題目

Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

Each row must contain the digits 1-9 without repetition.
Each column must contain the digits 1-9 without repetition.
Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

Example 1:

Input:
[
["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: true
Example 2:

Input:
[
["8","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: false
Explanation: Same as Example 1, except with the 5 in the top left corner being
modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.
Note:

• A Sudoku board (partially filled) could be valid but is not necessarily solvable.
• Only the filled cells need to be validated according to the mentioned rules.
• The given board contain only digits 1-9 and the character '.'.
• The given board size is always 9x9.

解題思路

玩過數(shù)獨(dú)的人都應(yīng)該清楚，本題就是要求對(duì)給出的9*9數(shù)組進(jìn)行驗(yàn)證祝沸，如果滿足：

1胳喷、橫向數(shù)字只有1-9且不重復(fù)（"."為補(bǔ)充占位晌坤，后續(xù)不再解釋）

2晨川、豎向數(shù)字只有1-9且不重復(fù)

3刷喜、把99的矩陣分成9個(gè)33的矩陣荣回，每個(gè)矩陣中數(shù)字只有1-9且不重復(fù)

依照上面的解題思路侄榴，就是要對(duì)9*9的矩陣進(jìn)行3次判斷雹锣，全部校驗(yàn)通過則通過，反之不通過癞蚕。

代碼實(shí)現(xiàn)

以下為具體代碼實(shí)現(xiàn)蕊爵，僅供參考

public class Main {
 
 
    public static void main(String[] args) {
        Main main = new Main();
        char[][] arr = main.init();
        main.isValidSudoku(arr);
 
    }
 
    // 包含元素集合
    private Character[] demo = {'1', '2', '3', '4', '5', '6', '7', '8', '9', '.'};
 
    public boolean isValidSudoku(char[][] board) {
        if (checkHorizontal(board) && checkVertical(board) && checkGrid(board)) {
            System.out.println(true);
            return true;
        } else {
            System.out.println(false);
            return false;
        }
 
    }
 
    /**
     * 初始化數(shù)組
     *
     * @return
     */
    private char[][] init() {
        char[][] arr = {
                {'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'}
        };
 
//        char[][] arr = {{'8', '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'}};
        return arr;
    }
 
    /**
     * 判斷橫向9個(gè)數(shù)字是否有重復(fù)
     *
     * @param arr
     * @return
     */
    private boolean checkHorizontal(char[][] arr) {
        List<Character> strings = Arrays.asList(demo);
        Set<Character> set = new HashSet<>();
        for (char[] a : arr) {
            set.clear();
            for (char aa : a) {
                if (aa == '.') {
                    continue;
                } else if (strings.contains(aa) && !set.contains(aa)) {
                    set.add(aa);
                } else {
                    return false;
                }
            }
        }
        return true;
    }
 
    /**
     * 判斷豎向9個(gè)數(shù)字是否有重復(fù)
     *
     * @param arr
     * @return
     */
    private boolean checkVertical(char[][] arr) {
        char[][] tem = new char[9][9];
        // 將原9*9矩陣翻轉(zhuǎn)
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                tem[j][i] = arr[i][j];
            }
        }
        return checkHorizontal(tem);
    }
 
    /**
     * 判斷3*3的9個(gè)數(shù)字是否有重復(fù)
     *
     * @param arr
     * @return
     */
    private boolean checkGrid(char[][] arr) {
        char[][] tem = new char[9][9];
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                // [i / 3 * 3 + j / 3]:確認(rèn)當(dāng)前元素屬于3*3矩陣中第幾塊
                // [j % 3 * 3 + i % 3]:確認(rèn)當(dāng)前元素在所屬元素塊中是第幾個(gè)元素
                tem[i / 3 * 3 + j / 3][j % 3 * 3 + i % 3] = arr[i][j];
            }
        }
        return checkHorizontal(tem);
    }
 
}