83 lines
5.7 KiB
Markdown
83 lines
5.7 KiB
Markdown
---
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id: 587d8257367417b2b2512c7d
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title: Find the Minimum and Maximum Height of a Binary Search Tree
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challengeType: 1
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videoUrl: ''
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localeTitle: 找到二叉搜索树的最小和最大高度
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---
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## Description
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<section id="description">在最后一个挑战中，我们描述了树可能变得不平衡的情景。为了理解平衡的概念，让我们看看另一个树属性：高度。树中的高度表示从根节点到任何给定叶节点的距离。高度分支的树结构中的不同路径可以具有不同的高度，但是对于给定的树，将具有最小和最大高度。如果树是平衡的，则这些值最多相差一个。这意味着在平衡树中，所有叶节点都存在于同一级别中，或者如果它们不在同一级别内，则它们最多相隔一个级别。平衡的属性对于树很重要，因为它决定了树操作的效率。正如我们在上一次挑战中所解释的那样，我们面临严重不平衡树木的最坏情况时间复杂性。自平衡树通常用于在具有动态数据集的树中解决此问题。这些的常见例子包括AVL树，红黑树和B树。这些树都包含额外的内部逻辑，当插入或删除创建不平衡状态时，它会重新平衡树。注意：与height相似的属性是depth，它指的是给定节点距根节点的距离。说明：为我们的二叉树编写两种方法： <code>findMinHeight</code>和<code>findMaxHeight</code> 。这些方法应分别返回给定二叉树内最小和最大高度的整数值。如果节点为空，请为其指定高度<code>-1</code> （这是基本情况）。最后，添加第三个方法<code>isBalanced</code> ，它返回<code>true</code>或<code>false</code>具体取决于树是否平衡。您可以使用刚才编写的前两种方法来确定这一点。 </section>
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## Instructions
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<section id="instructions">
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: 存在<code>BinarySearchTree</code>数据结构。
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testString: 'assert((function() { var test = false; if (typeof BinarySearchTree !== "undefined") { test = new BinarySearchTree() }; return (typeof test == "object")})(), "The <code>BinarySearchTree</code> data structure exists.");'
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- text: 二叉搜索树有一个名为<code>findMinHeight</code>的方法。
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testString: 'assert((function() { var test = false; if (typeof BinarySearchTree !== "undefined") { test = new BinarySearchTree() } else { return false; }; return (typeof test.findMinHeight == "function")})(), "The binary search tree has a method called <code>findMinHeight</code>.");'
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- text: 二叉搜索树有一个名为<code>findMaxHeight</code>的方法。
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testString: 'assert((function() { var test = false; if (typeof BinarySearchTree !== "undefined") { test = new BinarySearchTree() } else { return false; }; return (typeof test.findMaxHeight == "function")})(), "The binary search tree has a method called <code>findMaxHeight</code>.");'
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- text: 二叉搜索树有一个名为<code>isBalanced</code>的方法。
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testString: 'assert((function() { var test = false; if (typeof BinarySearchTree !== "undefined") { test = new BinarySearchTree() } else { return false; }; return (typeof test.isBalanced == "function")})(), "The binary search tree has a method called <code>isBalanced</code>.");'
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- text: <code>findMinHeight</code>方法返回树的最小高度。
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testString: 'assert((function() { var test = false; if (typeof BinarySearchTree !== "undefined") { test = new BinarySearchTree() } else { return false; }; if (typeof test.findMinHeight !== "function") { return false; }; test.add(4); test.add(1); test.add(7); test.add(87); test.add(34); test.add(45); test.add(73); test.add(8); return (test.findMinHeight() == 1); })(), "The <code>findMinHeight</code> method returns the minimum height of the tree.");'
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- text: <code>findMaxHeight</code>方法返回树的最大高度。
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testString: 'assert((function() { var test = false; if (typeof BinarySearchTree !== "undefined") { test = new BinarySearchTree() } else { return false; }; if (typeof test.findMaxHeight !== "function") { return false; }; test.add(4); test.add(1); test.add(7); test.add(87); test.add(34); test.add(45); test.add(73); test.add(8); return (test.findMaxHeight() == 5); })(), "The <code>findMaxHeight</code> method returns the maximum height of the tree.");'
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- text: 空树返回高度<code>-1</code> 。
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testString: 'assert((function() { var test = false; if (typeof BinarySearchTree !== "undefined") { test = new BinarySearchTree() } else { return false; }; if (typeof test.findMaxHeight !== "function") { return false; }; return (test.findMaxHeight() == -1); })(), "An empty tree returns a height of <code>-1</code>.");'
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- text: 如果树是平衡二叉搜索树，则<code>isBalanced</code>方法返回true。
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testString: 'assert((function() { var test = false; if (typeof BinarySearchTree !== "undefined") { test = new BinarySearchTree() } else { return false; }; if (typeof test.isBalanced !== "function") { return false; }; test.add(4); test.add(1); test.add(7); test.add(87); test.add(34); test.add(45); test.add(73); test.add(8); return test.isBalanced(); })(), "The <code>isBalanced</code> method returns true if the tree is a balanced binary search tree.");'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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var displayTree = (tree) => console.log(JSON.stringify(tree, null, 2));
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function Node(value) {
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this.value = value;
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this.left = null;
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this.right = null;
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}
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function BinarySearchTree() {
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this.root = null;
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// change code below this line
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// change code above this line
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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console.info('after the test');
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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