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。
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