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37. 解数独：

编写一个程序，通过填充空格来解决数独问题。

数独的解法需 遵循如下规则：

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）

数独部分空格内已填入了数字，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：[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]解释：输入的数独如上图所示，唯一有效的解决方案如下所示：

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字或者 '.'
• 题目数据 保证 输入数独仅有一个解

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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 solve_sudoku(board: &mut Vec<Vec<char>>) {let mut line = vec![vec![false; 9]; 9];let mut column = vec![vec![false; 9]; 9];let mut block = vec![vec![vec![false; 9]; 3]; 3];let mut spaces = Vec::new();(0..9).for_each(|i| {(0..9).for_each(|j| {if board[i][j] == '.' {spaces.push((i, j));} else {let digit = board[i][j].to_digit(10).unwrap() as usize - 1;line[i][digit] = true;column[j][digit] = true;block[i / 3][j / 3][digit] = true;}});});fn dfs(board: &mut Vec<Vec<char>>, spaces: &Vec<(usize, usize)>, line: &mut Vec<Vec<bool>>, column: &mut Vec<Vec<bool>>, block: &mut Vec<Vec<Vec<bool>>>, pos: usize) -> bool {if pos == spaces.len() {return true;}let (i, j) = spaces[pos];for digit in 0..9 {if !line[i][digit] && !column[j][digit] && !block[i / 3][j / 3][digit] {line[i][digit] = true;column[j][digit] = true;block[i / 3][j / 3][digit] = true;board[i][j] = (digit as u8 + b'1') as char;if dfs(board, spaces, line, column, block, pos + 1) {return true;}line[i][digit] = false;column[j][digit] = false;block[i / 3][j / 3][digit] = false;}}return false;}dfs(board, &mut spaces, &mut line, &mut column, &mut block, 0);}
}

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go

func solveSudoku(board [][]byte)  {var line, column [9][9]boolvar block [3][3][9]boolvar spaces [][2]intfor i := 0; i < 9; i++ {for j := 0; j < 9; j++ {b := board[i][j]if b == '.' {spaces = append(spaces, [2]int{i, j})} else {digit := b - '1'line[i][digit] = truecolumn[j][digit] = trueblock[i/3][j/3][digit] = true}}}var dfs func(int) booldfs = func(pos int) bool {if pos == len(spaces) {return true}i, j := spaces[pos][0], spaces[pos][1]for digit := byte(0); digit < 9; digit++ {if !line[i][digit] && !column[j][digit] && !block[i/3][j/3][digit] {line[i][digit] = truecolumn[j][digit] = trueblock[i/3][j/3][digit] = trueboard[i][j] = digit + '1'if dfs(pos + 1) {return true}line[i][digit] = falsecolumn[j][digit] = falseblock[i/3][j/3][digit] = false}}return false}dfs(0)
}

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c++

class Solution {
private:bool dfs(vector<vector<char>> &board, vector<pair<int, int>> &spaces, bool line[9][9], bool column[9][9], bool block[3][3][9], int pos) {if (pos == spaces.size()) {return true;}auto [i, j] = spaces[pos];for (int digit = 0; digit < 9; ++digit) {if (!line[i][digit] && !column[j][digit] && !block[i / 3][j / 3][digit]) {line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = true;board[i][j] = digit + '1';if (dfs(board, spaces, line, column, block, pos + 1)) {return true;}line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = false;}}return false;}
public:void solveSudoku(vector<vector<char>>& board) {bool line[9][9];bool column[9][9];bool block[3][3][9];vector<pair<int, int>> spaces;memset(line, false, sizeof(line));memset(column, false, sizeof(column));memset(block, false, sizeof(block));for (int i = 0; i < 9; ++i) {for (int j = 0; j < 9; ++j) {if (board[i][j] == '.') {spaces.emplace_back(i, j);}else {int digit = board[i][j] - '1';line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = true;}}}dfs(board, spaces, line, column, block, 0);}
};

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c

bool dfs(char **board, int *spaces[81], int spacesSize, bool line[9][9], bool column[9][9], bool block[3][3][9], int pos) {if (pos == spacesSize) {return true;}int i = spaces[pos][0], j = spaces[pos][1];for (int digit = 0; digit < 9; ++digit) {if (!line[i][digit] && !column[j][digit] && !block[i / 3][j / 3][digit]) {line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = true;board[i][j] = digit + '1';if (dfs(board, spaces, spacesSize, line, column, block, pos + 1)) {return true;}line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = false;}}return false;
}void solveSudoku(char **board, int boardSize, int *boardColSize) {bool line[9][9];bool column[9][9];bool block[3][3][9];int *spaces[81];int spacesSize = 0;memset(line, 0, sizeof(line));memset(column, 0, sizeof(column));memset(block, 0, sizeof(block));for (int i = 0; i < 9; ++i) {for (int j = 0; j < 9; ++j) {if (board[i][j] == '.') {spaces[spacesSize] = malloc(sizeof(int) * 2);spaces[spacesSize][0] = i;spaces[spacesSize++][1] = j;} else {int digit = board[i][j] - '1';line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = true;}}}dfs(board, spaces, spacesSize, line, column, block, 0);
}

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python

class Solution:def solveSudoku(self, board: List[List[str]]) -> None:"""Do not return anything, modify board in-place instead."""def dfs(pos: int) -> bool:if pos == len(spaces):return Truei, j = spaces[pos]for digit in range(9):if line[i][digit] == column[j][digit] == block[i // 3][j // 3][digit] == False:line[i][digit] = column[j][digit] = block[i // 3][j // 3][digit] = Trueboard[i][j] = str(digit + 1)if dfs(pos + 1):return Trueline[i][digit] = column[j][digit] = block[i // 3][j // 3][digit] = Falsereturn Falseline = [[False] * 9 for _ in range(9)]column = [[False] * 9 for _ in range(9)]block = [[[False] * 9 for _a in range(3)] for _b in range(3)]spaces = list()for i in range(9):for j in range(9):if board[i][j] == ".":spaces.append((i, j))else:digit = int(board[i][j]) - 1line[i][digit] = column[j][digit] = block[i // 3][j // 3][digit] = Truedfs(0)

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java

class Solution {public void solveSudoku(char[][] board) {boolean[][]   line   = new boolean[9][9];boolean[][]   column = new boolean[9][9];boolean[][][] block  = new boolean[3][3][9];List<int[]>   spaces = new ArrayList<int[]>();for (int i = 0; i < 9; ++i) {for (int j = 0; j < 9; ++j) {if (board[i][j] == '.') {spaces.add(new int[]{i, j});} else {int digit = board[i][j] - '1';line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = true;}}}dfs(board, spaces, line, column, block, 0);}private boolean dfs(char[][] board, List<int[]> spaces, boolean[][] line, boolean[][] column, boolean[][][] block, int pos) {if (pos == spaces.size()) {return true;}int[] space = spaces.get(pos);int   i     = space[0], j = space[1];for (int digit = 0; digit < 9; ++digit) {if (!line[i][digit] && !column[j][digit] && !block[i / 3][j / 3][digit]) {line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = true;board[i][j] = (char) (digit + '1');if (dfs(board, spaces, line, column, block, pos + 1)) {return true;}line[i][digit] = column[j][digit] = block[i / 3][j / 3][digit] = false;}}return false;}
}

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