10 - Easy - 有效的数独

判断一个 9x9 的数独是否有效。只需要根据以下规则，验证已经填入的数字是否有效即可。

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。

image

<small style="box-sizing: border-box; font-size: 12px;">上图是一个部分填充的有效的数独。</small>

数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1:

输入:
[
["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"]
]
输出: true

示例 2:

输入:
[
["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"]
]
输出: false
解释: 除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。
但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。</pre>

说明:

• 一个有效的数独（部分已被填充）不一定是可解的。
• 只需要根据以上规则，验证已经填入的数字是否有效即可。
• 给定数独序列只包含数字 1-9 和字符 '.' 。
• 给定数独永远是 9x9 形式的。

class Solution:
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        row = [[] for _ in range(9)]  # 行记录器
        col = [[] for _ in range(9)]  # 列记录器
        area = [[] for _ in range(9)]  # 子区域记录器
        for i in range(9):
            for j in range(9):
                element = board[i][j]  # 遍历所有元素
                if element != '.':  # 有数字才记录下来
                    top_id = i//3*3 + j//3  # 每个元素子区域的计算方法
                    if element in row[i] or element in col[j] or element in area[top_id]:  # 如果在这一行列子区域重读出现过了
                        return False
                    else:  # 没有出现过就加进去
                        row[i].append(element)
                        col[j].append(element)
                        area[top_id].append(element)
        return True

class Solution:
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        row = [[0 for _ in range(9)] for _ in range(9)]
        col = [[0 for _ in range(9)] for _ in range(9)]
        mat = [[0 for _ in range(9)] for _ in range(9)]
        for i in range(9):
            for j in range(9):
                if board[i][j] != ".":
                    num = int(board[i][j]) - 1
                    k = i // 3 * 3 + j // 3
                    if row[i][num] or col[j][num] or mat[k][num]:
                        return False
                    row[i][num] = col[j][num] = mat[k][num] = 1
        return True