0036. Valid Sudoku

---

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 == 9
• board[i].length == 9
• board[i][j] is a digit or '.'.

---

解法1

因为只有9个数,不用数组或者set来保存某个数字是否存在, 而是用二进制数位.

class Solution {
    public boolean isValidSudoku(char[][] board) {
        // 9行
        int[] row = new int[9];;
        // 9列
        int[] column = new int[9];
        // 9个3*3的box
        int[] box = new int[9];
        int temp;
        int indexBox;
        for(int r = 0 ; r < 9 ; r++){
            for(int c = 0; c < 9; c++){
                if(board[r][c]=='.')
                    continue;
                
                // 用2进制的中对应的数位是否为1,来表示当前数字是否存在(从右到左)
                // 比如 1表示1, 10 表示2, 100表示3, 1000表示4
                temp = 1 << (board[r][c] - '1');
                
                // 当前位置位于第几个box
                indexBox = (r / 3) * 3 + c / 3;
                
                // 如果有重复的数字, 返回false
                if((column[c] & temp) > 0 || (row[r] & temp) > 0 || (box[indexBox] & temp) > 0)
                    return false;
                
                // 如果当前数字符不违反规则,把当前数字录入数组
                column[c] |= temp;
                row[r] |= temp;
                box[indexBox] |= temp;
            }
        }
        return true;
    }
}