36. Valid Sudoku

这题的解法是brute force，复杂度是O(81 + 81)。。。判断每一行每一列的代码我的想法跟code ganker的一致：用一个数组表示map；难点是判断每个unit是否valid，这种数组下标确实很难思考。。需要在纸上模拟一下才能看懂。

    public boolean isValidSudoku(char[][] board) {
        if (board.length != 9 || board[0].length != 9) return false;
        int[] temp = new int[9];
        //判断每一行
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] != '.') {
                    if (temp[board[i][j] - '1'] != 0) {
                        return false;
                    }
                    temp[board[i][j] - '1'] = 1;
                }
            }
            temp = new int[9];
        }

        //判断每一列
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[j][i] != '.') {
                    if (temp[board[j][i] - '1'] != 0) {
                        return false;
                    }
                    temp[board[j][i] - '1'] = 1;
                }
            }
            temp = new int[9];
        }

        //判断9个小units
        for (int block = 0; block < 9; block++) {
            for (int i = block / 3 * 3; i < block / 3 * 3 + 3; i++) {
                for (int j = block % 3 * 3; j < block % 3 * 3 + 3; j++) {
                    if (board[i][j] != '.') {
                        if (temp[board[i][j] - '1'] != 0) {
                            return false;
                        }
                        temp[board[i][j] - '1'] = 1;
                    }
                }
            }
            temp = new int[9];
        }
        return true;

    }

然后看了solutions里的解法，有个人用hashset，然后用了i j的reuse，很简洁，复杂度也稍低一些：

public boolean isValidSudoku(char[][] board) {
    for(int i = 0; i<9; i++){
        HashSet rows = new HashSet();
        HashSet columns = new HashSet();
        HashSet cube = new HashSet();
        for (int j = 0; j < 9;j++){
            if(board[i][j]!='.' && !rows.add(board[i][j]))
                return false;
            if(board[j][i]!='.' && !columns.add(board[j][i]))
                return false;
            int RowIndex = 3*(i/3);
            int ColIndex = 3*(i%3);
            if(board[RowIndex + j/3][ColIndex + j%3]!='.' && !cube.add(board[RowIndex + j/3][ColIndex + j%3]))
                return false;
        }
    }
    return true;
}