本文共 16500 字,大约阅读时间需要 55 分钟。
本文中的代码在文章最后提供下载链接。
关于八皇后的问题,自己百度。回溯法的概念也可以自己维基百科中查看。
回溯法无非就是遍历解空间,如果合适的话就继续,不合适的话就放弃当前节点。可以采用递归实现。八皇后问题的经典算法就是采用回溯法。网上也有许多版本的解法,但是C#版本的似乎很少。笔者在此奉献上。
此处八皇后的算法的伪代码如下:
在第row行放置皇后(row)
{
for 第row行的格子
{
把当前位置加入作为候选解加入解决方案中
If 目前解决方案没有问题
{
再下一行放皇后,递归调用PlaceQueen(row+1);
如果是最后一行放完了,则成功,打印棋盘
}
else
将位置(row,col)上的皇后取走,尝试下一列位置 //回溯
}
伪代码的算法能理解之后,就可以写代码了。
对于棋盘,可以使用二维数组实现,但是本例中使用的是一个List序列,序列中有64个格子的信息。每个格子的定义如下。
//格子类。坐标x,y
- public class position
- {
- public int x { set; get; }
- public int y { set; get; }
- public override string ToString()
- {
- return string.Format("[{0},{1}]", x, y);
- }
- }
初始化格子的代码如下:
- #region 初始化格子
- for (int i = 1; i <= dimension; i++)
- {
- for (int j = 1; j <= dimension; j++)
- {
- lstAllPosition.Add(new position { x = i, y = j });
- }
- }
- #endregion
这样的话lstAllPosition就存放了64个格子了。由于采用了C#作为实现的语言,因此尽情的使用他的一些优点,比如采用Linq和拉姆达表达式来选定特定的行的元素。此处,需要有C#的一些知识。
对于放置皇后的实现。本人写了2种方法,2中方法本质都是一样的,只不过理解起来稍微有些不同。
第一种方法中规中矩。
看如下代码和注释:
- static void PlaceQueen(int row)
- {
- #region 实现方法一
- //当前行的元素
- var currentrow = lstAllPosition.Where(m => m.x == row).ToList();
- for (int index = 0; index < currentrow.Count;index++ )
- {
- //加入一个元素
- solution.Add(currentrow[index]);
- //如果有效的话,继续下面的递归
- if (Valid(solution))
- {
- //如果row是最后一行了,说明已经满足。打印。
- if (row == dimension)
- {
- print(solution);
- //找到一组解之后,删除该元素,继续下一组解的查找
- solution.Remove(solution.Last());
- }
- else
- {
- //递归调用下一行
- PlaceQueen(row + 1);
- }
- }
- else
- {
- solution.Remove(currentrow[index]);
- }
- //如果该行的元素每个都被试过了,但是还是没能运行到print(solution)方法中去,则该方法即将运行结束,结束前,把最后一个元素也删掉。
- //由于该方法是递归的,因此结束之后,会继续重新下一个元素。
- if (index == dimension-1 && solution.Count > 0)
- {
- solution.Remove(solution.Last());
- }
- }
- #endregion
- }
第二种方法也很好理解,只是把solution.Remove(item);删除元素的语句写到外面,表示,无论怎样,都会把刚加入的元素删除。
但是在删除元素之前,由于递归调用的结果,在某些情况下solution列的元素加满到8个时候,还没删除元素。这是就直接打印出结果,然后再删除最后一个元素。很容易推断,到最后一个元素放入solution的时候,肯定是递归嵌套了8层了。
- static void PlaceQueen(int row)
- {
- #region 实现方法二
- foreach (var item in lstAllPosition.Where(m => m.x == row).ToList())
- {
- //Console.WriteLine("-------");
- solution.Add(item);
- //solution.ForEach(m => Console.Write(m.ToString()));
- //Console.WriteLine();
- //如果有效的话,继续下面的递归
- if (Valid(solution))
- {
- //如果row是最后一行了,说明已经满足。打印。
- if (row == dimension)
- {
- print(solution);
- }
- else
- {
- //递归调用下一行
- PlaceQueen(row + 1);
- }
- }
- //Console.WriteLine("***");
- //把当前元素去除,尝试下一个元素。此语句,每一轮都会执行,除非该轮的调用,
- //每次递归调用PlaceQueen时Valid(solution)都是true,也就是说找到符合条件的结果集,打印完后。
- //还是会继续删除最厚放入的元素,继续尝试下一个元素是否匹配。
- solution.Remove(item);
- //solution.ForEach(m => Console.Write(m.ToString()));
- //Console.WriteLine();
- //Console.WriteLine("-------");
- }
- #endregion
- }
其中 验证当前集合是否有效的函数如下:
//验证有效性
- static bool Valid(List<position> solve)
- {
- var item2 = solve.Last();
- foreach (var item1 in solve)//把最后加入的元素后之前每一个元素做比较。
- {
- if (item1 == item2)
- {
- break;
- }
- if (item1.y == item2.y)//y轴相同
- {
- return false;
- }
- else if (Math.Abs(decimal.Parse((item1.y - item2.y).ToString()) / (item1.x - item2.x)) == 1)//斜线
- {
- return false;
- }
- }
- return true;
- }
打印棋盘的方法如下,使用了Linq和拉姆达表达式。
//打印棋盘
- static void print(List<position> solve)
- {
- Console.ForegroundColor = ConsoleColor.Gray;
- Console.WriteLine("-----" + (count++) + "-------");
- for (int i = 1; i <= dimension; i++)
- {
- foreach (var item in lstAllPosition.Where(m => m.x == i).ToList())
- {
- if (solve.Contains(item))
- {
- Console.ForegroundColor = ConsoleColor.Yellow;
- Console.Write("1 ");
- }
- else
- {
- Console.ForegroundColor = ConsoleColor.Gray;
- Console.Write("0 ");
- }
- }
- Console.WriteLine();
- }
- }
结果如下:共92个解。
所有的解集如下:
-----1-------
1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -----2------- 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -----3------- 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 -----4------- 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 -----5------- 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 -----6------- 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 -----7------- 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 -----8------- 0 1 0 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0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0转载地址:https://blog.csdn.net/weixin_33961829/article/details/85075863 如侵犯您的版权,请留言回复原文章的地址,我们会给您删除此文章,给您带来不便请您谅解!