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36. 有效的数独：

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：

• 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。
• 空白格用 '.' 表示。

样例 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

样例 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 ‘.’

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分析：

• 面对这道算法题目，二当家的陷入了沉思。
• 主要是如何存储行，列，以及3*3宫内出现过的值。
• 方法很多，集合，整形数组，布尔数组都可以，只有1-9，一共9个数，最优化的空间方式应该是仅仅用一个整形，然后用位运算。

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题解：

rust

impl Solution {pub fn is_valid_sudoku(board: Vec<Vec<char>>) -> bool {let mut rows = vec![vec![false; 9]; 9];let mut columns = vec![vec![false; 9]; 9];let mut sub_boxes = vec![vec![vec![false; 9]; 3]; 3];for i in 0..9 {for j in 0..9 {let c = board[i][j];if c != '.' {let index = (c as u8 - b'1') as usize;if rows[i][index] || columns[j][index] || sub_boxes[i / 3][j / 3][index] {return false;}rows[i][index] = true;columns[j][index] = true;sub_boxes[i / 3][j / 3][index] = true;}}}return true;}
}

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go

func isValidSudoku(board [][]byte) bool {var rows, columns [9][9]boolvar subBoxes [3][3][9]boolfor i, row := range board {for j, c := range row {if c != '.' {index := c - '1'if rows[i][index] || columns[j][index] || subBoxes[i/3][j/3][index] {return false}rows[i][index] = truecolumns[j][index] = truesubBoxes[i/3][j/3][index] = true}}}return true
}

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c++

class Solution {
public:bool isValidSudoku(vector<vector<char>>& board) {bool rows[9][9];bool columns[9][9];bool subBoxes[3][3][9];memset(rows, 0, sizeof(rows));memset(columns, 0, sizeof(columns));memset(subBoxes, 0, sizeof(subBoxes));for (int i = 0; i < 9; i++) {for (int j = 0; j < 9; j++) {char c = board[i][j];if (c != '.') {int index = c - '1';if (rows[i][index] || columns[j][index] || subBoxes[i / 3][j / 3][index]) {return false;}rows[i][index] = true;columns[j][index] = true;subBoxes[i / 3][j / 3][index] = true;}}}return true;}
};

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c

bool isValidSudoku(char** board, int boardSize, int* boardColSize){bool rows[9][9];bool columns[9][9];bool subBoxes[3][3][9];memset(rows, 0, sizeof(rows));memset(columns, 0, sizeof(columns));memset(subBoxes, 0, sizeof(subBoxes));for (int i = 0; i < 9; i++) {for (int j = 0; j < 9; j++) {char c = board[i][j];if (c != '.') {int index = c - '1';if (rows[i][index] || columns[j][index] || subBoxes[i / 3][j / 3][index]) {return false;}rows[i][index] = true;columns[j][index] = true;subBoxes[i / 3][j / 3][index] = true;}}}return true;
}

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python

class Solution:def isValidSudoku(self, board: List[List[str]]) -> bool:rows, columns, sub_boxes = [[False] * 9 for _ in range(9)], [[False] * 9 for _ in range(9)], [[[False] * 9 for _ in range(3)] for _ in range(3)]for i in range(9):for j in range(9):c = board[i][j]if c != '.':index = ord(c) - ord('1')if rows[i][index] or columns[j][index] or sub_boxes[i // 3][j // 3][index]:return Falserows[i][index] = Truecolumns[j][index] = Truesub_boxes[i // 3][j // 3][index] = Truereturn True

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java

class Solution {public boolean isValidSudoku(char[][] board) {boolean[][]   rows     = new boolean[9][9];boolean[][]   columns  = new boolean[9][9];boolean[][][] subBoxes = new boolean[3][3][9];for (int i = 0; i < 9; i++) {for (int j = 0; j < 9; j++) {char c = board[i][j];if (c != '.') {int index = c - '1';if (rows[i][index] || columns[j][index] || subBoxes[i / 3][j / 3][index]) {return false;}rows[i][index] = true;columns[j][index] = true;subBoxes[i / 3][j / 3][index] = true;}}}return true;}
}

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