Problem
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.
Constraints
0 ≤ limit ≤ 100,000. The upper bound is inclusive. Output tests verify results, not the exact algorithm used.
Examples
Example 1
Input:
limit = 12
Expected output:
expected = [2, 3, 5, 7, 11]Input:
long long limit = 12;
Expected output:
std::vector<long long> expected = {2, 3, 5, 7, 11};Input:
long limit = 12;
Expected output:
long[] expected = new long[] {2, 3, 5, 7, 11};Explanation
Mark multiples of 2 and 3 as composite. The remaining values up to 12 are 2, 3, 5, 7, and 11.
Example 2
Input:
limit = 1
Expected output:
expected = []Input:
long long limit = 1;
Expected output:
std::vector<long long> expected = {};Input:
long limit = 1;
Expected output:
long[] expected = new long[] {};Explanation
Prime numbers begin at 2, beyond this limit.
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.