题目
Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:
1.Each row must contain the digits 1-9 without repetition.
2.Each column must contain the digits 1-9 without repetition.
3.Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.
Note:
- A Sudoku board (partially filled) could be valid but is not necessarily solvable.
- Only the filled cells need to be validated according to the mentioned rules.
Example 1:
Input: 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"]]
Output: true
Example 2:
Input: 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"]]
Output: false
Explanation: Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.
Constraints:
board.length == 9board[i].length == 9-
board[i][j]is a digit1-9or'.'.
思路
方法1 （Java）
设置一个Set集合，遍历数独表二维数组，将当前遍历到的位置的元素以3个字符串形式记录下它所在的行，列和九宫格信息，并加入Set集合。若Set集合中存在某一元素的任意行/列/九宫格信息，则认为该表不符合规则。
设当前元素值为val，位置为(i, j)，位于第i/3*3+j/3个九宫格（从0开始），则该元素的信息可以设置为：
行信息："val in row i"
列信息："val in col j"
九宫格信息："val in box i/3*3+j/3"
class Solution {
public boolean isValidSudoku(char[][] board) {
HashSet<String> set = new HashSet<>();
for(int i = 0; i < 9; i++){
for(int j = 0; j < 9; j++){
if(board[i][j] == '.') continue;
String row = board[i][j] + " in row " + i;
String col = board[i][j] + " in col " + j;
String box = board[i][j] + " in box " + (i/3*3+j/3);
if(set.contains(row) || set.contains(col) || set.contains(box)) return false;
set.add(row);
set.add(col);
set.add(box);
}
}
return true;
}
}
方法2（Java）
从0-8，对每一个i，设置3个boolean数组分别检测第i行、第i列和第i个九宫格，数组的index代表被检测的值。
对于每个i的值，j从0-8意味着检测：
第i行, 第j个数是否已位于行i中；
第i列，第j个数是否已位于列i中；
第i个九宫格中，该九宫格从左上角到右下角的第j数是否已位于该九宫格中。
设置3个数组，boolean[] checkRow 检查位置(i, j)的值是否已存在第i行boolean[] checkCol 检查位置(j, i)的值是否已存在第i列boolean[] checkBox 检查位置(i/3*3+j/3, j%3*3+j%3)的值是否已存在第i个九宫格中
例如当i为4，j从0-8，对应行、列、九宫格的遍历过程
0 1 2 3 4 5 6 7 8
0 o o o | o 1 o | o o o
1 o o o | o 2 o | o o o
2 o o o | o 3 o | o o o
------------------------
3 o o o | o 4 o | o o o
4 1 2 3 | 4 5 6 | 7 8 9
5 o o o | o 6 o | o o o
------------------------
6 o o o | o 7 o | o o o
7 o o o | o 8 o | o o o
8 o o o | o 9 o | o o o
第4个九宫格中
1 2 3
4 5 6
7 8 9
class Solution {
public boolean isValidSudoku(char[][] board) {
for(int i = 0; i < 9; i++){
boolean[] checkRow = new boolean[9];
boolean[] checkCol = new boolean[9];
boolean[] checkBox = new boolean[9];
for(int j = 0; j < 9; j++){
if(board[i][j] == '.') {}
else if(checkRow[board[i][j]-'1']) return false;
else checkRow[board[i][j]-'1'] = true;
if(board[j][i] == '.'){}
else if(checkCol[board[j][i]-'1']) return false;
else checkCol[board[j][i]-'1'] = true;
int m = i/3*3+j/3, n = i%3*3+j%3;
if(board[m][n] == '.'){}
else if(checkBox[board[m][n]-'1']) return false;
else checkBox[board[m][n]-'1'] = true;
}
}
return true;
}
}