---
id: 5a23c84252665b21eecc7ed5
title: ナイトツアー
challengeType: 5
forumTopicId: 302297
dashedName: knights-tour
---

# --description--

[ナイトツアー](https://en.wikipedia.org/wiki/Knight%27s_tour)の問題: 空の `w` \* `h` のチェスボードがあり、その上の任意のマスに 1 つのナイトの駒が置いてあります。 ナイトは一連のルールに従って動き、チェスボード上のすべてのマスを 1 度だけ訪れなければなりません。 ツアーを「終了する」必要は*ない*ことに注意してください。つまり、ナイトは開始地点の一手以内を終了地点にする必要はありません。

# --instructions--

パラメータとして `w` と `h` を取る関数を記述し、上記のタスクの達成が可能な開始位置の数値を返してください。

# --hints--

`knightTour` は関数とします。

```js
assert(typeof knightTour == 'function');
```

`knightTour(6, 6)` は数値を返す必要があります.

```js
assert(typeof knightTour(6, 6) == 'number');
```

`knightTour(6, 6)` は `36` を返す必要があります。

```js
assert.equal(knightTour(6, 6), 36);
```

`knightTour(5, 6)` は `30` を返す必要があります。

```js
assert.equal(knightTour(5, 6), 30);
```

`knightTour(4, 6)` は `12` を返す必要があります。

```js
assert.equal(knightTour(4, 6), 12);
```

`knightTour(7, 3)` は `10` を返す必要があります。

```js
assert.equal(knightTour(7, 3), 10);
```

`knightTour(8, 6)` は `48` を返す必要があります。

```js
assert.equal(knightTour(8, 6), 48);
```

# --seed--

## --seed-contents--

```js
function knightTour(w, h) {

}
```

# --solutions--

```js
function knightTour(w, h) {
  function createBoards(rows, columns) {
    const board = [];
    const visited = [];
    for (let i = 0; i < rows; i++) {
      board.push(new Array(columns).fill(-1));
      visited.push(new Array(columns).fill(false));
    }
    return [board, visited];
  }

  function copyBoard(board) {
    const copied = [];
    for (let i = 0; i < board.length; i++) {
      copied.push([...board[i]]);
    }
    return copied;
  }

  function isOnBoard(value, limit) {
    return value >= 0 && value < limit;
  }

  function markVisited(board, visited, row, column) {
    visited[row][column] = true;
    board[row][column] = -1;
  }

  function areAllVisited(visited) {
    return (
      visited.filter(row => row.filter(column => column === false).length !== 0)
        .length === 0
    );
  }

  function getMovesFrom(board, row, column) {
    const possibleMoves = [];
    for (let i = 0; i < moves.length; i++) {
      const [rowChange, colChange] = moves[i];
      const [rowN, colN] = [row + rowChange, column + colChange];
      if (!isOnBoard(rowN, board.length) || !isOnBoard(colN, board[0].length)) {
        continue;
      }
      possibleMoves.push([rowN, colN]);
    }
    return possibleMoves;
  }

  function fillAllowedMovesCounts(board) {
    for (let row = 0; row < board.length; row++) {
      for (let column = 0; column < board[0].length; column++) {
        board[row][column] = getMovesFrom(board, row, column).length;
      }
    }
  }

  function updateAllowedMovesCounts(board, possibleMoves) {
    for (let i = 0; i < possibleMoves.length; i++) {
      const [row, column] = possibleMoves[i];
      if (board[row][column] > 0) {
        board[row][column]--;
      }
    }
  }

  function getBestNextMoves(board, allowedMoves) {
    let bestMoves = [];
    let fewestNextMoves = Infinity;
    let zeroMove = [];
    for (let i = 0; i < allowedMoves.length; i++) {
      const [moveRow, moveCol] = allowedMoves[i];
      const numMoves = board[moveRow][moveCol];
      if (numMoves === -1) {
        continue;
      }
      if (numMoves === 0) {
        zeroMove.push(allowedMoves[i]);
      }
      if (numMoves < fewestNextMoves) {
        bestMoves = [allowedMoves[i]];
        fewestNextMoves = numMoves;
      } else if (numMoves === fewestNextMoves) {
        bestMoves.push(allowedMoves[i]);
      }
    }

    if (bestMoves.length > 0) {
      return bestMoves;
    }
    return zeroMove;
  }

  function solve(board, visited, lastRow, lastColumn) {
    if (areAllVisited(visited)) {
      return true;
    }
    const nextMoves = getMovesFrom(board, lastRow, lastColumn);
    updateAllowedMovesCounts(board, nextMoves);
    const allowedMoves = nextMoves.filter(
      ([row, column]) => !visited[row][column]
    );

    const bestMoves = getBestNextMoves(board, allowedMoves);
    const restMoves = allowedMoves.filter(
      move => bestMoves.indexOf(move) === -1
    );
    const possibleMoves = [...bestMoves];
    possibleMoves.push(...getBestNextMoves(board, restMoves));

    for (let i = 0; i < possibleMoves.length; i++) {
      const [moveRow, moveCol] = possibleMoves[i];
      const newBoard = copyBoard(board);
      const newVisited = copyBoard(visited);
      markVisited(newBoard, newVisited, moveRow, moveCol);
      if (solve(newBoard, newVisited, moveRow, moveCol)) {
        return true;
      }
    }
    return false;
  }

  function solveStart(board, visited, startRow, startColumn) {
    const newBoard = copyBoard(board);
    const newVisited = copyBoard(visited);
    markVisited(newBoard, newVisited, startRow, startColumn);
    return solve(newBoard, newVisited, startRow, startColumn);
  }

  const moves = [
    [-1, -2],
    [-2, -1],
    [-2, 1],
    [-1, 2],
    [1, 2],
    [2, 1],
    [2, -1],
    [1, -2]
  ];

  const [baseBoard, baseVisited] = createBoards(h, w);
  fillAllowedMovesCounts(baseBoard);
  let solvedCount = 0;
  for (let row = 0; row < h; row++) {
    for (let column = 0; column < w; column++) {
      if (solveStart(baseBoard, baseVisited, row, column)) {
        solvedCount++;
      }
    }
  }
  return solvedCount;
}
```