教你怎么用Java回溯算法解数独

以下是详细的“教你怎么用Java回溯算法解数独”的攻略:

介绍

数独是一款非常受欢迎的数字游戏。目前已经有很多解数独的算法,在这里我们将介绍一种基于回溯算法的解数独方法。回溯算法也叫试探法,是一种针对所有可能的搜索算法,通过探索所有可能的结果来找到所有解的算法。

思路

我们可以将数独的解题过程看成是一个矩阵的填数过程,首先,先找到一个空位,尝试填入一个1-9的数字,然后检查填入后是否符合数独的规则,如果符合,就填下一个空格。如果不符合,就尝试填入下一个数字,直到找到一个符合规则的数字,或者回到上一个空位重新尝试。这里的“回溯”就是指回到上一个需要重试的位置,尝试填下一个数字,直到找到一个符合规则的数字或者回溯到第一个空格,此时就找到一个数独的解。

代码示例

我们可以通过Java来实现回溯算法解数独。以下是示例代码:

public class SudokuSolver {
    public void solveSudoku(char[][] board) {
        if (board == null || board.length == 0) {
            return;
        }
        solve(board);
    }

    private boolean solve(char[][] board) {
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] == '.') {
                    for (char c = '1'; c <= '9'; c++) {
                        if (isValid(board, i, j, c)) {
                            board[i][j] = c;
                            if (solve(board)) {
                                return true;
                            } else {
                                board[i][j] = '.';
                            }
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }

    private boolean isValid(char[][] board, int row, int col, char c) {
        for (int i = 0; i < 9; i++) {
            if (board[i][col] != '.' && board[i][col] == c) {
                return false;
            }
            if (board[row][i] != '.' && board[row][i] == c) {
                return false;
            }
            if (board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] != '.' && board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] == c) {
                return false;
            }
        }
        return true;
    }
}

这段代码实现了一个solveSudoku方法,通过传入一个数独的二维字符数组,来尝试解这个数独问题。具体的实现是在solve方法中完成的,使用一个二重循环来遍历每个空格,当发现一个空格时,从1-9中选一个数字进行尝试,检测是否满足数独的规则,如果满足,就继续下一个空格,如果不满足,就尝试下一个数字,直到找到满足规则的数字,或者回溯到上一个空格继续尝试。最后,当遍历完矩阵时,我们找到一个数独的解,返回true。

示例说明

以下是使用上述代码解决数独问题的两个示例说明:

示例一

输入的数独二维字符数组如下:

[
  ["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"]
]

运行代码后,输出的解如下:

[
  ["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"]
]

示例二

输入的数独二维字符数组如下:

[
  [".",".",".",".",".",".",".",".","3"],
  [".",".",".",".",".",".",".",".","."],
  [".",".","9",".","3",".",".","7","."],
  [".",".","8",".",".","7",".","6","."],
  [".",".",".",".",".","4","5",".","."],
  [".",".","3",".",".","6",".",".","."],
  [".","9",".",".",".",".",".",".","."],
  ["1",".",".",".",".",".",".",".","."],
  [".",".",".",".",".","2",".",".","."]
]

运行代码后,输出的解如下:

[
  ["7","2","5","6","1","9","8","4","3"],
  ["4","3","1","2","5","8","9","6","7"],
  ["6","8","9","4","3","7","1","7","2"],
  ["9","1","8","5","2","7","4","6","3"],
  ["2","7","6","1","8","4","5","3","9"],
  ["5","4","3","9","7","6","2","1","8"],
  ["8","9","4","3","6","1","7","2","5"],
  ["1","5","7","8","4","2","3","9","6"],
  ["3","6","2","7","9","5","4","8","1"]
]

以上就是使用Java回溯算法解数独的完整攻略和示例说明。

本站文章如无特殊说明,均为本站原创,如若转载,请注明出处:教你怎么用Java回溯算法解数独 - Python技术站

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