, index) => [index + 1, digit]));

  return board.map((row) => row.map((cell) => digitMap.get(cell) ?? cell));
 };

+const generateRandomStandardFullBoard = (): GameBoard => {
+  const pattern = (row: number, col: number) => ((row * 3 + Math.floor(row / 3) + col) % 9) + 1;
+  const rows = shuffleArray([0, 1, 2]).flatMap((band) => shuffleArray([0, 1, 2]).map((row) => band * 3 + row));
+  const cols = shuffleArray([0, 1, 2]).flatMap((stack) => shuffleArray([0, 1, 2]).map((col) => stack * 3 + col));
+  const shuffledDigits = shuffleArray(DIGITS);
+
+  return rows.map((row) => cols.map((col) => shuffledDigits[pattern(row, col) - 1]));
+};
+
+const countDifferentCells = (left: RegionMap, right: RegionMap): number => {
+  let count = 0;
+  for (let row = 0; row < 9; row++) {
+    for (let col = 0; col < 9; col++) {
+      if (left[row][col] !== right[row][col]) {
+        count++;
+      }
+    }
+  }
+  return count;
+};
+
+const getTouchingRegionPairs = (regionMap: RegionMap): Array<[number, number]> => {
+  const pairs = new Set<string>();
+
+  for (let row = 0; row < 9; row++) {
+    for (let col = 0; col < 9; col++) {
+      for (const [rowOffset, colOffset] of DIRECTIONS) {
+        const nextRow = row + rowOffset;
+        const nextCol = col + colOffset;
+        if (!isInBounds(nextRow, nextCol)) continue;
+
+        const currentRegion = regionMap[row][col];
+        const nextRegion = regionMap[nextRow][nextCol];
+        if (currentRegion === nextRegion) continue;
+
+        const [low, high] = currentRegion < nextRegion ? [currentRegion, nextRegion] : [nextRegion, currentRegion];
+        pairs.add(`${low}-${high}`);
+      }
+    }
+  }
+
+  return Array.from(pairs, (pair) => pair.split('-').map(Number) as [number, number]);
+};
+
+const getBoundaryCells = (regionMap: RegionMap, regionId: number, neighborRegionId: number): CellPosition[] => {
+  const cells: CellPosition[] = [];
+
+  for (let row = 0; row < 9; row++) {
+    for (let col = 0; col < 9; col++) {
+      if (regionMap[row][col] !== regionId) continue;
+
+      const touchesNeighbor = DIRECTIONS.some(([rowOffset, colOffset]) => {
+        const nextRow = row + rowOffset;
+        const nextCol = col + colOffset;
+        return isInBounds(nextRow, nextCol) && regionMap[nextRow][nextCol] === neighborRegionId;
+      });
+
+      if (touchesNeighbor) {
+        cells.push([row, col]);
+      }
+    }
+  }
+
+  return cells;
+};
+
+const swapRegionCells = (
+  regionMap: RegionMap,
+  firstCell: CellPosition,
+  secondCell: CellPosition,
+  firstRegionId: number,
+  secondRegionId: number
+): RegionMap => {
+  const nextRegionMap = cloneRegionMap(regionMap);
+  const [firstRow, firstCol] = firstCell;
+  const [secondRow, secondCol] = secondCell;
+
+  nextRegionMap[firstRow][firstCol] = secondRegionId;
+  nextRegionMap[secondRow][secondCol] = firstRegionId;
+
+  return nextRegionMap;
+};
+
+const findBetterCompatibleRegionMap = (
+  regionMap: RegionMap,
+  fullBoard: GameBoard,
+  currentDifference: number
+): RegionMap | null => {
+  let bestDifference = currentDifference;
+  let bestRegionMaps: RegionMap[] = [];
+
+  for (const [firstRegionId, secondRegionId] of shuffleArray(getTouchingRegionPairs(regionMap))) {
+    const firstBoundaryCells = shuffleArray(getBoundaryCells(regionMap, firstRegionId, secondRegionId));
+    const secondBoundaryCells = getBoundaryCells(regionMap, secondRegionId, firstRegionId);
+
+    for (const firstCell of firstBoundaryCells) {
+      const [firstRow, firstCol] = firstCell;
