Problema
Return all prime numbers from 2 through limit. A prime is an integer greater than 1 divisible only by 1 and itself. Use the sieve idea: keep the next unmarked number and mark its larger multiples as composite. List results in ascending order.
Implement sieve_primes(limit).
Input
limit: The largest number that may be included.
Output
Return the primes in ascending order, or an empty list if none exist.
Restrições
0 ≤ limit ≤ 100,000. The upper bound is inclusive. Output tests verify results, not the exact algorithm used.
Exemplos
Entrada:
limit = 12
Saída esperada:
expected = [2, 3, 5, 7, 11]Entrada:
long long limit = 12;
Saída esperada:
std::vector<long long> expected = {2, 3, 5, 7, 11};Entrada:
long limit = 12;
Saída esperada:
long[] expected = new long[] {2, 3, 5, 7, 11};Explicação
Mark multiples of 2 and 3 as composite. The remaining values up to 12 are 2, 3, 5, 7, and 11.
Entrada:
limit = 1
Saída esperada:
expected = []Entrada:
long long limit = 1;
Saída esperada:
std::vector<long long> expected = {};Entrada:
long limit = 1;
Saída esperada:
long[] expected = new long[] {};Explicação
Prime numbers begin at 2, beyond this limit.
Como abordar
Tente sozinho primeiro e depois abra uma dica de cada vez.
Dica 1
Mark composites starting from each unmarked prime candidate and continue through the limit.
Dica 2
Only numbers that stay unmarked at the end are prime.
Dica 3
Stop marking multiples once the candidate’s square exceeds the limit.
Complexidade esperada
O(n log log n) time, O(n) extra space
Referências
Este desafio foi adaptado para o CodeUtility. Siga o enunciado e as restrições acima.