简单。他们有大量的数据。他们有每一个可能的术语的统计数据，基于它被查询的频率，以及它的什么变化通常会产生用户点击的结果……因此，当他们看到你在搜索词中经常拼写错误时，他们会提出更常见的答案。

实际上，如果拼写错误实际上是搜索频率最高的词，算法就会把它当成正确的词。

使用Levenshtein距离，然后创建一个度量树(或Slim树)来索引单词。 然后运行1-Nearest Neighbour查询，就得到了结果。

有一种特定的数据结构——三元搜索树——自然地支持部分匹配和近邻匹配。

通常，产品拼写纠正器会使用几种方法来提供拼写建议。一些人:

Decide on a way to determine whether spelling correction is required. These may include insufficient results, results which are not specific or accurate enough (according to some measure), etc. Then: Use a large body of text or a dictionary, where all, or most are known to be correctly spelled. These are easily found online, in places such as LingPipe. Then to determine the best suggestion you look for a word which is the closest match based on several measures. The most intuitive one is similar characters. What has been shown through research and experimentation is that two or three character sequence matches work better. (bigrams and trigrams). To further improve results, weigh a higher score upon a match at the beginning, or end of the word. For performance reasons, index all these words as trigrams or bigrams, so that when you are performing a lookup, you convert to n-gram, and lookup via hashtable or trie. Use heuristics related to potential keyboard mistakes based on character location. So that "hwllo" should be "hello" because 'w' is close to 'e'. Use a phonetic key (Soundex, Metaphone) to index the words and lookup possible corrections. In practice this normally returns worse results than using n-gram indexing, as described above. In each case you must select the best correction from a list. This may be a distance metric such as levenshtein, the keyboard metric, etc. For a multi-word phrase, only one word may be misspelled, in which case you can use the remaining words as context in determining a best match.

谷歌显然建议搜索结果最好的问题，而不是拼写正确的问题。但在这种情况下，可能拼写纠正器会更可行。当然，您可以为每个查询存储一些值，基于它返回的结果有多好。

So,

You need a dictionary (english or based on your data) Generate a word trellis and calculate probabilities for the transitions using your dictionary. Add a decoder to calculate minimum error distance using your trellis. Of course you should take care of insertions and deletions when calculating distances. Fun thing is that QWERTY keyboard maximizes the distance if you hit keys close to each other.(cae would turn car, cay would turn cat) Return the word which has the minimum distance. Then you could compare that to your query database and check if there is better results for other close matches.

最简单的方法是动态规划。

这是一种从信息检索中借来的算法，在现代生物信息学中大量使用，以查看两个基因序列有多相似。

最优解采用动态规划和递归。

这是一个已经解决的问题，有很多解决方案。在你找到一些开源代码之前，一直在你的周围打转。