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企业做网站上海,seo搜索引擎优化工程师招聘,做网站一万,国内永久免费云服务器9930基础知识要求: Java: 方法、for循环、if else语句、数组 Python: 方法、for循环、if else语句、列表 题目: 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…

基础知识要求:

Java: 方法、for循环、if else语句、数组

Python: 方法、for循环、if else语句、列表

题目: 

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

  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。(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。

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:[["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

思路解析:

这个解题思路是一个典型的回溯算法在数独求解问题上的应用,它非常直观且易于理解。下面是对这个解题思路的总结:

  1. 初始化
    • 提供一个初始的数独板(在这个例子中是通过一个二维列表表示的)。
    • 如果数独板没有完全填充(即含有.作为占位符),则需要进行求解。
  2. 定义is_valid函数
    • 这是一个辅助函数,用于检查在给定位置(row, col)填入数字num是否有效。
    • 检查包括:当前行、当前列以及所在的3x3宫格内是否已存在该数字。
  3. 定义solve_sudoku函数
    • 这是求解数独的核心函数,它使用回溯法来尝试填充每一个空格。
    • 对于数独板上的每一个空格(即值为.的位置):
      • 尝试填入数字1到9。
      • 如果填入某个数字后,数独仍然有效(通过is_valid函数检查),则继续递归地求解剩余的空格。
      • 如果递归求解成功(即找到了一个解),则返回True。
      • 如果递归求解失败(即当前数字不合适),则回溯,将该空格重新置为.,并尝试下一个数字。
    • 如果尝试完所有数字后仍然没有找到解,则返回False。
    • 如果所有空格都成功填充,则返回True,表示找到了一个解。
  4. 求解与输出
    • 调用solve_sudoku函数来求解数独。
    • 如果求解成功,则打印出解出的数独板;否则,输出“无解”。

Java代码示例:

public class SudokuSolver {  // 检查数字在行、列和3x3宫格内是否有效  public static boolean isValid(char[][] board, int row, int col, char num) {  // 检查行  for (int i = 0; i < 9; i++) {  if (board[row][i] == num) {  return false;  }  }  // 检查列  for (int i = 0; i < 9; i++) {  if (board[i][col] == num) {  return false;  }  }  // 检查3x3宫格  int startRow = 3 * (row / 3);  int startCol = 3 * (col / 3);  for (int i = 0; i < 3; i++) {  for (int j = 0; j < 3; j++) {  if (board[i + startRow][j + startCol] == num) {  return false;  }  }  }  return true;  }  // 递归求解数独  public static boolean solveSudoku(char[][] board) {  for (int i = 0; i < 9; i++) {  for (int j = 0; j < 9; j++) {  if (board[i][j] == '.') {  for (char num = '1'; num <= '9'; num++) {  if (isValid(board, i, j, num)) {  board[i][j] = num;  // 递归尝试下一个空格  if (solveSudoku(board)) {  return true;  }  // 回溯  board[i][j] = '.';  }  }  // 尝试完所有数字都不可行,说明当前空格无解,返回false  return false;  }  }  }  // 所有空格都填满了,说明找到解了  return true;  }  // 主函数,用于测试  public static void main(String[] args) {  char[][] 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'}  };  if (solveSudoku(board)) {  // 格式化输出  for (char[] row : board) {  for (char num : row) {  System.out.print(num + " ");  }  System.out.println();  }  } else {  System.out.println("无解");  }  }  
}

Python代码示例:

def is_valid(board, row, col, num):  # 检查行中是否已存在该数字  for i in range(9):  if board[row][i] == num:  return False  # 检查列中是否已存在该数字  for i in range(9):  if board[i][col] == num:  return False  # 检查3x3宫格中是否已存在该数字  start_row = 3 * (row // 3)  start_col = 3 * (col // 3)  for i in range(3):  for j in range(3):  if board[i + start_row][j + start_col] == num:  return False  return Truedef solve_sudoku(board):  for i in range(9):  for j in range(9):  if board[i][j] == '.':  for num in ['1', '2', '3', '4', '5', '6', '7', '8', '9']:  if is_valid(board, i, j, num):  board[i][j] = num  if solve_sudoku(board):  return True  # 如果当前数字不合法,回溯  board[i][j] = '.'  # 尝试完所有数字都不可行,说明无解  return False  # 所有空格都填满了,说明找到解了  return True  # 示例输入  
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"]]  # 转换为二维列表  
board = [list(map(str, row)) for row in board]  # 求解数独  
if solve_sudoku(board):  # 格式化输出  for row in board:  print(row)  
else:  print("无解")

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