为Quadtrees写入太多模式匹配？ [英] Too many pattern matches to write down for Quadtrees?

问题描述

假设一个四叉树定义如下：

  data（Eq a，Show a）= > QT a = C a | Q（QT a）（QT a）（QT a）（QT a）
导出（Eq，Show）
 
 bad1 = Q uuuu其中u = C 255 
 bad2 = Q（C 0）（C 255）（Q uuuu）（C 64）其中u = C 255 
  

该构造函数允许您创建格式不正确的四叉树。 bad1 应该是简单的C 255和 bad2 也是无效的，因为它的右下四叉树（出于同样的原因，它应该是 Q（C 0）（C 255）（C 244）（C 64）。

检查它的良好形状只是递归检查其内部四叉树的问题。基本情况是当所有内部四叉树都是叶子时，所有颜色都不应该是'

  wellformed ::（等式a，显示a）=> QT a  - > Bool $ b （C c1）（C c2）（C c3）（C c4））=任何（c = c1）[c2，c3，c4] 
 ）se（C c4））=有效se 
  - 继续定义模式以匹配例如QCCC，CQQC等... 
  

问题：我可以避免输入所有可能的叶子和四叉树组合吗？

如果我的问题很奇怪，请耐心等待，但这是我的第二天Haskell-seaml ess-learing！

解决方案

  wellformed ::（等式a，显示a）=> QT a  - > Bool 
 wellformed（C_）= True 
 wellformed（Q（C c1）（C c2）（C c3）（C c4））= any（/ = c1）[c2，c3，c4] 
 wellformed（Q nw ne se sw）= wellformed nw&&良好的ne 
&&良好的se&& wellform sw 
  

编辑：甚至更好：

  wellformed ::（等式a，显示a）=> QT a  - > Bool 
 wellformed（C_）= True 
 wellformed（Q（C c1）（C c2）（C c3）（C c4））= any（/ = c1）[c2，c3，c4] 
 wellformed（Q nw ne se sw）= all wellformed [nw，ne，se，sw] 
  

编辑：请注意绑定错误，应该是：NW NE SW SE !!!

Imagine a quadtree defined as follow:

data (Eq a, Show a) => QT a = C a | Q (QT a) (QT a) (QT a) (QT a)
  deriving (Eq, Show)

bad1 = Q u u u u where u = C 255
bad2 = Q (C 0) (C 255) (Q u u u u) (C 64) where u = C 255

The constructor allows you to create not well-formed quadtrees. bad1 should be simply C 255 and bad2 is not valid too because its bottom-right quadtree (for the same reason, it should be Q (C 0) (C 255) (C 244) (C 64).

So far so good. Checking its well-formness is simply a matter of checking its inner quadtrees recursively. The base case is when all inner quadtrees are leafs, whereby all colors shouldn't be all equals.

wellformed :: (Eq a, Show a) => QT a -> Bool
wellformed (Q (C c1) (C c2) (C c3) (C c4)) = any (/= c1) [c2, c3, c4]
wellformed (Q (C c1) (C c2) se (C c4))     = valid se
-- continue defining patters to match e.g Q C C C, C Q Q C, and so on...

Question: Can I avoid typing all matches for all possible combination of leafs and quadtrees?

Please be patient if my question is quite odd, but it's my second-day-Haskell-seamless-learing!

解决方案

Nevermind...

wellformed :: (Eq a, Show a) => QT a -> Bool
wellformed (C _) = True
wellformed (Q (C c1) (C c2) (C c3) (C c4)) = any (/= c1) [c2, c3, c4]
wellformed (Q nw ne se sw) = wellformed nw && wellformed ne
   && wellformed se && wellformed sw

EDIT: or even better:

wellformed :: (Eq a, Show a) => QT a -> Bool
wellformed (C _) = True
wellformed (Q (C c1) (C c2) (C c3) (C c4)) = any (/= c1) [c2, c3, c4]
wellformed (Q nw ne se sw) = all wellformed [nw, ne, se, sw]

EDIT: note that the bindings are wrong, should be: NW NE SW SE!!!

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