泛函编程(8)-数据结构-Tree

来源:转载

    上节介绍了泛函数据结构List及相关的泛函编程函数设计使用,还附带了少许多态类型(Polymorphic Type)及变形(Type Variance)的介绍。有关Polymorphism的详细介绍会放在typeclass讨论中。为了更多了解泛函数据结构(Functional Data Structure),想在这个章节把另一个我们熟悉的数据结构-Tree做些简单介绍。

    Tree的状态不是枝(Branch)就是叶(Leaf),这个很容易理解。那么就按照上节设计List那样设计Tree类型:

1 trait Tree[+A]

2 case class Leaf[A](value: A) extends Tree[A]

3 case class Branch[A](left: Tree[A], right: Tree[A]) extends Tree[A]

类参数+A代表协变(covariant),这个在上节List中已经介绍过了。先创建一个Tree实例(Tree Instance):

 

1 val tree = Branch(Branch(Leaf(1),Leaf(2)),Branch(Branch(Leaf(10),Leaf(8)),Leaf(3)))

2 //> tree : ch3.tree.Branch[Int] = Branch(Branch(Leaf(1),Leaf(2)),Branch(Branch(

3 //| Leaf(10),Leaf(8)),Leaf(3)))

创建了一个Tree Instance tree,如下图:

 

数数有几个节点:

1 def size: Int = this match {

2 case Leaf(_) => 1

3 case Branch(l,r) => 1 + l.size + r.size

4 }

1 tree size //> res0: Int = 9

这是所有branch + leaf 总数。

分开计算branch 和 leaf 数量:

1 def countLeafs: Int = this match {

2 case Leaf(_) => 1

3 case Branch(l,r) => 0 + l.size + r.size

4 }

5 def countBranches: Int = this match {

6 case Leaf(_) => 0

7 case Branch(l,r) => 1 + l.size + r.size

8 }

9

1 tree.countLeafs //> res1: Int = 8

2 tree.countBranches //> res2: Int = 9

探探最深有多深:

1 def depth: Int = this match {

2 case Leaf(_) => 0

3 case Branch(l,r) => 1 + (l.depth max r.depth)

4 }

1 tree depth //> res1: Int = 3

找出最大值的Leaf:

 

1 def maxValue: Int = this match {

2 case Leaf(a: Int) => a

3 case Branch(l,r) => l.maxValue max r.maxValue

4 }

1 tree maxValue //> res2: Int = 10

可以从以上这些函数得出一下共性。把共性抽象出来用fold来实现:

1 def fold[B](f: A => B)(g: (B,B) => B): B = this match {

2 case Leaf(n) => f(n)

3 case Branch(l,r) => g(l.fold(f)(g), r.fold(f)(g))

4 }

函数fold分别收到两个方法f,g:f用来处理Leaf,g用来处理Branch。看看用fold来实现上面的函数:

 

1 def sizeByfold = fold(a => 1)(1 + _ + _)

2 def maxValueByfold(l: Tree[Int]) = l.fold(a => a)((x,y) => 0 + (x max y))

3 def depthByfold = fold(a => 0)((x,y) => 1 + (x max y))

1 tree sizeByfold //> res3: Int = 9

2

3 tree depthByfold //> res4: Int = 3

4

5 tree.maxValueByfold(tree) //> res5: Int = 10

 可能这个 tree.maxValueByfold(tree) 有点怪,但如果把函数实现放到 object Tree里然后import Tree._就可以了。

下面把map和flatMap实现了:

1 def map[B](f: A => B): Tree[B] = this match {

2 case Leaf(a) => Leaf(f(a))

3 case Branch(l,r) => Branch(l.map(f),r.map(f))

4 }

5 def flatMap[B](f: A => Tree[B]): Tree[B] = this match {

6 case Leaf(a) => f(a)

7 case Branch(l,r) => Branch(l.flatMap(f), r.flatMap(f))

8 }

 

 

 

 

 

 

 

 

 

 

 

 


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