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 '.'.

A partially filled sudoku which is valid.

Note:
A valid Sudoku board (partially filled) is not necessarily solvable. Only the filled cells need to be validated.

分析：检验数独是否有效。只用检查已经填充的部分，没填充的部分用 '.' 表示。

分别检查行、列以及小九宫格。为了避免麻烦，我用了map来迅速查找数字。运行时间46ms。

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        for(int i = 0; i < 9; i++){
            //check each row
            map<char, int> m;
            for(int j = 0; j < 9; j++){
                if(board[i][j] != '.'){
                    if(m.find(board[i][j]) != m.end()) return false;
                    else m[board[i][j]] = 1;
                }
            }
            
            //check each column
            map<char, int> n;
            for(int k = 0; k < 9; k++){
                if(board[k][i] != '.'){
                    if(n.find(board[k][i]) != n.end()) return false;
                    else n[board[k][i]] = 1;
                }
            }
        }
        //check each sub-boxes
        for(int i = 0; i < 9; i += 3){
            for(int j = 0; j < 9; j += 3){
                map<char, int> mm;
                for(int p = i; p < i + 3; p++){
                    for(int q = j; q < j + 3; q++){
                        if(board[p][q] != '.'){
                            if(mm.find(board[p][q]) != mm.end()) return false;
                            else{
                                mm[board[p][q]] = 1;
                            }
                        }
                    }
                }
            }
        }
        return true;
    }
};

 为了进一步优化，可以不用map进行数字重复测试。通过使用一个bool型数组，每出现一个数字，便将该数字相应下标置1，运行时间16ms！

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        for(int i = 0; i < 9; i++){
            //check each row
            bool arrRow[9];
            fill(arrRow, arrRow + 9, false);
            for(int j = 0; j < 9; j++){
                if(board[i][j] != '.'){
                    if(arrRow[board[i][j] - '1']) return false;
                    else arrRow[board[i][j] - '1'] = true;
                }
            }
            
            //check each column
            bool arrCol[9];
            fill(arrCol, arrCol + 9, false);
            for(int k = 0; k < 9; k++){
                if(board[k][i] != '.'){
                    if(arrCol[board[k][i] - '1']) return false;
                    else arrCol[board[k][i] - '1'] = true;
                }
            }
        }
        //check each sub-boxes
        for(int i = 0; i < 9; i += 3){
            for(int j = 0; j < 9; j += 3){
                bool arr[9];
                fill(arr, arr + 9, false);
                for(int p = i; p < i + 3; p++){
                    for(int q = j; q < j + 3; q++){
                        if(board[p][q] != '.'){
                            if(arr[board[p][q] - '1']) return false;
                            else arr[board[p][q] - '1'] = true;
                        }
                    }
                }
            }
        }
        return true;
    }
};