36#有效的数独
题目描述
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。
- 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。
上图是一个部分填充的有效的数独。
数独部分空格内已填入了数字,空白格用 '.'
表示。
示例 1:
输入:
[
["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:
[
["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。
说明:
- 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。
- 给定数独序列只包含数字
1-9
和字符'.'
。 - 给定数独永远是
9x9
形式的。
分析
一个直观的印象就是要把整个9×9
宫遍历一遍,对每一个元素进行判断。要使一个单元(一个单元指同一行/列/3×3
宫)内的元素没有重复,实际上就是查看当前的元素在对应的单元内是不是已经存在了。如果已经存在,说明有重复,这个数独不是有效的数独;如果所有的元素都遍历完了,也没有判断出重复,说明这个数独是有效的数独。
根据“查看当前的元素在对应的单元内是不是已经存在了”这一思路,我们可以设置一个哈希表,将每个非空元素添加进去,哈希表的add()
方法会返回一个boolean
变量,如果添加的元素已存在于表中,返回值是false
;如果添加的值不存在于表中,返回值是true
。添加不是简单地只把元素的值添加进去,同时要把它所附带的位置信息一起填入,这样每个元素才是独一无二的。
源码
class Solution {
public boolean isValidSudoku(char[][] board)
{
HashSet set = new HashSet();
for (int i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
char current = board[i][j];
if (current != '.') {
if (!set.add(current + " in row " + i) || // 判断当前行
!set.add(current + " in col " + j) || // 判断当前列
!set.add(current + " in box " + i / 3 + ", " + j/3)) // 判断当前3*3宫
return false;
}
}
}
return true;
}
}
测试用例
public static void main(String[] args)
{
ValidSudoku vs = new ValidSudoku();
char[][] board = 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(vs.isValidSudoku(board));
}