Create bloom_filters.md

Author: Joseph Luce

system_design/bloom_filters.md

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+# Bloom Filters
+
+## Use Case
+Given a word, figure out if it already exists or not.
+
+On a system design level, a hash table can work. 
+However, if you have a lot of words, say a billion+ words, you start running into performance issues.
+You cannot store this in memory and so there will be some overhead with disk input output and storage.
+You could try to optimize as much as you can, like sharding the data into buckets with sub-hash tables but this doesn't 100% solve the latency issue.
+
+This is where bloom filters come in, is it a popular usage for databases.
+If you imagine an API like check(word) and it returns True or False.
+However, the API is probabilistic, if it gives you a False it is 100% accurate, if it returns True its 90% accurate, more or less, depends.
+The difference is that bloom filter uses a lot less memory than the hash table method.
+
+## How it works
+1. Starting with a bit array of a set size, say 00000000 of 8 bits.
+2. Given a word, "cat", we will run this past multiple hash functions, each hash function outputs an index.
+For example, two hash functions hash1('cat') and hash2('cat') gives us two indexes 2 and 5.
+We will then set the bits to 00100100 in respect to its indexes.
+3. Then given another word, "dog", we will run it past the hash functions as well, giving us indexes 7 and 2.
+Again, setting the bit array accordingly to 00100101.
+4. If we wanted to check if the word "bird" exists, we would run it past the hash functions, for example it would return indexes 5 and 1.
+Since index 1 isn't set, we know "bird" does not exist.
+5. Simiarly if we tried another word, like "lion" and the hash functions returned 2 and 7, the API would believe that the word "lion" exists but we never saved it.
+
+This is why bloom filters will always accurately return if something doesn't exist but fail to 100% predict if a word does exist.
+To increase the likelihood that it is correct, bloom filters will use many hash functions, this is to increase the chances to find more indexes containing zeros.
+
+Lastly, since the bloom filters use a bit array, we can store the bit array as a string, each character containing 8 or 16 or 32 bits dependings on your operating system.
+Which results in something like A90bhl158, this can represent all the set bits in a condensed manner.
+
+## Limitations
+Bloom filters require a rough estimate of how many unique elements would be stored as it would require the bit array to be determined beforehand.
+Once the bit array is set, it will be hard to change it.
+Simiarly, once we add an element into the bit, it will forever be added and can never be removed.
+However, there is something called an invertible bloom filter, which can be used to determined which bits to remove.
+I won't be discussing this topic here as it shouldn't be needed for interviews.