HyperLogLog

HyperLogLog is a probabilistic algorithm that’s used for estimating the cardinality (or the number of distinct elements) of a set with very low memory usage. It was introduced by Philippe Flajolet and is particularly useful when dealing with large datasets or when memory efficiency is a concern. The HyperLogLog algorithm approximates the cardinality of a set by using a fixed amount of memory, regardless of the size of the set. It achieves this by exploiting the properties of hash functions and probabilistic counting.

The basic idea behind HyperLogLog is to hash each element of the set and determine the longest run of zeros in the binary representation of the hash values. The length of the longest run of zeros is used as an estimation of the cardinality. By averaging these estimations over multiple hash functions, a more accurate cardinality estimate can be obtained.

Let’s understand this by considering an example. The problem statement is, “We...