LeetCode-36-有效的数独

36. 有效的数独

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请你判断一个 9x9 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）

数独部分空格内已填入了数字，空白格用 '.' 表示。

注意：

• 一个有效的数独（部分已被填充）不一定是可解的。
• 只需要根据以上规则，验证已经填入的数字是否有效即可。

示例 1：

img

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：true

示例 2：

输入：board = 
[["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"]]
输出：false
解释：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字或者 '.'

准备三个有效验证的数组

boolean[][] row = new boolean[9][10];
boolean[][] col = new boolean[9][10];
boolean[][] bucket = new boolean[9][10];

row[2][7] 表示 第2行 7数字已经出现了

col[2][7] 表示 第2列 7数字已经出现了

bucket[2][7] 表示 第2个9*9的格子 7数字已经出现了

class Solution {
   public static boolean isValidSudoku(char[][] board) {
        boolean[][] row = new boolean[9][10];
        boolean[][] col = new boolean[9][10];
        boolean[][] bucket = new boolean[9][10];
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                int bid = 3 * (i / 3) + (j / 3);
                if (board[i][j] != '.') {
                    int num = board[i][j] - '0';
                    if (row[i][num] || col[j][num] || bucket[bid][num]) {
                        return false;
                    }
                    row[i][num] = true;
                    col[j][num] = true;
                    bucket[bid][num] = true;
                }
            }
        }
        return true;
    }
}

LeetCode-37-解数独

37. 解数独

难度困难830收藏分享切换为英文接收动态反馈

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：

img

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：

250px-sudoku-by-l2g-20050714_solutionsvg.png

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字或者 '.'
• 题目数据 保证 输入数独仅有一个解

使用第36题的有效性过滤条件来尝试填入的数字

for (int num = 1; num <= 9; num++) 每个格子使用1~9填入数字尝试

尝试前判断一下填入数组的有效性if ((!row[i][num]) && (!col[j][num]) && (!bucket[bid][num]))

class Solution {
    public static void solveSudoku(char[][] board) {
        boolean[][] row = new boolean[9][10];
        boolean[][] col = new boolean[9][10];
        boolean[][] bucket = new boolean[9][10];
        initMaps(board, row, col, bucket);
        process(board, 0, 0, row, col, bucket);
    }

    public static void initMaps(char[][] board, boolean[][] row, boolean[][] col, boolean[][] bucket) {
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                int bid = 3 * (i / 3) + (j / 3);
                if (board[i][j] != '.') {
                    int num = board[i][j] - '0';
                    row[i][num] = true;
                    col[j][num] = true;
                    bucket[bid][num] = true;
                }
            }
        }
    }

    public static boolean process(char[][] board, int i, int j, boolean[][] row, boolean[][] col, boolean[][] bucket) {
        if (i == 9) {
            return true;
        }
        int nexti = j != 8 ? i : i + 1;
        int nextj = j != 8 ? j + 1 : 0;
        if (board[i][j] != '.') {
            return process(board, nexti, nextj, row, col, bucket);
        } else {
            int bid = 3 * (i / 3) + (j / 3);
            for (int num = 1; num <= 9; num++) {
                if ((!row[i][num]) && (!col[j][num]) && (!bucket[bid][num])) {
                    row[i][num] = true;
                    col[j][num] = true;
                    bucket[bid][num] = true;
                    board[i][j] = (char) (num + '0');
                    if (process(board, nexti, nextj, row, col, bucket)) {
                        return true;
                    }
                    row[i][num] = false;
                    col[j][num] = false;
                    bucket[bid][num] = false;
                    board[i][j] = '.';
                }
            }
            return false;
        }
    }
}