Implementing a simple Trie for efficient Levenshtein Distance calculation
UPDATE 3
Done. Below is the code that finally passed all of my tests. Again, this is modeled after Murilo Vasconcelo's modified version of Steve Hanov's algorithm. Thanks to all that helped!
/**
* Computes the minimum Levenshtein Distance between the given word (represented as an array of Characters) and the
* words stored in theTrie. This algorithm is modeled after Steve Hanov's blog article "Fast and Easy Levenshtein
* distance using a Trie" and Murilo Vasconcelo's revised version in C++.
*
* http://stevehanov.ca/blog/index.php?id=114
* http://murilo.wordpress.com/2011/02/01/fast-and-easy-levenshtein-distance-using-a-trie-in-c/
*
* @param ArrayList<Character> word - the characters of an input word as an array representation
* @return int - the minimum Levenshtein Distance
*/
private int computeMinimumLevenshteinDistance(ArrayList<Character> word) {
theTrie.minLevDist = Integer.MAX_VALUE;
int iWordLength = word.size();
int[] currentRow = new int[iWordLength + 1];
for (int i = 0; i <= iWordLength; i++) {
currentRow[i] = i;
}
for (int i = 0; i < iWordLength; i++) {
traverseTrie(theTrie.root, word.get(i), word, currentRow);
}
return theTrie.minLevDist;
}
/**
* Recursive helper function. Traverses theTrie in search of the minimum Levenshtein Distance.
*
* @param TrieNode node - the current TrieNode
* @param char letter - the current character of the current word we're working with
* @param ArrayList<Character> word - an array representation of the current word
* @param int[] previousRow - a row in the Levenshtein Distance matrix
*/
private void traverseTrie(TrieNode node, char letter, ArrayList<Character> word, int[] previousRow) {
int size = previousRow.length;
int[] currentRow = new int[size];
currentRow[0] = previousRow[0] + 1;
int minimumElement = currentRow[0];
int insertCost, deleteCost, replaceCost;
for (int i = 1; i < size; i++) {
insertCost = currentRow[i - 1] + 1;
deleteCost = previousRow[i] + 1;
if (word.get(i - 1) == letter) {
replaceCost = previousRow[i - 1];
} else {
replaceCost = previousRow[i - 1] + 1;
}
currentRow[i] = minimum(insertCost, deleteCost, replaceCost);
if (currentRow[i] < minimumElement) {
minimumElement = currentRow[i];
}
}
if (currentRow[size - 1] < theTrie.minLevDist && node.isWord) {
theTrie.minLevDist = currentRow[size - 1];
}
if (minimumElement < theTrie.minLevDist) {
for (Character c : node.children.keySet()) {
traverseTrie(node.children.get(c), c, word, currentRow);
}
}
}
UPDATE 2
Finally, I've managed to get this to work for most of my test cases. My implementation is practically a direct translation from Murilo's C++ version of Steve Hanov's algorithm. So how should I refactor this algorithm and/or make optimizations? Below is the code...
public int search(String word) {
theTrie.minLevDist = Integer.MAX_VALUE;
int size = word.length();
int[] currentRow = new int[size + 1];
for (int i = 0; i <= size; i++) {
currentRow[i] = i;
}
for (int i = 0; i < size; i++) {
char c = word.charAt(i);
if (theTrie.root.children.containsKey(c)) {
searchRec(theTrie.root.children.get(c), c, word, currentRow);
}
}
return theTrie.minLevDist;
}
private void searchRec(TrieNode node, char letter, String word, int[] previousRow) {
int size = previousRow.length;
int[] currentRow = new int[size];
currentRow[0] = previousRow[0] + 1;
int insertCost, deleteCost, replaceCost;
for (int i = 1; i < size; i++) {
insertCost = currentRow[i - 1] + 1;
deleteCost = previousRow[i] + 1;
if (word.charAt(i - 1) == letter) {
replaceCost = previousRow[i - 1];
} else {
replaceCost = previousRow[i - 1] + 1;
}
currentRow[i] = minimum(insertCost, deleteCost, replaceCost);
}
if (currentRow[size - 1] < theTrie.minLevDist && node.isWord) {
theTrie.minLevDist = currentRow[size - 1];
}
if (minElement(currentRow) < theTrie.minLevDist) {
for (Character c : node.children.keySet()) {
searchRec(node.children.get(c), c, word, currentRow);
}
}
}
Thank you everyone who contributed to this question. I tried getting the Levenshtein Automata to work, but I couldn't make it happen.
