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The Flajolet-Martin algorithm is a probabilistic algorithm used in data science and big data processing to estimate the number of distinct or unique elements in a large data stream using very limited memory. In modern applications such as web analytics, network monitoring, transaction logs, and sensor data systems, data streams are often too large or fast to store and process entirely. Counting unique elements exactly would require storing all observed elements or maintaining large hash tables, which becomes infeasible for massive datasets. The Flajolet-Martin algorithm addresses this challenge by using randomness and hashing techniques to produce an approximate count while consuming only a small and fixed amount of memory. The algorithm is based on the idea that the probability of observing a hash value with many trailing zeros decreases exponentially. When elements in a data stream are hashed into binary numbers, the pattern of trailing zeros in these binary values can provide information about how many unique items have been observed. The key intuition is that if many distinct elements exist, there is a higher chance that at least one hashed value will end with a long sequence of zeros. Conversely, if the number _______ ________ ________ ______ __________ ____ _____ ___ _________ ______ ___.
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