definition
Suffix automaton ( \ (\ Automaton Suffix {text} \) , abbreviated \ (\ text the SAM} {\) ). For a string \ (S \) , which corresponds to a suffix automaton is minimal deterministic finite automaton ( \ (\ the DFA {text} \) ), and accepts only accept \ (S \) suffix.
For example, the string \ (S = \ underline aabbabd} {\) , which is a suffix automaton
Wherein \ (\ textcolor [rgb] { 1,0,0} { } red status \) is the end state. You can find for \ (S \) suffix, we can from \ (S \) departing along a path marked character ( \ (\ textColor [RGB] {0,0,1} {} blue solid line \ ) ) transfer, and finally to the end state.
In particular, for the (S \) \ substring will eventually reach a valid state. For other than \ (S \) String substring will eventually "nowhere to go."
\ (\ text {SAM} \ ) is essentially a \ (\ the DFA {text} \) , \ (\ the DFA text} {\) may be a five-tuple <character set, the state set, transfer function, starting state, end state set> to represent. For those \ (\ textcolor [rgb] { 0,1,0} { } green dotted line \) Although not \ (\ text {DFA} \ ) part, but it is \ (\ text {SAM} \ ) important part, with these links \ (\ text {SAM} \ ) is even more powerful, these Jiangzai go into detail later.
Here we introduce for a given string \ (S \) how to determine its corresponding set of states and the transition function .
SAM set of states (States)
First, a concept first introduced end position of the substring collection \ (endpos \)
For \ (S \) of a substring \ (S \) , \ (endpos (S) = S \) in the (S \) \ collection of all end position appears.
String \ (S = \ underline {aabbabd } \) Example
| status | Substring | \ (Endpos \) |
|---|---|---|
| \(S\) | \(\varnothing\) | \(\{0,1,2,3,4,5,6\}\) |
| \(1\) | \(a\) | \(\{{1,2,5}\}\) |
| \(2\) | \(aa\) | \(\{2\}\) |
| \(3\) | \ (Re \) | \(\{3\}\) |
| \(4\) | \ (Aabb, fig, bb \) | \(\{4\}\) |
| \(5\) | \(b\) | \(\{3,4,6\}\) |
| \(6\) | \ (Aabba, abba, my father, \) | \(\{5\}\) |
| \(7\) | \ (Aabbab, abbab, chapter, chapter \) | \(\{6\}\) |
| \(8\) | \(from\) | \(\{3,6\}\) |
| \(9\) | \ (Aabbabd, abbabd, bbabd, babd, abd, bd, d \) | \(\{7\}\) |