So I'm looking for suggestions on refactoring and/or optimizations regarding the above code. Please let me know if there's any confusion. As always, I can provide the rest of the source code as needed.
UPDATE 1
So I've implemented a simple Trie data structure and I've been trying to follow Steve Hanov's python tutorial to compute the Levenshtein Distance. Actually, I'm interested in computing the minimum Levenshtein Distance between a given word and the words in the Trie, thus I've been following Murilo Vasconcelos's version of Steve Hanov's algorithm. It's not working very well, but here's my Trie class:
public class Trie {
public TrieNode root;
public int minLevDist;
public Trie() {
this.root = new TrieNode(' ');
}
public void insert(String word) {
int length = word.length();
TrieNode current = this.root;
if (length == 0) {
current.isWord = true;
}
for (int index = 0; index < length; index++) {
char letter = word.charAt(index);
TrieNode child = current.getChild(letter);
if (child != null) {
current = child;
} else {
current.children.put(letter, new TrieNode(letter));
current = current.getChild(letter);
}
if (index == length - 1) {
current.isWord = true;
}
}
}
}
... and the TrieNode class:
public class TrieNode {
public final int ALPHABET = 26;
public char letter;
public boolean isWord;
public Map<Character, TrieNode> children;
public TrieNode(char letter) {
this.isWord = false;
this.letter = letter;
children = new HashMap<Character, TrieNode>(ALPHABET);
}
public TrieNode getChild(char letter) {
if (children != null) {
if (children.containsKey(letter)) {
return children.get(letter);
}
}
return null;
}
}
Now, I've tried to implement the search as Murilo Vasconcelos has it, but something is off and I need some help debugging this. Please give suggestions on how to refactor this and/or point out where the bugs are. The very first thing I'd like to refactor is the "minCost" global variable, but that's the smallest of things. Anyway, here's the code...
public void search(String word) {
int size = word.length();
int[] currentRow = new int[size + 1];
for (int i = 0; i <= size; i++) {
currentRow[i] = i;
}
for (int i = 0; i < size; i++) {
char c = word.charAt(i);
if (theTrie.root.children.containsKey(c)) {
searchRec(theTrie.root.children.get(c), c, word, currentRow);
}
}
}
private void searchRec(TrieNode node, char letter, String word, int[] previousRow) {
int size = previousRow.length;
int[] currentRow = new int[size];
currentRow[0] = previousRow[0] + 1;
int replace, insertCost, deleteCost;
for (int i = 1; i < size; i++) {
char c = word.charAt(i - 1);
insertCost = currentRow[i - 1] + 1;
deleteCost = previousRow[i] + 1;
replace = (c == letter) ? previousRow[i - 1] : (previousRow[i - 1] + 1);
currentRow[i] = minimum(insertCost, deleteCost, replace);
}
if (currentRow[size - 1] < minCost && !node.isWord) {
minCost = currentRow[size - 1];
}
Integer minElement = minElement(currentRow);
if (minElement < minCost) {
for (Map.Entry<Character, TrieNode> entry : node.children.entrySet()) {
searchRec(node, entry.getKey(), word, currentRow);
}
}
}
I apologize for the lack of comments. So what am I doing wrong?
