37. 解数独 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.

 

方法：

递归加回溯法

 

public class SudokuSolver {
    private boolean[][] row = new boolean[9][9];
    private boolean[][] col = new boolean[9][9];
    private boolean[][][] block = new boolean[3][3][9];
    private boolean valid = false;
    private List<int[]> spaces = new ArrayList<>();

    public void solveSudoku(char [][] board){
        for(int i = 0; i < 9; i++){
            for(int j = 0; j < 9; j++){
                if(board[i][j] == '.'){
                    spaces.add(new int[]{i, j});
                }else{
                    int digit = board[i][j] - '0' - 1;
                    row[i][digit] = col[j][digit] = block[i / 3][j / 3][digit] = true;
                }
            }
        }
        dfs(board , 0);

    }

    public void dfs(char[][] board, int pos){
        if(pos == spaces.size()){
            valid = true;
            return;
        }
        int [] space = spaces.get(pos);
        int i = space[0], j = space[1];
        for (int digit = 0; digit < 9 && !valid; ++digit){
            if(!row[i][digit] && !col[j][digit] && !block[i / 3][j / 3][digit]){
                row[i][digit] = col[j][digit] = block[i / 3][j / 3][digit] = true;
                board[i][j] = (char)(digit + '0' + 1);
                dfs(board, pos + 1);
                row[i][digit] = col[j][digit] = block[i / 3][j / 3][digit] = false;
            }
        }
    }

}

 

参考链接：

https://leetcode.com/problems/sudoku-solver/

https://leetcode-cn.com/problems/sudoku-solver/