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请你判断一个 9 x 9 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。
数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。(请参考示例图)
注意:
示例 1:
输入: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"]]
输出:true
示例 2:
输入: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"]]
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。
提示:
board.length == 9
board[i].length == 9
board[i][j] 是一位数字(1-9)或者 '.'
时间复杂度:
O
(
1
)
\Omicron(1)
O(1)【数独是固定大小的,所以都是常数级复杂度】
空间复杂度:
O
(
1
)
\Omicron(1)
O(1)【数独是固定大小的,所以都是常数级复杂度】
class Solution { public: bool isValidSudoku(vector<vector<char>>& board) { int n = board.size(), m = board[0].size(); for (int i = 0; i < n; i++) { vector<vector<bool>> num(3, vector<bool>(m, false)); for (int j = 0; j < m; j++) { // 行唯一 if (board[i][j] != '.') { if (num[0][board[i][j] - '1']) { return false; } else { num[0][board[i][j] - '1'] = true; } } if (board[j][i] != '.') { // 列唯一 if (num[1][board[j][i] - '1']) { return false; } else { num[1][board[j][i] - '1'] = true; } } int r = i / 3 * 3 + j / 3, c = (i % 3) * 3 + j % 3; if (board[r][c] != '.') { // 九宫格唯一 if (num[2][board[r][c] - '1']) { return false; } else { num[2][board[r][c] - '1'] = true; } } } } return true; } };
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