Problema
A prime is an integer greater than 1 divisible only by 1 and itself. Add every prime strictly smaller than limit. The limit itself is excluded even when it is prime.
Implement prime_sum(limit).
Input
limit: The exclusive upper bound.
Output
Return the sum of the eligible primes, or 0 when none exist.
Vincoli
0 ≤ limit ≤ 2,000,000. Return the sum using a signed 64-bit integer.
Esempi
Input:
limit = 12
Output atteso:
expected = 28Input:
long long limit = 12;
Output atteso:
long long expected = 28;Input:
long limit = 12;
Output atteso:
long expected = 28;Spiegazione
The primes below 12 are 2, 3, 5, 7, and 11; their sum is 28.
Input:
limit = 2
Output atteso:
expected = 0Input:
long long limit = 2;
Output atteso:
long long expected = 0;Input:
long limit = 2;
Output atteso:
long expected = 0;Spiegazione
There are no primes strictly below 2.
Come affrontarlo
Prova prima da solo, poi apri un suggerimento alla volta.
Suggerimento 1
The main cost is finding primes efficiently; naive divisibility checks for every number will be too slow.
Suggerimento 2
Use a sieve-like approach to mark composites, then add the numbers that remain unmarked and below the limit.
Suggerimento 3
Remember that the limit itself is excluded, even when it is prime, and small limits may contribute nothing.
Complessità attesa
O(limit log log limit) time, O(limit) extra space
Riferimenti
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