SML 二叉树节点值之和

Question

我需要编写一个函数，以查找二叉树中所有元素的总和。

二叉树的定义如下：

datatype 'a tree= Leaf of 'a | Node of 'a tree * 'a * 'a tree

我不知道该怎么做。我承认我是SML的初学者。

例如：sumTree (Node (Node (Leaf 1, 3, Leaf 2), 7, Leaf 4)) 应该返回17。sumTree是函数名。

谢谢您的帮助。

- ssukienn

Answer 1

我希望你能花时间理解这个。如果有任何问题，请让我知道：

(*
 * This is a recursive datatype, because the Node constructor contains two
 * elements of type `tree`, the type which we're currently defining.
 *)
datatype 'a tree =
    Leaf of 'a
  | Node of 'a tree * 'a * 'a tree

(*
 * Notice how the structure of the `sumTree` function follows the structure
 * of the `tree` datatype. But `tree` is a recursive datatype, which means
 * that `sumTree` will probably be a recursive function. This is called
 * structural recursion. We recurse accordingly to the structure of the type.
 *)
fun sumTree (Leaf n) = n
  | sumTree (Node (left, n, right)) = (sumTree left) + n + (sumTree right)

基本思路是解决简单情况（Leaf），并在复杂情况（Node）中依赖于简单情况的解决方案。

- Ionuț G. Stan