From 20f26762d01ce11902a98bfba8d38c1f2293b6a2 Mon Sep 17 00:00:00 2001 From: Volodya <91135251+nartherion@users.noreply.github.com> Date: Sun, 15 Jun 2025 14:00:45 +0200 Subject: [PATCH] Bug in range sieve when left boundry is 0 In case when `L = 0` and `R > 0`, algorithm will say that 0 and 1 are primes. Index initialization improvement --- src/algebra/sieve-of-eratosthenes.md | 21 +++++++++++++-------- 1 file changed, 13 insertions(+), 8 deletions(-) diff --git a/src/algebra/sieve-of-eratosthenes.md b/src/algebra/sieve-of-eratosthenes.md index 560d176e7..acd78ae17 100644 --- a/src/algebra/sieve-of-eratosthenes.md +++ b/src/algebra/sieve-of-eratosthenes.md @@ -207,7 +207,7 @@ To solve such a problem, we can use the idea of the Segmented sieve. We pre-generate all prime numbers up to $\sqrt R$, and use those primes to mark all composite numbers in the segment $[L, R]$. ```cpp -vector segmentedSieve(long long L, long long R) { +vector segmented_sieve(long long L, long long R) { // generate all primes up to sqrt(R) long long lim = sqrt(R); vector mark(lim + 1, false); @@ -222,10 +222,12 @@ vector segmentedSieve(long long L, long long R) { vector isPrime(R - L + 1, true); for (long long i : primes) - for (long long j = max(i * i, (L + i - 1) / i * i); j <= R; j += i) + for (long long j = max(i, (L + i - 1) / i) * i; j <= R; j += i) isPrime[j - L] = false; - if (L == 1) - isPrime[0] = false; + if (L == 0) + isPrime[L] = false; + if (L <= 1) + isPrime[min(1 - L, R - L)] = false; return isPrime; } ``` @@ -234,14 +236,16 @@ Time complexity of this approach is $O((R - L + 1) \log \log (R) + \sqrt R \log It's also possible that we don't pre-generate all prime numbers: ```cpp -vector segmentedSieveNoPreGen(long long L, long long R) { +vector segmented_sieve_no_pre_gen(long long L, long long R) { vector isPrime(R - L + 1, true); long long lim = sqrt(R); for (long long i = 2; i <= lim; ++i) - for (long long j = max(i * i, (L + i - 1) / i * i); j <= R; j += i) + for (long long j = max(i, (L + i - 1) / i) * i; j <= R; j += i) isPrime[j - L] = false; - if (L == 1) - isPrime[0] = false; + if (L == 0) + isPrime[L] = false; + if (L <= 1) + isPrime[min(1 - L, R - L)] = false; return isPrime; } ``` @@ -258,6 +262,7 @@ However, this algorithm also has its own weaknesses. * [Leetcode - Four Divisors](https://leetcode.com/problems/four-divisors/) * [Leetcode - Count Primes](https://leetcode.com/problems/count-primes/) +* [Leetcode - Closest Prime Numbers in Range](https://leetcode.com/problems/closest-prime-numbers-in-range/) * [SPOJ - Printing Some Primes](http://www.spoj.com/problems/TDPRIMES/) * [SPOJ - A Conjecture of Paul Erdos](http://www.spoj.com/problems/HS08PAUL/) * [SPOJ - Primal Fear](http://www.spoj.com/problems/VECTAR8/) pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.

Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy