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37. Sudoku Solver 👍

  • Time: NP-Complete
  • Space: $O(1)$
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class Solution {
 public:
  void solveSudoku(vector<vector<char>>& board) {
    solve(board, 0);
  }

 private:
  bool solve(vector<vector<char>>& board, int s) {
    if (s == 81)
      return true;

    const int i = s / 9;
    const int j = s % 9;

    if (board[i][j] != '.')
      return solve(board, s + 1);

    for (char c = '1'; c <= '9'; ++c)
      if (isValid(board, i, j, c)) {
        board[i][j] = c;
        if (solve(board, s + 1))
          return true;
        board[i][j] = '.';
      }

    return false;
  }

  bool isValid(vector<vector<char>>& board, int row, int col, char c) {
    for (int i = 0; i < 9; ++i)
      if (board[i][col] == c || board[row][i] == c ||
          board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] == c)
        return false;
    return true;
  }
};

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class Solution {
  public void solveSudoku(char[][] board) {
    dfs(board, 0);
  }

  private boolean dfs(char[][] board, int s) {
    if (s == 81)
      return true;

    final int i = s / 9;
    final int j = s % 9;

    if (board[i][j] != '.')
      return dfs(board, s + 1);

    for (char c = '1'; c <= '9'; ++c)
      if (isValid(board, i, j, c)) {
        board[i][j] = c;
        if (dfs(board, s + 1))
          return true;
        board[i][j] = '.';
      }

    return false;
  }

  private boolean isValid(char[][] board, int row, int col, char c) {
    for (int i = 0; i < 9; ++i)
      if (board[i][col] == c || board[row][i] == c ||
          board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] == c)
        return false;
    return true;
  }
}

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class Solution:
  def solveSudoku(self, board: list[list[str]]) -> None:
    def isValid(row: int, col: int, c: str) -> bool:
      for i in range(9):
        if (board[i][col] == c or
            board[row][i] == c or
                board[3 * (row // 3) + i // 3][3 * (col // 3) + i % 3] == c):
          return False
      return True

    def solve(s: int) -> bool:
      if s == 81:
        return True

      i = s // 9
      j = s % 9

      if board[i][j] != '.':
        return solve(s + 1)

      for c in string.digits[1:]:
        if isValid(i, j, c):
          board[i][j] = c
          if solve(s + 1):
            return True
          board[i][j] = '.'

      return False

    solve(0)