3 articles
Count primes below n sounds trivial — until your naive solution times out on n=5,000,000. Master the Sieve of Eratosthenes, one of the most elegant algorithms in all of computer science, and learn the exact intuition that separates candidates who pass Amazon and Google screens from those who do not.
LC 204 Count Primes is the gateway sieve problem at Google and Amazon. Master the Sieve of Eratosthenes, understand why you start marking at p*p, and apply the technique to interval queries, prime factorization, and every sieve variant an interviewer can ask.
Prime factorization is the workhorse of number-theoretic interview problems at Amazon and Microsoft. Master trial division in O(sqrt n), the smallest-prime-factor sieve for batched factorization in O(log n) per query, and the divisor-counting tricks they unlock.