二叉树的 SML 和答案

【问题标题】：SML sum of binary tree二叉树的 SML 和
【发布时间】：2023-03-03 13:21:01
【问题描述】：

我必须编写一个函数来查找二叉树中所有元素的总和。

这就是它的定义（树）：

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 是函数的名称。

感谢您的帮助。

【问题讨论】：

标签： function sum binary-tree sml

【解决方案1】：

我希望您能花时间理解这一点。如果您对此有任何疑问，请告诉我：

(*
 * 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)

基本思想是解决简单情况（Leaf）的问题，复杂情况（Node）依靠简单情况的解决方案。

【讨论】：