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Android 的 Google 应用，我们只需要在 Google 搜索框上开始键入关键字，就可以看到联想词了。\n\n![](https://imgkr.cn-bj.ufileos.com/17ed83bf-e028-4db2-9503-5a3b4e64deee.gif)\n\n在上图示例中，我们可以看到，输入关键字 `juej`，Google 搜索会联想到“掘金”、“掘金小册”、“绝句”等等，好处就是，我们无须输入完整的关键字即可轻松完成针对这些 topics 的搜索。\n\n谷歌搜索的自动补全功能对于使用移动设备的用户来说特别有用，用户可以轻松在难以键入的小屏幕上完成搜索。当然，对于移动设备用户和台式机用户而言，这都节省了大量的时间。根据 Google 官方报告，自动补全功能可以减少大约 25% 的打字，累积起来，预计每天可以节省 200 多年的打字时间。是的，每天！\n\n> 注意，本文所提到的“**联想词**”与“**预测**”，是同一个意思。\n\n## 基于“预测”而非“建议”\nGoogle 官方将自动补全功能称之为“预测”，而不是“建议”，为什么呢？其实是有充分理由的。自动补全功能是为了**帮助用户完成他们打算进行的搜索**，而不是建议用户要执行什么搜索。\n\n那么，Google 是如何确定这些“预测”的？其实，Google 会根据趋势搜索 [trends](https://trends.google.com/trends/?geo=US) 给到我们这些“预测”。简单来说，哪个热门、哪个搜索频率高，就更可能推给我们。当然，这也与我们当前所处的位置以及我们的搜索历史相关。\n\n另外，这些“预测”也会随着我们键入的关键字的变更而更改。例如，当我们把键入的关键字从 `juej` 更改为 `juex` 时，与“掘金”相关的预测会“消失”，同时，与“觉醒”、“决心”相关联的词会出现。\n\n![](https://imgkr.cn-bj.ufileos.com/5b17dc99-606d-42c1-9f86-e09e88aaa822.gif)\n\n## 为什么看不到某些联想词？\n如果我们在输入某个关键字时看不到联想词，那么表明 Google 的算法可能检测到：\n\n- 这个关键字不是热门字词；\n- 搜索的字词太新了，我们可能需要等待几天或几周才能看到联想词；\n- 这是一个侮辱性或敏感字词，这个搜索字词违反了 Google 的相关政策。更加详细的情况，可以了解 [Google 搜索自动补全政策](https://support.google.com/websearch/answer/7368877)。\n\n## 为什么会看到某些不当的联想词？\nGoogle 拥有专门设计的系统，可以自动捕获不适当的预测结果而不显示出来。然而，Google 每天需要处理数十亿次搜索，这意味着 Google 每天会显示数十亿甚至上百亿条预测。再好的系统，也可能存在缺陷，不正确的预测也可能随时会出现。\n\n我们作为 Google 搜索的用户，如果认定某条预测违反了相关的搜索自动补全政策，可以进行举报反馈，点击右下角“**举报不当的联想查询**”并勾选相关选项即可。\n\n![](https://imgkr.cn-bj.ufileos.com/6ca8185d-12c6-4550-bb4e-e49cfbf56db7.gif)\n\n## 如何实现自动补全算法？\n目前，Google 官方似乎并没有公开搜索自动补全的算法实现，但是业界在这方面已经有了不少研究。\n\n一个好的自动补全器必须是快速的，并且在用户键入下一个字符后立即更新联想词列表。**自动补全器的核心是一个函数，它接受输入的前缀，并搜索以给定前缀开头的词汇或语句列表**。通常来说，只需要返回少量的数目即可。\n\n接下来，我们先从一个简单且低效的实现开始，并在此基础上逐步构建更高效的方法。\n\n### 词汇表实现\n一个**简单粗暴的实现方式**是：顺序查找词汇表，依次检查每个词汇，看它是否以给定的前缀开头。\n\n但是，此方法需要将前缀与每个词汇进行匹配检查，若词汇量较少，这种方式可能勉强行得通。但是，如果词汇量规模较大，效率就太低了。\n\n一个**更好的实现方式是**：让词汇按字典顺序排序。借助二分搜索算法，可以快速搜索有序词汇表中的前缀。由于二分搜索的每一步都会将搜索的范围减半，因此，总的搜索时间与词汇表中单词数量的对数成正比，即时间复杂度是 `O(log N)`。