Trie and Suffix

前缀树(trie)和后缀树(suffix)是两种非常重要的数据结构，往往用来加速字符串的匹配和查找。

具体的介绍可见下面的资料：

http://blog.youkuaiyun.com/luowen3405/archive/2011/04/01/6295839.aspx

http://blog.youkuaiyun.com/TsengYuen/archive/2009/11/16/4815921.aspx

 

Trie和Suffix最大的不同是，Trie是面向一个字符串的集合，而Suffix是面向一个字符串

 

在面试题目中，一些经典的前缀和后缀应用如下：

Suffix Tree:

求两个字符串的最长公共子串。

1. The longest common substring of two strings, txt1 and txt2, can be found by building a generalized suffix tree for txt1 and txt2: Each node is marked to indicate if it represents a suffix of txt1 or txt2 or both. The 

deepest node marked for both txt1 and txt2 represents the longest common substring.

2. Equivalently, one can build a (basic) suffix tree for the string txt1$txt2#, where `$' is a special terminator for txt1 and `#' is a special terminator for txt2. The longest common substring is indicated by the deepest fork node that has both `...$...' and `...#...' (no $) beneath it.

求一个字符串的最长重复子串
       Add a special end of string character, e.g. `$', to txt[1..n] and build a suffix tree; the longest repeated substring of txt[1..n] is indicated by the deepest fork node in the suffix tree, where depth is measured by the number of characters traversed from the root, i.e., `issi' in the case of `mississippi'. The longest repeated substring can be found in O(n) time using a suffix tree.

      求一个字符串的最长回文
        A palindrome is a string, P, such that P=reverse(P). e.g. `abba'=reverse(`abba'). e.g. `ississi' is the longest palindrome in `mississippi'. The longest palindrome of txt[1..n] can be found in O(n) time, e.g. by building the suffix tree for txt$reverse(txt)# or by building the generalized suffix tree for txt and reverse(txt).

 

Trie

      字典
        A common application of a trie is storing a dictionary, such as one found on a mobile telephone. Such applications take advantage of a trie's ability to quickly search for, insert, and delete entries; however, if 
storing dictionary words is all that is required (i.e. storage of information auxiliary to each word is not required), a minimal acyclic deterministic finite automaton would use less space than a trie.