解数独

37. 解数独 - 力扣（LeetCode）

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 1：

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：

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

class Solution {
    public void solveSudoku(char[][] board) {
        traversal(board);
    }


    public boolean traversal(char[][] board){
        for(int i = 0; i < board.length; i++){
            for(int j = 0; j < board[0].length; j++){
                if(board[i][j] != '.'){
                    continue;
                }else{//找到为空的位置
                    //尝试从9个数中放入一个，如果能放入，继续递归
                    for(char k ='1'; k <= '9'; k++){
                        if(isVaild(board, i, j, k)){
                            board[i][j] = k;
                            if(traversal(board)) return true;
                            board[i][j] = '.';
                        }
                    }
                    //9个数都不能放入，无解
                    return false;
                }
            }
        }
        return true;
    }


    public boolean isVaild(char[][] board, int x, int y, char k){
        //同行不能出现重复数字
        for(int j = 0; j < board[0].length; j++){
            if(board[x][j] == k){
                return false;
            }
        }
        //同列不能出现重复数字
        for(int i = 0; i < board.length; i++){
            if(board[i][y] == k){
                return false;
            }
        }

        //同一个9宫格不能出现重复元素
        int startRow = x/3 * 3;
        int startCol = y/3 * 3;
        for(int i = startRow; i < startRow + 3 ; i++){
            for(int j = startCol; j < startCol + 3; j++){
                if(board[i][j] == k){
                    return false;
                }
            }
        }
        return true;
    }
}