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//! Sudoku Solver [leetcode: sudoku_solver](https://leetcode.com/problems/sudoku-solver/) //! //! Write a program to solve a Sudoku puzzle by filling the empty cells. //! //! A sudoku solution must satisfy **all of the following rules**: //! 1. Each of the digits `1-9` must occur exactly once in each row. //! 2. Each of the digits `1-9` must occur exactly once in each column. //! 3. Each of the the digits `1-9` must occur exactly once in each of the 9 `3x3` sub-boxes of the grid. //! 4. Empty cells are indicated by the character `'.'`. //! //! <div> //! <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png" style="height:250px; width:250px"> //! </div> //! //! A sudoku puzzle... //! <div> //! <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sudoku-by-L2G-20050714_solution.svg/250px-Sudoku-by-L2G-20050714_solution.svg.png" style="height:250px; width:250px"> //! </div> //! //! ...and its solution numbers marked in red. //! //! **Note**: //! //! * The given board contain only digits `1-9` and the character `'.'`. //! * You may assume that the given Sudoku puzzle will have a single unique solution. //! * The given board size is always `9x9`. //! /// # Solutions /// /// # Approach 1: DFS /// /// * Time complexity: /// /// * Space complexity: /// /// * Runtime: 12 ms /// * Memory: 2.4 MB /// /// ```rust /// impl Solution { /// pub fn solve_sudoku(board: &mut Vec<Vec<char>>) { /// if board.is_empty() { return; } /// Self::solve(board); /// } /// /// pub fn solve(board: &mut Vec<Vec<char>>) -> bool { /// for row in 0..board.len() { /// for col in 0..board[row].len() { /// if board[row][col] != '.' { continue; } /// /// for c in "123456789".chars().collect::<Vec<_>>() { /// if !Self::is_valid(&board, row, col, c) { continue; } /// /// board[row][col] = c; /// /// if Self::solve(board) { return true; } /// /// board[row][col] = '.'; /// } /// /// return false; /// } /// } /// return true; /// } /// /// pub fn is_valid(board: &Vec<Vec<char>>, row: usize, col: usize, c: char) -> bool { /// for i in 0..9 { /// if board[row][i] != '.' && board[row][i] == c { return false; } // check row /// if board[i][col] != '.' && board[i][col] == c { return false; } // check col /// let block = board[(3 * (row as i32 / 3) + i as i32 / 3) as usize][(3 * (col as i32 / 3) + i as i32 % 3) as usize]; /// if block != '.' && block == c { return false; } // check 3 * 3 block; /// } /// true /// } /// } /// ``` /// /// # Approach 2: DFS /// /// * Time complexity: /// /// * Space complexity: /// /// * Runtime: 0 ms /// * Memory: 2.5 MB /// /// ```rust /// use std::char; /// /// impl Solution { /// pub fn solve_sudoku(board: &mut Vec<Vec<char>>) { /// if board.is_empty() { return; } /// /// // 快速检索第i, j列, 第k宫的数字是否被占用 /// let mut lines = [[false; 9]; 9]; /// let mut columns = [[false; 9]; 9]; /// let mut ceils = [[false; 9]; 9]; /// let mut origins = [[false; 9]; 9]; /// /// // initialize lines columns ceils and origins /// for row in 0..9 { /// for col in 0..9 { /// let num = match board[row][col].to_digit(10) { /// Some(n) => (n - 1) as usize, /// None => continue, /// }; /// /// lines[row][num] = true; /// columns[col][num] = true; /// origins[row][col] = true; /// ceils[Self::ceil_pos((row, col))][num] = true; /// } /// } /// /// Self::solve(board, (0, 0), &mut lines, &mut columns, &mut ceils, &mut origins); /// } /// /// pub fn solve(board: &mut Vec<Vec<char>>, /// (row, col): (usize, usize), /// lines: &mut[[bool; 9]; 9], /// columns: &mut[[bool; 9]; 9], /// ceils: &mut[[bool; 9]; 9], /// origins: &mut[[bool; 9]; 9]) -> bool { /// /// if row >= 9 { return true; } /// let next_pos = (row + (col + 1) / 9, (col + 1) % 9); /// if origins[row][col] { return Self::solve(board, next_pos, lines, columns, ceils, origins); } /// /// let mut flag = false; /// for num in 0..9 { /// let ceil = Self::ceil_pos((row, col)); /// if lines[row][num] || columns[col][num] || ceils[ceil][num] { continue; } /// /// // 数字num + 1没用过 /// lines[row][num] = true; /// columns[col][num] = true; /// ceils[ceil][num] = true; /// /// board[row][col] = char::from_digit(num as u32 + 1, 10).unwrap(); /// /// flag |= Self::solve(board, next_pos, lines, columns, ceils, origins); /// /// if flag { break; } // 已填数 OK /// lines[row][num] = false; /// columns[col][num] = false; /// ceils[ceil][num] = false; /// } /// /// flag /// } /// /// // 求出pos属于第几个ceil /// pub fn ceil_pos(pos: (usize, usize)) -> usize { /// (pos.0 / 3) * 3 + pos.1 / 3 /// } /// } /// pub fn solve_sudoku(board: &mut Vec<Vec<char>>) { if board.is_empty() { return; } solve(board); } pub fn solve(board: &mut Vec<Vec<char>>) -> bool { for row in 0..board.len() { for col in 0..board[row].len() { if board[row][col] != '.' { continue; } for c in "123456789".chars().collect::<Vec<_>>() { if !is_valid(&board, row, col, c) { continue; } board[row][col] = c; if solve(board) { return true; } board[row][col] = '.'; } return false; } } return true; } pub fn is_valid(board: &Vec<Vec<char>>, row: usize, col: usize, c: char) -> bool { for i in 0..9 { if board[row][i] != '.' && board[row][i] == c { return false; } // check row if board[i][col] != '.' && board[i][col] == c { return false; } // check col let block = board[(3 * (row as i32 / 3) + i as i32 / 3) as usize][(3 * (col as i32 / 3) + i as i32 % 3) as usize]; if block != '.' && block == c { return false; } // check 3 * 3 block; } true }