Determine if a Sudoku is valid, according to: Sudoku Puzzles - The Rules.
The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

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Solution1：Regular 方法 global 3 * 9 * 9 Hashset

实现1a: 用ArrayList<set>
实现1b: 其实可以直接二位数组对应位置boolean

Solution2：tmp 3 * 9 Hashset

思路：1行/1列/1Box 各用一个hashset，i次遍历，因为是正方形对称，所以可以同时check的是第i行和第i列(by i, j 调换)，并找到box位置check。
Time Complexity: O(n^2) Space Complexity: O(n^2) n*n矩阵

Solution1a Code：

class Solution {
    public boolean isValidSudoku(char[][] board) {
        ArrayList<HashSet<Character>> row = new ArrayList<HashSet<Character>>(); // max: 9x9
        ArrayList<HashSet<Character>> col = new ArrayList<HashSet<Character>>(); // max: 9x9
        ArrayList<HashSet<Character>> box = new ArrayList<HashSet<Character>>(); // max: 9x9
        
        for(int i = 0; i < board.length; ++i) row.add(new HashSet<Character>());
        for(int i = 0; i < board.length; ++i) col.add(new HashSet<Character>());
        for(int i = 0; i < board.length; ++i) box.add(new HashSet<Character>());
        
        
        for(int i = 0; i < board.length; ++i) {
            for(int j = 0; j < board[0].length; ++j) {
                if(board[i][j] == '.') continue;
                
                // check row and col
                if(!row.get(i).add(board[i][j]) || !col.get(j).add(board[i][j])) {
                    return false;   
                }
                
                // check box
                int box_num = i / 3 * 3 + j / 3;
                if(!box.get(box_num).add(board[i][j])) {
                    return false;
                }
            }
        }
        return true;
    }
}

Solution1b Code：

class Solution {
    public boolean isValidSudoku(char[][] board) {
        boolean[][] row = new boolean[9][9];
        boolean[][] col = new boolean[9][9];
        boolean[][] box = new boolean[9][9];
        
        
        for(int i = 0; i < board.length; ++i) {
            for(int j = 0; j < board[0].length; ++j) {
                if(board[i][j] == '.') continue;
                
                int num = board[i][j] - '0' - 1;
                // check row and col
                if(row[i][num] || col[j][num]) {
                    return false;   
                }
                // check box
                int box_num = i / 3 * 3 + j / 3;
                if(box[box_num][num]) {
                    return false;
                }
                // update
                row[i][num] = col[j][num] = box[box_num][num] = true;
            }
        }
        return true;
    }
}

Solution2 Code：

class Solution {
    public boolean isValidSudoku(char[][] board) {
        for(int i = 0; i < 9; i++){
            HashSet<Character> row = new HashSet<Character>();
            HashSet<Character> column = new HashSet<Character>();
            HashSet<Character> box = new HashSet<Character>();
            for (int j = 0; j < 9; j++){
                if(board[i][j] != '.' && !row.add(board[i][j])) {
                    return false;
                }
                if(board[j][i]!='.' && !column.add(board[j][i])) {
                    return false;
                }
                int RowIndex = 3 * (i / 3);
                int ColIndex = 3 * (i % 3);
                if(board[RowIndex + j / 3][ColIndex + j % 3] != '.' && !box.add(board[RowIndex + j / 3][ColIndex + j % 3])) {
                    return false;
                }
            }
        }
        return true;
    }
}