# Package org.apache.lucene.util.fst

Finite state transducers

See: Description

- Class Summary
  Class | Description
  --- | ---
  Builder<T> | Builds a minimal FST (maps an IntsRef term to an arbitrary output) from pre-sorted terms with outputs.
  Builder.Arc<T> | Expert: holds a pending (seen but not yet serialized) arc.
  Builder.UnCompiledNode<T> | Expert: holds a pending (seen but not yet serialized) Node.
  ByteSequenceOutputs | An FST `Outputs` implementation where each output is a sequence of bytes.
  BytesRefFSTEnum<T> | Enumerates all input (BytesRef) + output pairs in an FST.
  BytesRefFSTEnum.InputOutput<T> | Holds a single input (BytesRef) + output pair.
  CharSequenceOutputs | An FST `Outputs` implementation where each output is a sequence of characters.
  FST<T> | Represents an finite state machine (FST), using a compact byte[] format.
  FST.Arc<T> | Represents a single arc.
  FST.BytesReader | Reads bytes stored in an FST.
  IntSequenceOutputs | An FST `Outputs` implementation where each output is a sequence of ints.
  IntsRefFSTEnum<T> | Enumerates all input (IntsRef) + output pairs in an FST.
  IntsRefFSTEnum.InputOutput<T> | Holds a single input (IntsRef) + output pair.
  NoOutputs | A null FST `Outputs` implementation; use this if you just want to build an FSA.
  Outputs<T> | Represents the outputs for an FST, providing the basic algebra required for building and traversing the FST.
  PairOutputs<A,B> | An FST `Outputs` implementation, holding two other outputs.
  PairOutputs.Pair<A,B> | Holds a single pair of two outputs.
  PositiveIntOutputs | An FST `Outputs` implementation where each output is a non-negative long value.
  Util | Static helper methods.
  Util.FSTPath<T> | Represents a path in TopNSearcher.
  Util.Result<T> | Holds a single input (IntsRef) + output, returned by `shortestPaths()`.
  Util.TopNSearcher<T> | Utility class to find top N shortest paths from start point(s).
  Util.TopResults<T> | Holds the results for a top N search using `Util.TopNSearcher`

- Enum Summary
  Enum | Description
  --- | ---
  FST.INPUT_TYPE | Specifies allowed range of each int input label for this FST.

## Package org.apache.lucene.util.fst Description

Finite state transducers

This package implements Finite State Transducers with the following characteristics:

- Fast and low memory overhead construction of the minimal FST (but inputs must be provided in sorted order)
- Low object overhead and quick deserialization (byte[] representation)
- `Lookup-by-output` when the outputs are in sorted order (e.g., ordinals or file pointers)
- Pluggable `Outputs` representation
- `N-shortest-paths` search by weight
- Enumerators (`IntsRef` and `BytesRef`) that behave like `SortedMap` iterators

FST Construction example:

         // Input values (keys). These must be provided to Builder in Unicode sorted order!
         String inputValues[] = {"cat", "dog", "dogs"};
         long outputValues[] = {5, 7, 12};

         PositiveIntOutputs outputs = PositiveIntOutputs.getSingleton();
         Builder<Long> builder = new Builder<Long>(INPUT_TYPE.BYTE1, outputs);
         BytesRef scratchBytes = new BytesRef();
         IntsRefBuilder scratchInts = new IntsRefBuilder();
         for (int i = 0; i < inputValues.length; i++) {
           scratchBytes.copyChars(inputValues[i]);
           builder.add(Util.toIntsRef(scratchBytes, scratchInts), outputValues[i]);
         }
         FST<Long> fst = builder.finish();

Retrieval by key:

         Long value = Util.get(fst, new BytesRef("dog"));
         System.out.println(value); // 7

Retrieval by value:

         // Only works because outputs are also in sorted order
         IntsRef key = Util.getByOutput(fst, 12);
         System.out.println(Util.toBytesRef(key, scratchBytes).utf8ToString()); // dogs

Iterate over key-value pairs in sorted order:

         // Like TermsEnum, this also supports seeking (advance)
         BytesRefFSTEnum<Long> iterator = new BytesRefFSTEnum<Long>(fst);
         while (iterator.next() != null) {
           InputOutput<Long> mapEntry = iterator.current();
           System.out.println(mapEntry.input.utf8ToString());
           System.out.println(mapEntry.output);
         }

N-shortest paths by weight:

         Comparator<Long> comparator = new Comparator<Long>() {
           public int compare(Long left, Long right) {
             return left.compareTo(right);
           }
         };
         Arc<Long> firstArc = fst.getFirstArc(new Arc<Long>());
         MinResult<Long> paths[] = Util.shortestPaths(fst, firstArc, comparator, 2);
         System.out.println(Util.toBytesRef(paths[0].input, scratchBytes).utf8ToString()); // cat
         System.out.println(paths[0].output); // 5
         System.out.println(Util.toBytesRef(paths[1].input, scratchBytes).utf8ToString()); // dog
         System.out.println(paths[1].output); // 7

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