36. Valid Sudoku

Problem

Determine if a 9x9 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: 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 (Java)

class Solution {
    public boolean isValidSudoku(char[][] board) {
        int [] vset = new int [9];
        int [] hset = new int [9];
        int [] bckt = new int [9];
        int idx = 0;
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] != '.') {
                    idx = 1 << (board[i][j] - '0') ;
                    if ((hset[i] & idx) > 0 ||
                        (vset[j] & idx) > 0 ||
                        (bckt[(i / 3) * 3 + j / 3] & idx) > 0) return false;
                    hset[i] |= idx;
                    vset[j] |= idx;
                    bckt[(i / 3) * 3 + j / 3] |= idx;
                }
            }
        }
        return true;
    }
}

Solution (Javascript)

/**
 * @param {character[][]} board
 * @return {boolean}
 */
var isValidSudoku = function(board) {
  var map = {};
  var tmp = 0;
  for (var i = 0; i < 9; i++) {
    for (var j = 0; j < 9; j++) {
      tmp = board[i][j];
      if (tmp === '.') continue;
      if (map['i' + i + tmp] || map['j' + j + tmp] || map['b' + Math.floor(i / 3) + Math.floor(j / 3) + tmp]) return false;
      map['i' + i + tmp] = 1;
      map['j' + j + tmp] = 1;
      map['b' + Math.floor(i / 3) + Math.floor(j / 3) + tmp] = 1;
    }
  }
  return true;
};

Explain:

哈希表：

i、j、b 开头的键分别代表 某行、某列、某块 中，某数字是否已存在

Complexity:

• Time complexity : O(n^2).
• Space complexity : O(n).