37. 解数独

编写一个程序，通过填充空格来解决数独问题。

数独的解法需 遵循如下规则：

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）

数独部分空格内已填入了数字，空白格用 '.' 表示。

 

示例 1：

输入：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"]]
输出：[["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"]]
解释：输入的数独如上图所示，唯一有效的解决方案如下所示：

class Solution {
    boolean[][] row;
    boolean[][] col;
    boolean[][][] map = new boolean[3][3][10];
    int n;
    int[][] dir = new int[][]{{1,0},{-1,0},{0,1},{0,-1}};
    
    public void solveSudoku(char[][] board) {
        n = 9;
        row = new boolean[9][10];
        col = new boolean[9][10];
        int cnt = 0;
        for(int i = 0 ; i < n ; i++){
            for(int j = 0 ; j < n ; j++){
                if(board[i][j] != '.'){
                    int t = board[i][j] - '0'; 
                    row[i][t] = true;
                    col[j][t] = true;
                    map[i/3][j/3][t] = true;
                }else｛
                   cnt++;
               ｝
            }
        }
        boolean[][] vis = new boolean[9][9];
        dfs(board, 0, 0, cnt, vis);
    }

    boolean dfs(char[][] board , int i , int j ,  int cnt , boolean[][] vis){
        if(cnt == 0) return true;
        if(vis[i][j]) return false;
        for(int[] d : dir){
            int x = i + d[0];
            int y = j + d[1];
            if(x>=0 && y >= 0 && x < n && y < n ){
                if(board[x][y] == '.'){
                    int target = -1;
                    for(int a = 1 ; a <= 9 ; a++){
                        if(!row[x][a] && !col[y][a] && !map[x/3][y/3][a] && !vis[x][y]){
                            target = a;
                            board[x][y] = (char)('0' + target); 
                            row[x][target] = true; 
                            col[y][target] = true;
                            map[x/3][y/3][target] = true;
                            vis[x][y] = true;
                            if(dfs(board,x,y,cnt-1,vis)) return true;
                            vis[x][y] = false;
                            row[x][target] = false;
                            col[y][target] = false;
                            map[x/3][y/3][target] = false;
                            board[x][y] = '.';
                        }
                    }
                }else{
                    vis[i][j] = true;
                    if(dfs(board,x,y,cnt,vis)) return true;
                    vis[i][j] = false;
                }
            }
        }
        return false;
    }
}