Java tutorial
/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You under the Apache License, Version 2.0 * (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.lucene.util.automaton; import java.util.Iterator; import java.util.SortedSet; import java.util.TreeSet; import org.apache.lucene.util.UnicodeUtil; /** * Class to construct DFAs that match a word within some edit distance. * <p> * Implements the algorithm described in: * Schulz and Mihov: Fast String Correction with Levenshtein Automata * @lucene.experimental */ public class LevenshteinAutomata { /** Maximum edit distance this class can generate an automaton for. * @lucene.internal */ public static final int MAXIMUM_SUPPORTED_DISTANCE = 2; /* input word */ final int word[]; /* the automata alphabet. */ final int alphabet[]; /* the maximum symbol in the alphabet (e.g. 255 for UTF-8 or 10FFFF for UTF-32) */ final int alphaMax; /* the ranges outside of alphabet */ final int rangeLower[]; final int rangeUpper[]; int numRanges = 0; ParametricDescription descriptions[]; /** * Create a new LevenshteinAutomata for some input String. * Optionally count transpositions as a primitive edit. */ public LevenshteinAutomata(String input, boolean withTranspositions) { this(codePoints(input), Character.MAX_CODE_POINT, withTranspositions); } /** * Expert: specify a custom maximum possible symbol * (alphaMax); default is Character.MAX_CODE_POINT. */ public LevenshteinAutomata(int[] word, int alphaMax, boolean withTranspositions) { this.word = word; this.alphaMax = alphaMax; // calculate the alphabet SortedSet<Integer> set = new TreeSet<>(); for (int i = 0; i < word.length; i++) { int v = word[i]; if (v > alphaMax) { throw new IllegalArgumentException("alphaMax exceeded by symbol " + v + " in word"); } set.add(v); } alphabet = new int[set.size()]; Iterator<Integer> iterator = set.iterator(); for (int i = 0; i < alphabet.length; i++) alphabet[i] = iterator.next(); rangeLower = new int[alphabet.length + 2]; rangeUpper = new int[alphabet.length + 2]; // calculate the unicode range intervals that exclude the alphabet // these are the ranges for all unicode characters not in the alphabet int lower = 0; for (int i = 0; i < alphabet.length; i++) { int higher = alphabet[i]; if (higher > lower) { rangeLower[numRanges] = lower; rangeUpper[numRanges] = higher - 1; numRanges++; } lower = higher + 1; } /* add the final endpoint */ if (lower <= alphaMax) { rangeLower[numRanges] = lower; rangeUpper[numRanges] = alphaMax; numRanges++; } descriptions = new ParametricDescription[] { null, /* for n=0, we do not need to go through the trouble */ withTranspositions ? new Lev1TParametricDescription(word.length) : new Lev1ParametricDescription(word.length), withTranspositions ? new Lev2TParametricDescription(word.length) : new Lev2ParametricDescription(word.length), }; } private static int[] codePoints(String input) { int length = Character.codePointCount(input, 0, input.length()); int word[] = new int[length]; for (int i = 0, j = 0, cp = 0; i < input.length(); i += Character.charCount(cp)) { word[j++] = cp = input.codePointAt(i); } return word; } /** * Compute a DFA that accepts all strings within an edit distance of <code>n</code>. * <p> * All automata have the following properties: * <ul> * <li>They are deterministic (DFA). * <li>There are no transitions to dead states. * <li>They are not minimal (some transitions could be combined). * </ul> */ public Automaton toAutomaton(int n) { return toAutomaton(n, ""); } /** * Compute a DFA that accepts all strings within an edit distance of <code>n</code>, * matching the specified exact prefix. * <p> * All automata have the following properties: * <ul> * <li>They are deterministic (DFA). * <li>There are no transitions to dead states. * <li>They are not minimal (some transitions could be combined). * </ul> */ public Automaton toAutomaton(int n, String prefix) { assert prefix != null; if (n == 0) { return Automata.makeString(prefix + UnicodeUtil.newString(word, 0, word.length)); } if (n >= descriptions.length) return null; final int range = 2 * n + 1; ParametricDescription description = descriptions[n]; // the number of states is based on the length of the word and n final int numStates = description.size(); final int numTransitions = numStates * Math.min(1 + 2 * n, alphabet.length); final int prefixStates = prefix != null ? prefix.codePointCount(0, prefix.length()) : 0; final Automaton a = new Automaton(numStates + prefixStates, numTransitions); int lastState; if (prefix != null) { // Insert prefix lastState = a.createState(); for (int i = 0, cp = 0; i < prefix.length(); i += Character.charCount(cp)) { int state = a.createState(); cp = prefix.codePointAt(i); a.addTransition(lastState, state, cp, cp); lastState = state; } } else { lastState = a.createState(); } int stateOffset = lastState; a.setAccept(lastState, description.isAccept(0)); // create all states, and mark as accept states if appropriate for (int i = 1; i < numStates; i++) { int state = a.createState(); a.setAccept(state, description.isAccept(i)); } // TODO: this creates bogus states/transitions (states are final, have self loops, and can't be reached from an init state) // create transitions from state to state for (int k = 0; k < numStates; k++) { final int xpos = description.getPosition(k); if (xpos < 0) continue; final int end = xpos + Math.min(word.length - xpos, range); for (int x = 0; x < alphabet.length; x++) { final int ch = alphabet[x]; // get the characteristic vector at this position wrt ch final int cvec = getVector(ch, xpos, end); int dest = description.transition(k, xpos, cvec); if (dest >= 0) { a.addTransition(stateOffset + k, stateOffset + dest, ch); } } // add transitions for all other chars in unicode // by definition, their characteristic vectors are always 0, // because they do not exist in the input string. int dest = description.transition(k, xpos, 0); // by definition if (dest >= 0) { for (int r = 0; r < numRanges; r++) { a.addTransition(stateOffset + k, stateOffset + dest, rangeLower[r], rangeUpper[r]); } } } a.finishState(); assert a.isDeterministic(); return a; } /** * Get the characteristic vector <code>X(x, V)</code> * where V is <code>substring(pos, end)</code> */ int getVector(int x, int pos, int end) { int vector = 0; for (int i = pos; i < end; i++) { vector <<= 1; if (word[i] == x) vector |= 1; } return vector; } /** * A ParametricDescription describes the structure of a Levenshtein DFA for some degree n. * <p> * There are four components of a parametric description, all parameterized on the length * of the word <code>w</code>: * <ol> * <li>The number of states: {@link #size()} * <li>The set of final states: {@link #isAccept(int)} * <li>The transition function: {@link #transition(int, int, int)} * <li>Minimal boundary function: {@link #getPosition(int)} * </ol> */ static abstract class ParametricDescription { protected final int w; protected final int n; private final int[] minErrors; ParametricDescription(int w, int n, int[] minErrors) { this.w = w; this.n = n; this.minErrors = minErrors; } /** * Return the number of states needed to compute a Levenshtein DFA */ int size() { return minErrors.length * (w + 1); }; /** * Returns true if the <code>state</code> in any Levenshtein DFA is an accept state (final state). */ boolean isAccept(int absState) { // decode absState -> state, offset int state = absState / (w + 1); int offset = absState % (w + 1); assert offset >= 0; return w - offset + minErrors[state] <= n; } /** * Returns the position in the input word for a given <code>state</code>. * This is the minimal boundary for the state. */ int getPosition(int absState) { return absState % (w + 1); } /** * Returns the state number for a transition from the given <code>state</code>, * assuming <code>position</code> and characteristic vector <code>vector</code> */ abstract int transition(int state, int position, int vector); private final static long[] MASKS = new long[] { 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f, 0xff, 0x1ff, 0x3ff, 0x7ff, 0xfff, 0x1fff, 0x3fff, 0x7fff, 0xffff, 0x1ffff, 0x3ffff, 0x7ffff, 0xfffff, 0x1fffff, 0x3fffff, 0x7fffff, 0xffffff, 0x1ffffff, 0x3ffffff, 0x7ffffff, 0xfffffff, 0x1fffffff, 0x3fffffff, 0x7fffffffL, 0xffffffffL, 0x1ffffffffL, 0x3ffffffffL, 0x7ffffffffL, 0xfffffffffL, 0x1fffffffffL, 0x3fffffffffL, 0x7fffffffffL, 0xffffffffffL, 0x1ffffffffffL, 0x3ffffffffffL, 0x7ffffffffffL, 0xfffffffffffL, 0x1fffffffffffL, 0x3fffffffffffL, 0x7fffffffffffL, 0xffffffffffffL, 0x1ffffffffffffL, 0x3ffffffffffffL, 0x7ffffffffffffL, 0xfffffffffffffL, 0x1fffffffffffffL, 0x3fffffffffffffL, 0x7fffffffffffffL, 0xffffffffffffffL, 0x1ffffffffffffffL, 0x3ffffffffffffffL, 0x7ffffffffffffffL, 0xfffffffffffffffL, 0x1fffffffffffffffL, 0x3fffffffffffffffL, 0x7fffffffffffffffL }; protected int unpack(long[] data, int index, int bitsPerValue) { final long bitLoc = bitsPerValue * index; final int dataLoc = (int) (bitLoc >> 6); final int bitStart = (int) (bitLoc & 63); //System.out.println("index=" + index + " dataLoc=" + dataLoc + " bitStart=" + bitStart + " bitsPerV=" + bitsPerValue); if (bitStart + bitsPerValue <= 64) { // not split return (int) ((data[dataLoc] >> bitStart) & MASKS[bitsPerValue - 1]); } else { // split final int part = 64 - bitStart; return (int) (((data[dataLoc] >> bitStart) & MASKS[part - 1]) + ((data[1 + dataLoc] & MASKS[bitsPerValue - part - 1]) << part)); } } } }