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----
-title: "Bloom Filter"
-date: 2024-07-14T17:46:40+01:00
-draft: false # I don't care for draft mode, git has branches for that
-description: "Probably cool"
-tags:
-  - algorithms
-  - data structures
-  - python
-categories:
-  - programming
-series:
-- Cool algorithms
-favorite: false
-disable_feed: false
----
-
-The [_Bloom Filter_][wiki] is a probabilistic data structure for set membership.
-
-The filter can be used as an inexpensive first step when querying the actual
-data is quite costly (e.g: as a first check for expensive cache lookups or large
-data seeks).
-
-[wiki]: https://en.wikipedia.org/wiki/Bloom_filter
-
-<!--more-->
-
-## What does it do?
-
-A _Bloom Filter_ can be understood as a hash-set which can either tell you:
-
-* An element is _not_ part of the set.
-* An element _may be_ part of the set.
-
-More specifically, one can tweak the parameters of the filter to make it so that
-the _false positive_ rate of membership is quite low.
-
-I won't be going into those calculations here, but they are quite trivial to
-compute, or one can just look up appropriate values for their use case.
-
-## Implementation
-
-I'll be using Python, which has the nifty ability of representing bitsets
-through its built-in big integers quite easily.
-
-We'll be assuming a `BIT_COUNT` of 64 here, but the implementation can easily be
-tweaked to use a different number, or even change it at construction time.
-
-### Representation
-
-A `BloomFilter` is just a set of bits and a list of hash functions.
-
-```python
-BIT_COUNT = 64
-
-class BloomFilter[T]:
-    _bits: int
-    _hash_functions: list[Callable[[T], int]]
-
-    def __init__(self, hash_functions: list[Callable[[T], int]]) -> None:
-        # Filter is initially empty
-        self._bits = 0
-        self._hash_functions = hash_functions
-```
-
-### Inserting a key
-
-To add an element to the filter, we take the output from each hash function and
-use that to set a bit in the filter. This combination of bit will identify the
-element, which we can use for lookup later.
-
-```python
-def insert(self, val: T) -> None:
-    # Iterate over each hash
-    for f in self._hash_functions:
-        n = f(val) % BIT_COUNT
-        # Set the corresponding bit
-        self._bit |= 1 << n
-```
-
-### Querying a key
-
-Because the _Bloom Filter_ does not actually store its elements, but some
-derived data from hashing them, it can only definitely say if an element _does
-not_ belong to it. Otherwise, it _may_ be part of the set, and should be checked
-against the actual underlying store.
-
-```python
-def may_contain(self, val: T) -> bool:
-    for f in self._hash_functions:
-        n = f(val) % BIT_COUNT
-        # If one of the bits is unset, the value is definitely not present
-        if not (self._bit & (1 << n)):
-            return False
-    # All bits were matched, `val` is likely to be part of the set
-    return True
-```