Sudoku Solver LeetCode Solution | Easy Approach

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Sudoku Solver | Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

  1. Each of the digits 1-9 must occur exactly once in each row.
  2. Each of the digits 1-9 must occur exactly once in each column.
  3. Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

The '.' character indicates empty cells.

Example 1:

Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
Output: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
Explanation: The input board is shown above and the only valid solution is shown below:


Constraints:

  • board.length == 9
  • board[i].length == 9
  • board[i][j] is a digit or '.'.
  • It is guaranteed that the input board has only one solution.

Sudoku Solver Solutions

Time: NP-Complete
Space: O(1)

C++

 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;
  }
};

Java

 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;
  }
}

Python

class Solution:
  def solveSudoku(self, board: List[List[str]]) -> None:
    def isValid(row: int, col: int, c: chr) -> 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)
 

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