dict-trie: Basic implementation of a trie.

## Project description

# Trie implementation using nested dictionaries
This library provides a [trie](https://en.wikipedia.org/wiki/Trie)
implementation using nested dictionaries. Apart from the basic operations, a
number of functions for *approximate matching* are implemented.

## Installation Via [pypi](https://pypi.python.org/pypi/dict-trie):

pip install dict-trie

From source:

git clone https://github.com/jfjlaros/dict-trie.git cd dict-trie pip install .

## Usage The library provides the Trie class.

### Basic operations
Initialisation of the trie is done via the constructor by providing a list of
words.
``python
>>> from dict_trie import Trie
>>>
>>> trie = Trie(['abc', 'te', 'test'])
``

Alternatively, an empty trie can be made to which words can be added with the
add function.
``python
>>> trie = Trie()
>>> trie.add('abc')
>>> trie.add('te')
>>> trie.add('test')
``

Membership can be tested with the in statement.
``python
>>> 'abc' in trie
True
``

Test whether a prefix is present by using the has_prefix function.
``python
>>> trie.has_prefix('ab')
True
``

Remove a word from the trie with the remove function. This function returns
False if the word was not in the trie.
``python
>>> trie.remove('abc')
True
>>> 'abc' in trie
False
>>> trie.remove('abc')
False
``

Iterate over all words in a trie.
``python
>>> list(trie)
['abc', 'te', 'test']
``

### Approximate matching A trie can be used to efficiently find a word that is similar to a query word. This is implemented via a number of functions that search for a word, allowing a given number of mismatches. These functions are divided in two families, one using the Hamming distance which only allows substitutions, the other using the Levenshtein distance which allows substitutions, insertions and deletions.

To find a word that has at most Hamming distance 2 to the word ‘abe’, the
hamming function is used.
``python
>>> trie = Trie(['abc', 'aaa', 'ccc'])
>>> trie.hamming('abe', 2)
'aaa'
``

To get all words that have at most Hamming distance 2 to the word ‘abe’, the
all_hamming function is used. This function returns a generator.
``python
>>> list(trie.all_hamming('abe', 2))
['aaa', 'abc']
``

In order to find a word that is closest to the query word, the best_hamming
function is used. In this case a word with distance 1 is returned.
``python
>>> trie.best_hamming('abe', 2)
'abc'
``

The functions levenshtein, all_levenshtein and best_levenshtein are used in a similar way.

### Other functionalities
A trie can be populated with all words of a fixed length over an alphabet by
using the fill function.
``python
>>> trie = Trie()
>>> trie.fill(('a', 'b'), 2)
>>> list(trie)
['aa', 'ab', 'ba', 'bb']
``

The trie data structure can be accessed via the root member variable.
``python
>>> trie.root
{'a': {'a': {'': 1}, 'b': {'': 1}}, 'b': {'a': {'': 1}, 'b': {'': 1}}}
>>> trie.root.keys()
['a', 'b']
``

The distance functions all_hamming and all_levenshtein also have counterparts that give the developer more information by returning a list of tuples containing not only the matched word, but also its distance to the query string and a [CIGAR](https://samtools.github.io/hts-specs/SAMv1.pdf)-like string.

The following encoding is used in the CIGAR-like string:

- character | meaning

- –: | :–
- = | match X | mismatch I | insertion D | deletion

In the following example, we search for all words with Hamming distance 1 to
the word ‘acc’. In the results we see a match with the word ‘abc’ having
distance 1 and a mismatch at position 2.
``python
>>> trie = Trie(['abc'])
>>> list(trie.all_hamming_('acc', 1))
[('abc', 1, '=X=')]
``

Similarly, we can search for all words having Levenshtein distance 2 to the
word ‘acb’. The word ‘abc’ matches three times, once by deleting the ‘b’ on
position 2 and inserting a ‘b’ after position 3, once by inserting a ‘c’ after
position 1 and deleting the last character and once by introducing two
mismatches.
``python
>>> list(trie.all_levenshtein_('acb', 2))
[('abc', 2, '=D=I'), ('abc', 2, '=XX'), ('abc', 2, '=I=D')]
``

## Project details

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