二分搜索的性能很好，但有没有更好的实现呢？当然有，往下看。\n\n### 前缀树实现\n通常来说，许多词汇都以相同的前缀开头，比如 `need`、`nested` 都以 `ne` 开头，`seed`、`speed` 都以 `s` 开头。要是为每个单词分别存储公共前缀似乎很浪费。\n\n![](https://imgkr.cn-bj.ufileos.com/7cc3cf37-040a-420e-8ef9-d05e92c82cfd.png)\n\n前缀树是一种利用公共前缀来加速补全速度的数据结构。前缀树在节点树中排列一组单词，单词沿着从根节点到叶子节点的路径存储，树的层次对应于前缀的字母位置。\n\n前缀的补全是顺着前缀定义的路径来查找的。例如，在上图的前缀树中，前缀 `ne` 对应于从子节点取左边缘 `N` 和唯一边缘 `E` 的路径。然后可以通过继续遍历从 `E` 节点可以达到的所有叶节点来生成补全列表。在图中，`ne` 的补全可以是两个分支：`-ed` 和 `-sted`。如果在数中找不到由前缀定义的路径，则说明词汇表中不包含以该前缀开头的单词。\n\n### 有限状态自动机(DFA)实现\n前缀树可以有效处理公共前缀，但是，对于其他共享词部分，仍会分别存储在每个分支中。比如，后缀 `ed`、`ing`、`tion` 在英文单词中特别常见。在上一个例子中，`e`、`d` 分别存放在了每一个分支上。\n\n有没有一种方法可以更加节省存储空间呢？有的，那就是 DFA。\n\n<center>\n<img src="https://imgkr.cn-bj.ufileos.com/02bc143e-e1a7-4b3c-bd5d-8d6d39139f0a.png" style="width: 50%;"></center>\n\n在上面的例子中，单词 `need`、`nested`、`seed` 和 `speed` 仅由 9 个节点组成，而上一张图中的前缀树包含了 17 个节点。\n\n可以看出，最小化前缀树 DFA 可以在很大程度上减少数据结构的大小。即使词汇量很大，最小化 DFA 通常也适合在内存中存储，避免昂贵的磁盘访问是实现快速自动补全的关键。\n\n### 一些扩展\n上面介绍了如何利用合理的数据结构实现基本的自动补全功能。这些数据结构可以通过多种方式进行扩展，从而改善用户体验。\n\n通常，满足特定前缀的词汇可能很多，而用户界面上能够显示的却不多，我们更希望能显示最常搜索或者最有价值的词汇。这通常可以通过为词汇表中的每个单词增加一个代表单词值的**权重** `weight`，并且按照权重高低来排序自动补全列表。\n\n- 对于排序后的词汇表来说，在词汇表每个元素上增加 `weight` 属性并不难；\n- 对于前缀树来说，将 `weight` 存储在叶子节点中，也是很简单的一个实现；\n- 对于 `DFA` 来说，则较为复杂。因为一个叶子节点可以通过多条路径到达。一种解决方案是将权重关联到路径而不是叶子节点。\n\n目前有不少开源库都提供了这个功能，比如主流的搜索引擎框架 [Elasticsearch](https://www.elastic.co/products/elasticsearch)、[Solr](https://lucene.apache.org/solr/) 等，基于此，我们可以实现高效而强大的自动补全功能。\n\n#### 推荐阅读\n- [阿里又一个 20k+ stars 开源项目诞生，恭喜 fastjson！](https://mp.weixin.qq.com/s/RNKDCK2KoyeuMeEs6GUrow)\n- [刷掉 90% 候选人的互联网大厂海量数据面试题（附题解 + 方法总结）](https://mp.weixin.qq.com/s/rjGqxUvrEqJNlo09GrT1Dw)\n- [好用！期待已久的文本块功能究竟如何在 Java 13 中发挥作用？](https://mp.weixin.qq.com/s/kalGv5T8AZGxTnLHr2wDsA)\n- [2019 GitHub 开源贡献排行榜新鲜出炉！微软谷歌领头，阿里跻身前 12！](https://mp.weixin.qq.com/s/_q812aGD1b9QvZ2WFI0Qgw)\n\n---\n\n欢迎关注我的公众号“**Doocs开源社区**”，原创技术文章第一时间推送。\n\n<center>\n    <img 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