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37. Sudoku Solver

Difficulty: Hard

LeetCode Problem View on GitHub

37. Sudoku Solver

Hard

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.

Solution

class Solution {
    public void solveSudoku(char[][] board) {
        int n = board.length, m = board[0].length;
        solve_sudoku(board);
    }
    private boolean solve_sudoku(char board[][]) {
        int n = board.length, m = board[0].length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (board[i][j] == '.') {
                    for (char t = '1'; t <= '9'; t++) {
                        if (isPossible(t, i, j, board)) {
                            board[i][j] = t;
                            if (solve_sudoku(board) == true) 
                                return true;
                            else 
                                board[i][j] = '.'; 
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }
    private boolean isPossible(char ch, int row, int col, char board[][]) {
        for (int i = 0; i < 9; i++) {
            if (board[i][col] == ch) 
                return false;
            if (board[row][i] == ch) 
                return false;
            if (board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] == ch) 
                return false;
        }
        return true;
    }
}

Complexity Analysis

  • Time Complexity: O(?)
  • Space Complexity: O(?)

Approach

Detailed explanation of the approach will be added here