36.Valid Sudoku
===
###### tags: `Medium`,`Array`,`Hash Table`,`Matrix`

[36. Valid Sudoku](https://leetcode.com/problems/valid-sudoku/)

### 題目描述

Determine if a `9 x 9` 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 nine `3 x 3` sub-boxes of the grid must contain the digits `1-9` without repetition.

**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.

白話文：就是驗證數獨。

### 範例


Input: board = 
[["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

Input: board = 
[["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.

**Constraints**:

* `board.length == 9`
* `board[i].length == 9`
* `board[i][j]` is a digit `1-9` or `'.'`.

### 解答

#### Javascript

function isValidSudoku(board) {
  const block = [];
  for (let i = 0; i < 9; i++) {
    for (let j = 0; j < 9; j++) {
      if (board[i][j] === '.') continue;

      // 檢查橫的跟直的
      for (let k = 0; k < 9; k++) {
        if (board[i][k] === board[i][j] && k !== j) return false;
        if (board[k][j] === board[i][j] && k !== i) return false;
      }

      // 檢查九宮格
      const blockIndex = ~~(i / 3) * 3 + ~~(j / 3);
      if (!block[blockIndex]) block[blockIndex] = [];
      for (let k = 0; k < block[blockIndex].length; k++) {
        if (block[blockIndex][k] === board[i][j]) return false;
      }
      block[blockIndex].push(board[i][j]);
    }
  }

  return true;
}

> [name=Marsgoat] [time= Nov 23, 2022]

#### C++

bool isValidSudoku(vector<vector<char>>& board) {
    unordered_map<int,unordered_set<char>> horizon_appear;
    unordered_map<int,unordered_set<char>> vertical_appear;
    unordered_map<int,unordered_set<char>> block_appear;

    int row_n = board.size(), col_n = board[0].size();
    for(int row = 0; row < row_n; row++)
    {            
        for(int col = 0; col < col_n; col++)
        {
            char cur = board[row][col];
            if(cur == '.')
                continue;
            if(horizon_appear.count(row) && horizon_appear[row].count(cur))
                return false;
            if(vertical_appear.count(col) && vertical_appear[col].count(cur))
                return false;
            if(block_appear.count((col/3)*3+row/3) && block_appear[(col/3)*3+row/3].count(cur))
                return false;
            horizon_appear[row].insert(cur);
            vertical_appear[col].insert(cur);
            block_appear[(col/3)*3+row/3].insert(cur);
        }
    }
    return true;
}

Time: $O(N^2)$
Space: $O(N^2)$

更少的Space: $O(N)$
可以更換map成`vector<int> rows(N), cols(N), squares(N);`
用int儲存bitmask, 第i個位置代表數字i有無出現
[Reference](https://leetcode.com/problems/valid-sudoku/discuss/1414911/C%2B%2BJavaPython-2-solutions%3A-HashSet-Bitmasking-Clean-and-Concise-O(49))

> [name=XD] [time= Nov 23, 2022]

### Reference

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