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2596. Check Knight Tour Configuration 👍

  • Time: $O(8n^2) = O(n^2)$
  • Space: $O(1)$
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class Solution {
 public:
  bool checkValidGrid(vector<vector<int>>& grid) {
    if (grid[0][0] != 0)
      return false;

    const int n = grid.size();
    int i = 0;
    int j = 0;

    for (int target = 1; target < n * n; ++target) {
      const auto [x, y] = nextGrid(grid, i, j, target);
      if (x == -1 && y == -1)
        return false;
      // Move (x, y) to (i, j).
      i = x;
      j = y;
    }

    return true;
  }

 private:
  static constexpr int dirs[8][2] = {{-2, 1}, {-1, 2}, {1, 2},   {2, 1},
                                     {2, -1}, {1, -2}, {-1, -2}, {-2, -1}};

  // Returns (x, y), where grid[x][y] == target if (i, j) can reach target.
  pair<int, int> nextGrid(const vector<vector<int>>& grid, int i, int j,
                          int target) {
    const int n = grid.size();
    for (const auto& [dx, dy] : dirs) {
      const int x = i + dx;
      const int y = j + dy;
      if (x < 0 || x >= n || y < 0 || y >= n)
        continue;
      if (grid[x][y] == target)
        return {x, y};
    }
    return {-1, -1};
  }
};

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class Solution {
  public boolean checkValidGrid(int[][] grid) {
    if (grid[0][0] != 0)
      return false;

    final int n = grid.length;
    int i = 0;
    int j = 0;

    for (int target = 1; target < n * n; ++target) {
      Pair<Integer, Integer> pair = nextGrid(grid, i, j, target);
      final int x = pair.getKey();
      final int y = pair.getValue();
      if (x == -1 && y == -1)
        return false;
      // Move (x, y) to (i, j).
      i = x;
      j = y;
    }

    return true;
  }

  private static final int[][] dirs = {{-2, 1}, {-1, 2}, {1, 2},   {2, 1},
                                       {2, -1}, {1, -2}, {-1, -2}, {-2, -1}};

  // Returns (x, y), where grid[x][y] == target if (i, j) can reach target.
  private Pair<Integer, Integer> nextGrid(int[][] grid, int i, int j, int target) {
    final int n = grid.length;
    for (int[] dir : dirs) {
      final int x = i + dir[0];
      final int y = j + dir[1];
      if (x < 0 || x >= n || y < 0 || y >= n)
        continue;
      if (grid[x][y] == target)
        return new Pair<>(x, y);
    }
    return new Pair<>(-1, -1);
  }
}

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class Solution:
  def checkValidGrid(self, grid: list[list[int]]) -> bool:
    if grid[0][0] != 0:
      return False

    dirs = ((1, 2), (2, 1), (2, -1), (1, -2),
            (-1, -2), (-2, -1), (-2, 1), (-1, 2))
    n = len(grid)
    i = 0
    j = 0

    def nextGrid(i: int, j: int, target: int) -> tuple[int, int]:
      """
      Returns (x, y), where grid[x][y] == target if (i, j) can reach target.
      """
      for dx, dy in dirs:
        x = i + dx
        y = j + dy
        if x < 0 or x >= n or y < 0 or y >= n:
          continue
        if grid[x][y] == target:
          return (x, y)
      return (-1, -1)

    for target in range(1, n * n):
      x, y = nextGrid(i, j, target)
      if x == -1 and y == -1:
        return False
      # Move (x, y) to (i, j).
      i = x
      j = y

    return True