LeetCode-36-Valid Sudoku

算法描述：

Determine if a 9x9 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 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

Example 1:

Input:
[
  ["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:
[
  ["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.

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.
• The given board contain only digits 1-9 and the character '.'.
• The given board size is always 9x9.

解题思路：这道题就是分别对每一行每一列以及每一个小块分别进行判断，最终得到判断结果。其中，对与小块的判断要非常仔细。

原数       1 2 3 4 5 6 7 8 9

3*(i/3)     0 0 0 3 3 3 6 6 6

3*(i%3)   0 1 2 0 1 2 0 1 2

j / 3         0 0 0 1 1 1 2 2 2

j %3        0 1 2 0 1 2 0 1 2

bool isValidSudoku(vector<vector<char>>& board) {
        for(int i=0; i < board.size(); i++){
            unordered_map<int, bool> row;
            unordered_map<int, bool> col;
            unordered_map<int, bool> cub;
            for(int j=0; j < board[0].size(); j++){
                if(board[i][j]!='.'){
                    if(!row[board[i][j]]) row[board[i][j]] = true;
                    else return false;
                } 
                
                if(board[j][i]!='.'){
                    if(!col[board[j][i]]) col[board[j][i]] = true;
                    else return false;
                } 
                
                int rowIndex = 3*(i / 3);
                int colIndex = 3*(i % 3);
                if(board[rowIndex + j/3][colIndex + j%3]!='.'){
                    if(!cub[board[rowIndex+j/3][colIndex+j%3]])
                        cub[board[rowIndex+j/3][colIndex+j%3]] = true;
                    else return false;
                }
            }
        }
        return true;
    }