Determine if a 9×9 Sudoku board is valid. Only the filled cells need to be validated **according to the following rules**:

- Each row must contain the digits
`1-9`

without repetition. - Each column must contain the digits
`1-9`

without repetition. - 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:falseExplanation:Same as Example 1, except with the5in the top left corner being modified to8. 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`

.

**Solution: HashTable**

Use hashtable to store the numbers of each row, column and each 3×3 box. If there number appears more than once then it’s an invalid Sudoku.

Time complexity: O(1)

Space complexity: O(1)

## C++

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// Author: Huahua class Solution { public: bool isValidSudoku(vector<vector<char> > &board) { for (int i = 0; i < 9;i++) { set<char> r, c; for (int j = 0; j < 9; j++) { if (board[i][j] != '.' && !r.insert(board[i][j]).second) return false; if (board[j][i] != '.' && !c.insert(board[j][i]).second) return false; } } for (int p = 0; p < 3; p++) for (int q = 0; q < 3; q++) { set<char> b; for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) { int x = p * 3 + i; int y = q * 3 + j; if (board[y][x] != '.' && !b.insert(board[y][x]).second) return false; } } return true; } }; |

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