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Flip游戏规则

Flip game is played on a rectangular 4x4 field with two-sided pieces placed on each of its 16 squares. One side of each piece is white and the other one is black and each piece is lying either its black or white side up. Each round you flip 3 to 5 pieces, thus changing the color of their upper side from black to white and vice versa. The pieces to be flipped are chosen every round according to the following rules:

Consider the following position as an example:

bwbw wwww bbwb bwwb

Here "b" denotes pieces lying their black side up and "w" denotes pieces lying their white side up. If we choose to flip the 1st piece from the 3rd row (this choice is shown at the picture), the field will become:

bwww wwwb wwwb

The goal of the game is to flip either all pieces white side up or all pieces black side up. You are to write a program that will search for the minimum number of rounds needed to achieve this goal.

棋盘反转说明

棋盘反转的具体规则和例子已经说得比较清楚。要点总结如下：

输入格式

输入包括4行，每行包含4个字符，可以是“w”或“b”。

输出格式

输出一个整数，表示最少回合数。如果目标已经实现，则输出0。如果无法实现，则输出“Impossible”。

样例输入：

bwwb bbwb bwwb bwww

样例输出：

4

攻略解析

一开始我没有头绪，找规律比较麻烦。后来依靠搜索相关资料，决定使用DFS加上枚举的方法。这是一个常见的组合优化问题，常用DFS或BFS解决。

具体方法：

注意事项：

• 状态表示透：按行、列记录当前状态。
• 硬币翻转操作影响范围大：每次翻转后需要重新计算状态。
• 需要剪枝机制：避免重复状态访问。
• 目标对称性检查：使任务方便。

代码实现注意事项：

• 确保索引的合法性，避免越界。
• 状态变化记录：使用二维数组或哈希表。
• 队列优化：按层处理搜索，保证优先级。

最后，通过代码验证我的解决方案是否正确。将样例输入带入程序，得到输出，发现计算结果与预期一致。这样可以确信代码是正确的。

好了，这就是我思考如何解决Flip游戏的问题总结。感谢这段时间的努力，现在我有了可行的方案。