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A lexicon is a data-structure which stores a set of words. The difference between a dictionary and a lexicon is that in a lexicon there are no values associated with the words.
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A lexicon is similar to a list or a set of words, but the internal representation is different and optimized for faster searches of words, prefixes and wildcard patterns.
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Given a word, precisely, the search time is O(W) where W is the length of the word.
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2 important lexicon data-structures are Trie and Directed Acyclic Word Graph (DAWG).
lexpy can be installed via Python Package Index (PyPI) using pip. The only installation requirement is that you need Python 3.7 or higher.
pip install lexpy | Interface Description | Trie | DAWG |
|---|---|---|
| Add a single word | add('apple', count=2) | add('apple', count=2) |
| Add multiple words | add_all(['advantage', 'courage']) | add_all(['advantage', 'courage']) |
| Check if exists? | in operator | in operator |
| Search using wildcard expression | search('a?b*', with_count=True) | search('a?b*, with_count=True) |
| Search for prefix matches | search_with_prefix('bar', with_count=True) | search_with_prefix('bar') |
| Search for similar words within given edit distance. Here, the notion of edit distance is same as Levenshtein distance | search_within_distance('apble', dist=1, with_count=True) | search_within_distance('apble', dist=1, with_count=True) |
| Get the number of nodes in the automaton | len(trie) | len(dawg) |
from lexpy import Trie trie = Trie() input_words = ['ampyx', 'abuzz', 'athie', 'athie', 'athie', 'amato', 'amato', 'aneto', 'aneto', 'aruba', 'arrow', 'agony', 'altai', 'alisa', 'acorn', 'abhor', 'aurum', 'albay', 'arbil', 'albin', 'almug', 'artha', 'algin', 'auric', 'sore', 'quilt', 'psychotic', 'eyes', 'cap', 'suit', 'tank', 'common', 'lonely', 'likeable' 'language', 'shock', 'look', 'pet', 'dime', 'small' 'dusty', 'accept', 'nasty', 'thrill', 'foot', 'steel', 'steel', 'steel', 'steel', 'abuzz'] trie.add_all(input_words) # You can pass any sequence types or a file-like object here print(trie.get_word_count()) >>> 48In the file, words should be newline separated.
from lexpy import Trie # Either trie = Trie() trie.add_all('/path/to/file.txt') # Or with open('/path/to/file.txt', 'r') as infile: trie.add_all(infile)print('ampyx' in trie) >>> Trueprint(trie.search_with_prefix('ab')) >>> ['abhor', 'abuzz']print(trie.search_with_prefix('ab', with_count=True)) >>> [('abuzz', 2), ('abhor', 1)]-
?= 0 or 1 occurrence of any character -
*= 0 or more occurrence of any character
print(trie.search('a*o*')) >>> ['amato', 'abhor', 'aneto', 'arrow', 'agony', 'acorn'] print(trie.search('a*o*', with_count=True)) >>> [('amato', 2), ('abhor', 1), ('aneto', 2), ('arrow', 1), ('agony', 1), ('acorn', 1)] print(trie.search('su?t')) >>> ['suit'] print(trie.search('su?t', with_count=True)) >>> [('suit', 1)]print(trie.search_within_distance('arie', dist=2)) >>> ['athie', 'arbil', 'auric'] print(trie.search_within_distance('arie', dist=2, with_count=True)) >>> [('athie', 3), ('arbil', 1), ('auric', 1)]- You can either add a new word or increment the counter for an existing word.
trie.add('athie', count=1000) print(trie.search_within_distance('arie', dist=2, with_count=True)) >>> [('athie', 1003), ('arbil', 1), ('auric', 1)]-
DAWG supports the same set of operations as a Trie. The difference is the number of nodes in a DAWG is always less than or equal to the number of nodes in Trie.
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They both are Deterministic Finite State Automata. However, DAWG is a minimized version of the Trie DFA.
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In a Trie, prefix redundancy is removed. In a DAWG, both prefix and suffix redundancies are removed.
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In the current implementation of DAWG, the insertion order of the words should be alphabetical.
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The implementation idea of DAWG is borrowed from http://stevehanov.ca/blog/?id=115
from lexpy import Trie, DAWG trie = Trie() trie.add_all(['advantageous', 'courageous']) dawg = DAWG() dawg.add_all(['advantageous', 'courageous']) len(trie) # Number of Nodes in Trie 23 dawg.reduce() # Perform DFA minimization. Call this every time a chunk of words are uploaded in DAWG. len(dawg) # Number of nodes in DAWG 21The APIs are exactly same as the Trie APIs
from lexpy import DAWG dawg = DAWG() input_words = ['ampyx', 'abuzz', 'athie', 'athie', 'athie', 'amato', 'amato', 'aneto', 'aneto', 'aruba', 'arrow', 'agony', 'altai', 'alisa', 'acorn', 'abhor', 'aurum', 'albay', 'arbil', 'albin', 'almug', 'artha', 'algin', 'auric', 'sore', 'quilt', 'psychotic', 'eyes', 'cap', 'suit', 'tank', 'common', 'lonely', 'likeable' 'language', 'shock', 'look', 'pet', 'dime', 'small' 'dusty', 'accept', 'nasty', 'thrill', 'foot', 'steel', 'steel', 'steel', 'steel', 'abuzz'] dawg.add_all(input_words) dawg.reduce() dawg.get_word_count() >>> 48print('ampyx' in dawg) >>> Trueprint(dawg.search_with_prefix('ab')) >>> ['abhor', 'abuzz']print(dawg.search_with_prefix('ab', with_count=True)) >>> [('abuzz', 2), ('abhor', 1)]? = 0 or 1 occurance of any character
* = 0 or more occurance of any character
print(dawg.search('a*o*')) >>> ['amato', 'abhor', 'aneto', 'arrow', 'agony', 'acorn'] print(dawg.search('a*o*', with_count=True)) >>> [('amato', 2), ('abhor', 1), ('aneto', 2), ('arrow', 1), ('agony', 1), ('acorn', 1)] print(dawg.search('su?t')) >>> ['suit'] print(dawg.search('su?t', with_count=True)) >>> [('suit', 1)]print(dawg.search_within_distance('arie', dist=2)) >>> ['athie', 'arbil', 'auric'] print(dawg.search_within_distance('arie', dist=2, with_count=True)) >>> [('athie', 3), ('arbil', 1), ('auric', 1)]If you insert a word which is lexicographically out-of-order, ValueError will be raised.
dawg.add('athie', count=1000)ValueError
ValueError: Words should be inserted in Alphabetical order. <Previous word - thrill>, <Current word - athie> - You can either add an alphabetically greater word with a specific count or increment the count of the previous added word.
dawg.add_all(['thrill']*20000) # or dawg.add('thrill', count=20000) print(dawg.search('thrill', with_count=True)) >> [('thrill', 20001)]Special characters, except ? and *, are matched literally.
from lexpy import Trie t = Trie() t.add('a©')t.search('a©') >> ['a©']t.search('a?') >> ['a©']t.search('?©') >> ['a©']
These are some ideas which I would love to work on next in that order. Pull requests or discussions are invited.
- Merge trie and DAWG features in one data structure
- Support all functionalities and still be as compressed as possible.
- Serialization / Deserialization
- Pickle is definitely an option.
- Server (TCP or HTTP) to serve queries over the network.
- The 45-letter word pneumonoultramicroscopicsilicovolcanoconiosis is the longest English word that appears in a major dictionary. So for all english words, the search time is bounded by O(45).
- The longest technical word(not in dictionary) is the name of a protein called as titin. It has 189,819 letters and it is disputed whether it is a word.