posts: trie: add fuzzy matching
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@ -114,3 +114,58 @@ def remove(self, key: str) -> bool:
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# Otherwise, recurse on the child corresponding to the first letter
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return self._children[key[0]].remove(key[1:])
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```
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### Fuzzy matching
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Fuzzily matching a given word is where the real difficulty is: the key is to
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realize we can use the prefix-tree nature of a _Trie_ to avoid doing wasteful
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work.
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By leveraging the prefix visit order of the tree, we can build an iterative
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Levenshtein distance matrix, in much the same way one would do so in its
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[Dynamic Programming] implementation (see the [Wagner-Fisher algorithm]).
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[Dynamic Programming]: https://en.wikipedia.org/wiki/Dynamic_programming
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[Wagner-Fisher algorithm]: https://en.wikipedia.org/wiki/Wagner%E2%80%93Fischer_algorithm
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```python
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class FuzzyResult[T](NamedTuple):
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distance: int
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key: str
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value: T
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def get_fuzzy(self, key: str, max_distance: int = 0) -> Iterator[FuzzyResult[T]]:
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def helper(
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current_word: str,
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node: Trie[T],
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previous_row: list[int],
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) -> Iterator[tuple[int, T]]:
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# Iterative Levenshtein
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current_row = [previous_row[0] + 1]
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current_char = current_word[-1]
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for column, key_char in enumerate(key, start=1):
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insertion = current_row[column - 1] + 1
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deletion = previous_row[column] + 1
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replacement = previous_row[column - 1] + (key_char != current_char)
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current_row.append(min(insertion, deletion, replacement))
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# If we are under the max distance, match this node
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if (distance := current_row[-1]) <= max_distance and node._value != None:
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# Only if it has a value of course
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yield FuzzyResult(distance, current_word, node._value)
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# If we can potentially still match children, recurse
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if min(current_row) <= max_distance:
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for c, child in node._children.items():
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yield from helper(current_word + c, child, current_row)
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# Build the first row -- the edit distance from the empty string
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row = list(range(len(key) + 1))
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# Base case for the empty string
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if (distance := row[-1]) <= max_distance and self._value != None:
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yield FuzzyResult(distance, "", self._value)
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for c, child in self._children.items():
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yield from helper(c, child, row)
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```
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