INITIAL POST
I've been reading an article, Fast and Easy Levenshtein distance using a Trie, in hopes of figuring out an efficient way to compute the Levenshtein Distance between two Strings. My main goal with this is, given a large set of words, to be able to find the minimal Levenshtein Distance between an input word(s) and this set of words.
In my trivial implementation, I compute the Levenshtein Distance between an input word and the set of words, for each input word, and return the minimum. It works, but it is not efficient...
I've been looking for implementations of a Trie, in Java, and I've come across two seemingly good sources:
However, these implementations seem too complicated for what I'm trying to do. As I've been reading through them to understand how they work and how Trie data structures work in general, I've only become more confused.
So how would I implement a simple Trie data structure in Java? My intuition tells me that each TrieNode should store the String it represents and also references to letters of the alphabet, not necessarily all letters. Is my intuition correct?
Once that is implemented, the next task is to compute the Levenshtein Distance. I read through the Python code example in the article above, but I don't speak Python, and my Java implementation runs out of Heap memory once I hit the recursive searching. So how would I compute the Levenshtein Distance using the Trie data structure? I have a trivial implementation, modeled after this source code, but it doesn't use a Trie... it is inefficient.
It would be really nice to see some code in addition to your comments and suggestions. After all, this is a learning process for me... I've never implemented a Trie... so I have plenty to learn from this experience.
Thanks.
ps I can provide any source code if need be. Also, I've already read through and tried using a BK-Tree as suggested in Nick Johnson's blog, but its not as efficient as I think it can be... or maybe my implementation is wrong.
I've implemented the algo described on "Fast and Easy Levenshtein distance using a Trie" article in C++ and it is really fast. If you want (understand C++ better than Python), I can past the code in somewhere.
Edit: I posted it on my blog.
From what I can tell you don't need to improve the efficiency of Levenshtein Distance, you need to store your strings in a structure that stops you needing to run distance computations so many times ie by pruning the search space.
Since Levenshtein distance is a metric, you can use any of the metric spaces indices which take advantage of triangle inequality - you mentioned BK-Trees, but there are others eg. Vantage Point Trees, Fixed-Queries Trees, Bisector Trees, Spatial Approximation Trees. Here are their descriptions:
Burkhard-Keller Tree
Nodes are inserted into the tree as follows: For the root node pick an arbitary element from the space; add unique edge-labeled children such that the value of each edge is the distance from the pivot to that element; apply recursively, selecting the child as the pivot when an edge already exists.
Fixed-Queries Tree
As with BKTs except: Elements are stored at leaves; Each leaf has multiple elements; For each level of the tree the same pivot is used.
Bisector Tree
Each node contains two pivot elements with their covering radius (maximum distance between the centre element and any of its subtree elements); Filter into two sets those elements which are closest to the first pivot and those closest to the second, and recursively build two subtrees from these sets.
Spatial Approximation Tree
Initially all elements are in a bag; Choose an arbitrary element to be the pivot; Build a collection of nearest neighbours within range of the pivot; Put each remaining element into the bag of the nearest element to it from collection just built; Recursively form a subtree from each element of this collection.
Vantage Point Tree
Choose a pivot from the set abitrarily; Calculate the median distance between this pivot and each element of the remaining set; Filter elements from the set into left and right recursive subtrees such that those with distances less than or equal to the median form the left and those greater form the right.
Here is an example of Levenshtein Automata in Java.These will probably also be helpful:
http://svn.apache.org/repos/asf/lucene/dev/trunk/lucene/src/java/org/apache/lucene/util/automaton/ http://svn.apache.org/repos/asf/lucene/dev/trunk/lucene/src/test/org/apache/lucene/util/automaton/
It looks like the experimental Lucene code is based off of the dk.brics.automaton package.
Usage appears to be something similar to below:
LevenshteinAutomata builder = new LevenshteinAutomata(s);
Automaton automata = builder.toAutomaton(n);
boolean result1 = BasicOperations.run(automata, "foo");
boolean result2 = BasicOperations.run(automata, "bar");
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