11.1打卡

1. 有效的数独（36）

请你判断一个 9 x 9 的数独是否有效。只需要 根据以下规则 ，验证已经填入的数字是否有效即可。

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）

class Solution {
    public boolean isValidSudoku(char[][] board) {
     HashMap<Integer, Set<Integer>> row = new HashMap<>();
            HashMap<Integer, Set<Integer>> col = new HashMap<>();
            HashMap<Integer, Set<Integer>> area = new HashMap<>();

            for (int i = 0; i < 9; i++) {
                row.put(i,new HashSet<>());
                col.put(i,new HashSet<>());
                area.put(i,new HashSet<>());
            }


            for (int i = 0; i < 9; i++) {
                for (int j = 0; j <9 ; j++) {
                    char c = board[i][j];
                    if(c=='.') continue;
                    int u = c-'0';
                    int idx = i/3*3+j/3;
                    if(row.get(i).contains(u)||col.get(j).contains(u)||area.get(idx).contains(u))
                        return false;
                    row.get(i).add(u);
                    col.get(j).add(u);
                    area.get(idx).add(u);
                }
            }
            return true;
    }
}

2.解数独

编写一个程序，通过填充空格来解决数独问题

class Solution {
   private boolean[][] line = new boolean[9][9];
    private boolean[][] column = new boolean[9][9];
    private boolean[][][] block = new boolean[3][3][9];
    private boolean valid = false;
    private List<int[]> spaces = new ArrayList<int[]>();

    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;
                    line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = true;
                }
            }
        }

        recusiveSolveSudoku(board, 0);

    }

    public void recusiveSolveSudoku(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 (!line[i][digit] && !column[j][digit] && !block[i / 3][j / 3][digit]) {
                line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = true;
                board[i][j] = (char) (digit + '0' + 1);
                recusiveSolveSudoku(board, pos + 1);
                line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = false;
            }
        }
    }
}