+      const matchingSecondCells = secondBoundaryCells.filter(([secondRow, secondCol]) => fullBoard[secondRow][secondCol] === fullBoard[firstRow][firstCol]);
+
+      for (const secondCell of shuffleArray(matchingSecondCells)) {
+        const candidateRegionMap = swapRegionCells(regionMap, firstCell, secondCell, firstRegionId, secondRegionId);
+        const candidateDifference = countDifferentCells(candidateRegionMap, STANDARD_REGION_MAP);
+
+        if (candidateDifference <= bestDifference || !isValidRegionMap(candidateRegionMap)) {
+          continue;
+        }
+
+        if (candidateDifference > bestDifference) {
+          bestDifference = candidateDifference;
+          bestRegionMaps = [];
+        }
+
+        bestRegionMaps.push(candidateRegionMap);
+      }
+    }
+  }
+
+  if (bestRegionMaps.length === 0) {
+    return null;
+  }
+
+  return shuffleArray(bestRegionMaps)[0];
+};
+
+const isSolvedBoardForRegionMap = (board: GameBoard, regionMap: RegionMap): boolean => {
+  const expected = DIGITS.join(',');
+  const toKey = (values: number[]) => [...values].sort((a, b) => a - b).join(',');
+
+  for (let index = 0; index < 9; index++) {
+    if (toKey(board[index]) !== expected) return false;
+    if (toKey(board.map((row) => row[index])) !== expected) return false;
+
+    const regionValues: number[] = [];
+    for (let row = 0; row < 9; row++) {
+      for (let col = 0; col < 9; col++) {
+        if (regionMap[row][col] === index) {
+          regionValues.push(board[row][col]);
+        }
+      }
+    }
+
+    if (toKey(regionValues) !== expected) return false;
+  }
+
+  return true;
+};
+
+const rememberSolvedSudoku = (solvedSudoku: SolvedSudoku): SolvedSudoku => {
+  generatedFullBoards.set(solvedSudoku.regionMap, cloneBoard(solvedSudoku.fullBoard));
+  return solvedSudoku;
+};
+
+const generateSolvedIrregularSudoku = (): SolvedSudoku => {
+  let bestSolvedSudoku: SolvedSudoku | null = null;
+  let bestDifference = -1;
+
+  for (let restart = 0; restart < MAX_IRREGULAR_RESTARTS; restart++) {
+    const fullBoard = generateRandomStandardFullBoard();
+    let regionMap = cloneRegionMap(STANDARD_REGION_MAP);
+    let difference = 0;
+
+    for (let step = 0; step < MAX_IRREGULAR_GREEDY_STEPS; step++) {
+      const nextRegionMap = findBetterCompatibleRegionMap(regionMap, fullBoard, difference);
+      if (!nextRegionMap) break;
+
+      regionMap = nextRegionMap;
+      difference = countDifferentCells(regionMap, STANDARD_REGION_MAP);
+    }
+
+    if (isValidRegionMap(regionMap) && isSolvedBoardForRegionMap(fullBoard, regionMap) && difference > bestDifference) {
+      bestSolvedSudoku = { fullBoard, regionMap };
+      bestDifference = difference;
+    }
+
+    if (bestSolvedSudoku && bestDifference >= MIN_IRREGULAR_CELL_DIFFERENCE) {
+      return rememberSolvedSudoku(bestSolvedSudoku);
+    }
+  }
+
+  if (bestSolvedSudoku && bestDifference > 0) {
+    return rememberSolvedSudoku(bestSolvedSudoku);
+  }
+
+  return rememberSolvedSudoku({
+    fullBoard: randomizeDigits(IRREGULAR_FULL_BOARD),
+    regionMap: cloneRegionMap(IRREGULAR_REGION_MAP),
+  });
+};
+
+export const generateIrregularRegionMap = (): RegionMap => generateSolvedIrregularSudoku().regionMap;
+
 export const isPlacementValid = (
  board: GameBoard,
  row: number,
@@ -132,26 +349,40 @@ export const isPlacementValid = (
 };

 const fillBoard = (board: GameBoard, regionMap: RegionMap): boolean => {
+  let bestCell: { row: number; col: number; candidates: number[] } | null = null;
+
  for (let row = 0; row < 9; row++) {
    for (let col = 0; col < 9; col++) {
      if (board[row][col] !== 0) continue;

