【算法训练】LeetCode#36 有效的数独

一、描述

36. 有效的数独

请你判断一个 9 x 9 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）

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。
• 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：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。

二、思路

按照要求逐一判别即可。

三、解题

public class LeetCode36 {

    public static boolean isValidSudoku(char[][] board) {
        // 先判断9个3*3是否有效
        for (int i = 0 ; i < 7 ; i+=3){
            for (int j = 0 ; j < 7 ; j+=3){
                int[] arr = new int[10]; // 10个空间，对应0-9,默认都为0，存在记1，记数时arr[i]等于1，则无效
                for (int row = i ; row < i+3 ; row++){
                    for (int col = j ; col < j+3 ; col++){
                        if (board[row][col] == '.'){
                            continue;
                        }
                        if (arr[board[row][col]-'0'] > 0){
                            return false;
                        } else {
                            arr[board[row][col]-'0'] = 1;
                        }
                    }
                }
            }
        }

        // 判断每行
        for (int i = 0 ; i < 9 ; i++){
            int[] arr = new int[10]; // 10个空间，对应0-9,默认都为0，存在记1，记数时arr[i]等于1，则无效
            for (int j = 0 ; j < 9 ; j++){
                if (board[i][j] == '.'){
                    continue;
                }
                if (arr[board[i][j]-'0'] > 0){
                    return false;
                } else {
                    arr[board[i][j]-'0'] = 1;
                }
            }
        }

        // 判断每列
        for (int i = 0 ; i < 9 ; i++){
            int[] arr = new int[10]; // 10个空间，对应0-9,默认都为0，存在记1，记数时arr[i]等于1，则无效
            for (int j = 0 ; j < 9 ; j++){
                if (board[j][i] == '.'){
                    continue;
                }
                if (arr[board[j][i]-'0'] > 0){
                    return false;
                } else {
                    arr[board[j][i]-'0'] = 1;
                }
            }
        }
        return true;
    }

    public static void main(String[] args) {
        char[][] arr = new char[][]{{'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'}};
        System.out.println(isValidSudoku(arr));
    }
}