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.

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)

// 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;
  }
};

Follow up:

• https://zxi.mytechroad.com/blog/searching/leetcode-37-sudoku-solver/

The post 花花酱 LeetCode 36. Valid Sudoku appeared first on Huahua's Tech Road.