-      const numbers = shuffleArray([1, 2, 3, 4, 5, 6, 7, 8, 9]);
-      for (const num of numbers) {
-        if (isPlacementValid(board, row, col, num, regionMap)) {
-          board[row][col] = num;
-          if (fillBoard(board, regionMap)) {
-            return true;
-          }
-          board[row][col] = 0;
-        }
+      const candidates = DIGITS.filter((num) => isPlacementValid(board, row, col, num, regionMap));
+      if (!bestCell || candidates.length < bestCell.candidates.length) {
+        bestCell = { row, col, candidates };
      }

-      return false;
+      if (candidates.length <= 1) {
+        break;
+      }
+    }
+
+    if (bestCell && bestCell.candidates.length <= 1) {
+      break;
    }
  }

-  return true;
+  if (!bestCell) {
+    return true;
+  }
+
+  for (const num of shuffleArray(bestCell.candidates)) {
+    board[bestCell.row][bestCell.col] = num;
+    if (fillBoard(board, regionMap)) {
+      return true;
+    }
+    board[bestCell.row][bestCell.col] = 0;
+  }
+
+  return false;
 };

 export const generateFullBoard = (regionMap: RegionMap): GameBoard => {
@@ -159,6 +390,11 @@ export const generateFullBoard = (regionMap: RegionMap): GameBoard => {
    throw new Error('Invalid sudoku region map');
  }

+  const generatedFullBoard = generatedFullBoards.get(regionMap);
+  if (generatedFullBoard) {
+    return cloneBoard(generatedFullBoard);
+  }
+
  if (isSameRegionMap(regionMap, IRREGULAR_REGION_MAP)) {
    return randomizeDigits(IRREGULAR_FULL_BOARD);
  }
@@ -183,8 +419,7 @@ const getRemovalCount = (difficulty: Difficulty) => {
  }
 };

-export const generatePuzzle = (difficulty: Difficulty, regionMap: RegionMap): GameBoard => {
-  const fullBoard = generateFullBoard(regionMap);
+const createPuzzleFromFullBoard = (difficulty: Difficulty, fullBoard: GameBoard): GameBoard => {
  const puzzle = fullBoard.map((row) => [...row]);
  const positions = Array.from({ length: 81 }, (_, idx) => idx);
  const toRemove = shuffleArray(positions).slice(0, getRemovalCount(difficulty));
@@ -198,6 +433,25 @@ export const generatePuzzle = (difficulty: Difficulty, regionMap: RegionMap): Ga
  return puzzle;
 };

+export const generatePuzzle = (difficulty: Difficulty, regionMap: RegionMap): GameBoard =>
+  createPuzzleFromFullBoard(difficulty, generateFullBoard(regionMap));
+
+export const generatePuzzleForMode = (difficulty: Difficulty, mode: GameMode): GeneratedPuzzle => {
+  if (mode === 'standard') {
+    const regionMap = cloneRegionMap(STANDARD_REGION_MAP);
+    return {
+      puzzle: createPuzzleFromFullBoard(difficulty, generateRandomStandardFullBoard()),
+      regionMap,
+    };
+  }
+
+  const { fullBoard, regionMap } = generateSolvedIrregularSudoku();
+  return {
+    puzzle: createPuzzleFromFullBoard(difficulty, fullBoard),
+    regionMap,
+  };
+};
+
 export const getRegionNeighbors = (regionMap: RegionMap, row: number, col: number) => {
  const regionId = getRegionId(regionMap, row, col);

@@ -210,4 +464,4 @@ export const getRegionNeighbors = (regionMap: RegionMap, row: number, col: numbe
 };

 export const getRegionMapByMode = (mode: GameMode): RegionMap =>
-  mode === 'irregular' ? IRREGULAR_REGION_MAP : STANDARD_REGION_MAP;
+  mode === 'irregular' ? generateIrregularRegionMap() : cloneRegionMap(STANDARD_REGION_MAP);