Table of Contents
Suffix AutomatonImplementationSuffix TreeImplementationGenerate Suffix Array from Suffix TreeGenerate Suffix Tree from Suffix ArrayGenerate Suffix Tree from Suffix AutomatonExample: Standing OutSuffix Structure Problems (Array, Automaton, Tree)Extending Palindromic TreeProblemsEdit on GithubString Suffix Structures
Authors: Siyong Huang, Benjamin Qi
Prerequisites
Suffix Automata, Suffix Trees, and Palindromic Trees
Table of Contents
Suffix AutomatonImplementationSuffix TreeImplementationGenerate Suffix Array from Suffix TreeGenerate Suffix Tree from Suffix ArrayGenerate Suffix Tree from Suffix AutomatonExample: Standing OutSuffix Structure Problems (Array, Automaton, Tree)Extending Palindromic TreeProblemsEdit on Github
A lot of problems can be solved with Suffix Arrays, Suffix Automata, or Suffix Trees. The solution may just be slightly easier/harder with the various data structures.
Suffix Automaton
The Suffix Automaton is a directed acyclic word graph (DAWG), such that each path in the graph traces out a distinct substring of the original string.
| Resources | |||
|---|---|---|---|
| CF | Explanation of Suffix Automata | ||
| cp-algo | Excellent Suffix Automaton tutorial | ||
| CF | More problems! | ||
Implementation
| Resources | |||
|---|---|---|---|
| Benq | |||
Suffix Tree
The Suffix Tree is a trie that contains all suffixes of a string. Naively, this would take up memory, but path compression enables it to be represented and computed in linear memory.
| Resources | |||
|---|---|---|---|
| SO | example + diagrams | ||
| CF | brief explanation of Ukkonen's Algorithm + code | ||
Implementation
| Resources | |||
|---|---|---|---|
| Benq | based off adamant's above | ||
| cp-algo | implementation of Ukkonen's Algorithm | ||
Generate Suffix Array from Suffix Tree
A suffix array can be generated by the suffix tree by taking the dfs traversal of the suffix tree.
Sample Code: Suffix Array from Suffix Tree
Generate Suffix Tree from Suffix Array
Of course, the above operation can be reversed as well. Each element in the suffix array corresponds to a leaf in the suffix tree. The LCP array stores information about the Lowest Common Ancestor of two adjacent elements in the suffix array. Using these two pieces of information, we can construct the suffix tree from the suffix array in linear time.
Pro Tip!
Frequently, string suffix structures are greatly simplified by adding a 'terminator' character, such as $ or -, to the end of the string. In the following samples, these terminators will be explicitly added.
Sample Code: Suffix Tree from Suffix Array
Generate Suffix Tree from Suffix Automaton
One interesting thing about Suffix Trees and Suffix Automata is that the link tree of a Suffix Automaton is equivalent to the Suffix Tree of the reversed string. Since Suffix Automata are much easier to create than Suffix Trees, we can use this as an alternate method to build a Suffix Tree, all in linear time too!
Sample Code: Suffix Tree from Suffix Automaton
Example: Standing Out
| Status | Source | Problem Name | Difficulty | Tags | Solution | URL |
|---|---|---|---|---|---|---|
| Plat | Hard | External Sol |
With Suffix Automaton
Suffix Structure Problems (Array, Automaton, Tree)
Extending Palindromic Tree
Problems
Module Progress:
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