Add Bloom Filter post

content/posts/2024-07-14-bloom-filter/index.md

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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
+```