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curriculum/challenges/chinese/10-coding-interview-prep/data-structures/add-a-new-element-to-a-binary-search-tree.md
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---
id: 587d8257367417b2b2512c7b
title: Add a New Element to a Binary Search Tree
title: 将新元素添加到二叉搜索树
challengeType: 1
forumTopicId: 301618
dashedName: add-a-new-element-to-a-binary-search-tree
@ -8,27 +8,27 @@ dashedName: add-a-new-element-to-a-binary-search-tree
# --description--
This series of challenges will introduce the tree data structure. Trees are an important and versatile data structure in computer science. Of course, their name comes from the fact that when visualized they look much like the trees we are familiar with in the natural world. A tree data structure begins with one node, typically referred to as the root, and from here branches out to additional nodes, each of which may have more child nodes, and so on and so forth. The data structure is usually visualized with the root node at the top; you can think of it as a natural tree flipped upside down.
这一系列的挑战将介绍树形数据结构。 树是计算机科学中一个重要的、通用的数据结构。 当然，它们的名称来自这样一个事实：当可视化时，它们看起来很像我们在自然界中熟悉的树木。 树数据结构从一个节点（通常称为根）开始，并从此处分支到其他节点，每个节点可能具有更多的子节点，依此类推。 数据结构通常以根节点为顶点进行可视化；你可以把它想象成一棵倒过来的自然树。
First, let's describe some common terminology we will encounter with trees. The root node is the top of the tree. Data points in the tree are called nodes. Nodes with branches leading to other nodes are referred to as the parent of the node the branch leads to (the child). Other more complicated familial terms apply as you might expect. A subtree refers to all the descendants of a particular node, branches may be referred to as edges, and leaf nodes are nodes at the end of the tree that have no children. Finally, note that trees are inherently recursive data structures. That is, any children of a node are parents of their own subtree, and so on. The recursive nature of trees is important to understand when designing algorithms for common tree operations.
首先，让我们描述一下我们将遇到的关于树的一些常见术语。 根节点（root）是树的顶部。 树中的数据点称为节点（node）。 分支通向其他节点的节点称为分支通向的节点（即子节点）的父节点。 如你所料，其他更复杂的家庭术语也适用。 子树指的是某一特定节点的所有后代，分支可称为边，而叶子节点是位于树的末端的且没有子节点的节点。 最后，请注意，树本质上是递归的数据结构。 也就是说，一个节点的任何子节点都是其自己的子树的父节点，依此类推。 在为常见的树操作设计算法时，树的递归性质很重要。
To begin, we will discuss a particular type of a tree, the binary tree. In fact, we will actually discuss a particular binary tree, a binary search tree. Let's describe what this means. While the tree data structure can have any number of branches at a single node, a binary tree can only have two branches for every node. Furthermore, a binary search tree is ordered with respect to the child subtrees, such that the value of each node in the left subtree is less than or equal to the value of the parent node, and the value of each node in the right subtree is greater than or equal to the value of the parent node. It's very helpful to visualize this relationship in order to understand it better:
首先，我们将讨论树的一个特殊类型，即二叉树。 实际上，我们将讨论特定的二叉树，即二叉搜索树。 让我们来看看这意味着什么。 虽然树形数据结构在一个节点上可以有任意数量的分支，但二叉树每个节点只能有两个分支。 此外，一个二叉搜索树相对于其子子树是有序的，即对于一个节点而言，其左子树中每个节点的值都小于或等于该节点的值，而其右子树中每个节点的值都大于或等于该节点的值。 为了更好地理解这种关系，将这种关系形象化是非常有帮助的：
<div style='width: 100%; display: flex; justify-content: center; align-items: center;'><img style='width: 100%; max-width: 350px; background-color: var(--gray-05);' src='https://user-images.githubusercontent.com/18563015/32136009-1e665d98-bbd6-11e7-9133-63184f9f9182.png'></div>
Now this ordered relationship is very easy to see. Note that every value to the left of 8, the root node, is less than 8, and every value to the right is greater than 8. Also notice that this relationship applies to each of the subtrees as well. For example, the first left child is a subtree. 3 is the parent node, and it has exactly two child nodes — by the rules governing binary search trees, we know without even looking that the left child of this node (and any of its children) will be less than 3, and the right child (and any of its children) will be greater than 3 (but also less than the structure's root value), and so on.
现在，这种有序的关系是非常容易看到的。 注意，根节点 8 左边的每个值都小于 8，右边的每个值都大于 8。 还要注意的是，这种关系也适用于每个子树。 例如，第一个左孩子节点是一个子树。 3 是父节点，它正好有两个子节点——根据二进制搜索树的规则，我们甚至不用看就知道这个节点的左子节点（以及它的任何子节点）都将小于 3，右子节点（以及它的任何子节点）都将大于 3（但也小于根结点的值），依此类推。
Binary search trees are very common and useful data structures because they provide logarithmic time in the average case for several common operations such as lookup, insertion, and deletion.
二叉搜索树是非常常见且有用的数据结构，因为它们在几种常见操作（例如查找、插入和删除）的平均情况下提供对数的时间复杂度。
# --instructions--
We'll start simple. We've defined the skeleton of a binary search tree structure here in addition to a function to create nodes for our tree. Observe that each node may have a left and right value. These will be assigned child subtrees if they exist. In our binary search tree, you will create a method to add new values to our binary search tree. The method should be called `add` and it should accept an integer value to add to the tree. Take care to maintain the invariant of a binary search tree: the value in each left child should be less than or equal to the parent value, and the value in each right child should be greater than or equal to the parent value. Here, let's make it so our tree cannot hold duplicate values. If we try to add a value that already exists, the method should return `null`. Otherwise, if the addition is successful, `undefined` should be returned.
我们将从简单的内容开始。 我们在这里定义了一个二叉搜索树结构的骨架，此外还有一个为我们的树创建节点的函数。 注意观察每个节点可能有一个左值和右值。 如果子树存在，它们将被分配给对应的子树。 在我们的二叉搜索树中，你将创建一个方法来向我们的二叉搜索树添加新的值。 该方法应该被称为`add` ，它应该接受一个整数值来添加到树中。 注意保持二叉搜索树的不变量：每个左子项中的值应小于或等于父值，并且每个右子项中的值应大于或等于父值。 在这里，让我们确保我们的树不会含有重复的值。 如果我们尝试添加已存在的值，则该方法应返回`null` 。 否则，如果添加成功，则应返回`undefined` 。
**Hint:** trees are naturally recursive data structures!
**提示：** 树是自然的递归数据结构！
# --hints--
The `BinarySearchTree` data structure should exist.
存在 `BinarySearchTree` 的数据结构。
```js
assert(
@ -42,7 +42,7 @@ assert(
);
```
The binary search tree should have a method called `add`.
二叉搜索树应该有一个名为 `add` 的方法。
```js
assert(
@ -58,7 +58,7 @@ assert(
);
```
The add method should add elements according to the binary search tree rules.
添加的方法应该根据二叉搜索树的规则来添加元素。
```js
assert(
@ -87,7 +87,7 @@ assert(
);
```
Adding an element that already exists should return `null`.
添加一个已经存在的元素应该返回 `null`。
```js
assert(