我怎样才能生成所有Tetrominos的名单？ [英] How can I generate a list of all Tetrominos?

问题描述

我怎么能生成所有Tetrominos的名单？ 或者，更一般地，如何可以生成限制到多个小区

How can I generate a list of all Tetrominos? Or, more generally, how can I generate a subset of the polyominoes restricted to a number of cells?

推荐答案

有很多方法可以做到这一点。我发现一个选项可以很好的考虑一下递归和更普遍。特别是：

There are many ways to do this. One option that I've found works well is to think about it recursively and more generally. In particular:

1. 在一个矩形是1 omino。
2. 对于任何正omino，你可以通过把块邻近任何从正omino块的创建（N + 1）-omino。

这给你列出所有可能的正ominos的递归方法。你必须要小心，虽然，因为这将产生多次旋转和相同的正ominos的翻译。你可以挑选一些参考坐标系统，然后翻译正omino，使其始终与该系统的轴平齐解决这个问题。一旦你的工作，你可以通过只旋转所产生的正omino绕轴，则其转换回典型位置生成所有转。

This gives you a recursive way of listing all possible n-ominos. You need to be careful, though, since this will generate multiple rotations and translations of the same n-ominos. You can fix this by picking some reference coordinate system and then translating the n-omino so that it is always flush with the axes of that system. Once you've got that working, you can generate all rotations by just rotating the resulting n-omino around the axes, then translating it back to the canonical position.

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