leetcode-解数独

这是我参与8月更文挑战的第26天，活动详情查看：8月更文挑战

昨晚乒乓球赛赢了，挺开心的。本周的锻炼目标也达成，而且本周末之后，8月更文挑战也就完成的差不多了。行百步者半九十，差不多最后一周的时间就共勉吧。
今天做的是leetcode的第37题。

题目

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：

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
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。

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：

思路

今天的题目是昨天题目的延续，昨天是校验是否有效，今天是需要求解。
其实也没什么可以特别说的，根据数独的规则，每行、每列、每个小方块，都是1-9各出现1次。
反映到程序上，用3个boolean二维数组：
line的第1维代表数组的0-8行，第2维代表1-9这9个数字是否出现过
column的第1维代表数组的0-8列，第2维代表1-9这9个数字是否出现过
box的第1维代表0-8个小方框，第2维代表1-9这9个数字是否出现过
然后就是一个深度搜索+回溯。

Java版本代码

class Solution {
    public void solveSudoku(char[][] board) {
        // 预处理
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] != '.') {
                    int val = board[i][j] - '0';
                    line[i][val-1] = true;
                    column[j][val-1] = true;
                    box[i/3*3 + j/3][val-1] = true;
                } else {
                    space.add(new Point(i, j));
                }
            }
        }
        // 深度搜索
        shuduDfs(board, 0);
    }

    private static boolean[][] line = new boolean[9][9];
    private static boolean[][] column = new boolean[9][9];
    private static boolean[][] box = new boolean[9][9];
    private static List<Point> space = new ArrayList();
    static boolean isValid = false;

    static class Point {

        private int x;

        private int y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public int getX() {
            return x;
        }

        public int getY() {
            return y;
        }
    }

    private static void shuduDfs(char[][] board, int num) {
        if (num == space.size()) {
            isValid = true;
            return;
        }
        Point point = space.get(num);
        int x = point.getX();
        int y = point.getY();
        for (int val = 1; val <= 9 && !isValid; val++) {
            if (!line[x][val-1] && !column[y][val-1] && !box[x/3*3 + y/3][val-1]) {
                line[x][val-1] = column[y][val-1] = box[x/3*3 + y/3][val-1] = true;
                board[x][y] = (char) ('0' + val);
                shuduDfs(board, num + 1);
                line[x][val-1] = column[y][val-1] = box[x/3*3 + y/3][val-1] = false;
            }
        }
    }
}