0037.解数独.java

/*
 * @lc app=leetcode.cn id=37 lang=java
 *
 * [37] 解数独
 *
 * https://leetcode-cn.com/problems/sudoku-solver/description/
 *
 * algorithms
 * Hard (55.97%)
 * Likes:    253
 * Dislikes: 0
 * Total Accepted:    12.6K
 * Total Submissions: 21.9K
 * Testcase Example:  '[["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"]]'
 *
 * 编写一个程序，通过已填充的空格来解决数独问题。
 * 
 * 一个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。
 * 
 * 
 * 空白格用 '.' 表示。
 * 
 * 
 * 
 * 一个数独。
 * 
 * 
 * 
 * 答案被标成红色。
 * 
 * Note:
 * 
 * 
 * 给定的数独序列只包含数字 1-9 和字符 '.' 。
 * 你可以假设给定的数独只有唯一解。
 * 给定数独永远是 9x9 形式的。
 * 
 * 
 */

// @lc code=start
class Solution {
    public void solveSudoku(char[][] board) {
        boolean[][] row = new boolean[9][10];
        boolean[][] col = new boolean[9][10];
        boolean[][] block = new boolean[9][10];

        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] != '.') {
                    int num = board[i][j] - '0';
                    row[i][num] = true;
                    col[j][num] = true;
                    int blockIndex = i / 3 * 3 + j / 3;
                    block[blockIndex][num] = true;
                }
            }
        }
        dfs(board, row, col, block, 0, 0);
    }

    private boolean dfs(char[][] board, boolean[][] row, boolean[][] col, boolean[][] block, int i, int j) {
        while (board[i][j] != '.') {
            if (++j >= 9) {
                i++;
                j = 0;
            }
            if (i >= 9) {
                return true;
            }
        }
        for (int num = 1; num <= 9; num++) {
            int blockIndex = i / 3 * 3 + j / 3;
            if (!row[i][num] && !col[j][num] && !block[blockIndex][num]) {
                board[i][j] = (char) ('0' + num);
                row[i][num] = true;
                col[j][num] = true;
                block[blockIndex][num] = true;
                if (dfs(board, row, col, block, i, j)) {
                    return true;
                } else {
                    row[i][num] = false;
                    col[j][num] = false;
                    block[blockIndex][num] = false;
                    board[i][j] = '.';
                }
            }
        }
        return false;
    }
}
// @lc code=end