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- Sieve of Eratosthenes - Algorithms for Competitive Programming
Sieve of Eratosthenes is an algorithm for finding all the prime numbers in a segment $[1;n]$ using $O(n \log \log n)$ operations The algorithm is very simple: at the beginning we write down all numbers between 2 and $n$
- Eulers totient sieve of Eratosthenes - Teckbakers Blog
So, for those who don't know what "Sieve of Eratosthenes" is, it is just a faster way to calculate all the prime numbers between 1 to n (in general, n can be upto 1e5 1e6) With time complexity O(n * log(log(n))) and space complexity O(n) So, how do we do it?
- Time complexity of Sieve of Eratosthenes algorithm
A loose upper-bound is n(1+1 2+1 3+1 4+1 5+1 6+…1 n) (sum of reciprocals of all numbers up to n), which is O(n log n): see Harmonic number A more proper upper-bound is n(1 2 + 1 3 + 1 5 + 1 7 + …), that is sum of reciprocals of primes up to n, which is O(n log log n)
- Time Complexity of Sieve of Eratosthenes Algorithm
In this tutorial, we’ve discussed the Sieve of Eratosthenes algorithm in detail We presented the pseudocode of the algorithm and analyzed the time complexity
- The fastest way to count prime number that smaller or equal N
Use a sparse table plus a segmented sieve This can be quite fast, as the sparse table holds the counts at selected intervals, meaning you only need to sieve from the closest table point Mathematically no more interesting than the previous option, but in practice this helps
- Sum of divisors summatory function with Erathosthenes sieve
You create a table d where you store the sum of the divisors of k, for k = 1 to M, where M = $5 · 10^6$ That's the part that is time critical Then you create a table s where you store the sum of divisors for all 1 ≤ j ≤ k, for k = 1 to M
- Find primes using Sieve of Eratosthenes - OpenGenus IQ
Sieve of Eratosthenes is a simple and ancient algorithm (over 2200 years old) used to find the prime numbers up to any given limit It is one of the most efficient ways to find small prime numbers (<= $10^8$)
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