36. Valid Sudoku

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'.'.

思路：先全局后局部

public class Solution {
    public boolean isValidSudoku(char[][] board) {
        // check big board
        for (int i=0;i<9;i++){
            HashSet<Character> rows = new HashSet<Character>();
            HashSet<Character> cols = new HashSet<Character>();
            for (int j=0;j<9;j++){
                if (board[i][j]!='.'&&!rows.add(board[i][j])){
                    return false;
                }
                if (board[j][i]!='.'&&!cols.add(board[j][i])){
                    return false;
                }
            }
        }

        // check cube
        for (int i=0;i<3;i++){
            for (int j=0;j<3;j++){
                HashSet<Character> cubes = new HashSet<Character>();
                for (int m=0;m<3;m++){
                    for (int n=0;n<3;n++){
                        int rowNum = i*3+m;
                        int colNum = j*3+n;
                        if (board[rowNum][colNum]!='.'&&!cubes.add(board[rowNum][colNum])){
                            return false;
                        }
                    }
                }
            }
        }
        return true;
    }
}