問題
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.
制約
0 ≤ limit ≤ 2,000,000. Return the sum using a signed 64-bit integer.
例
入力：
limit = 12
期待される出力：
expected = 28入力：
long long limit = 12;
期待される出力：
long long expected = 28;入力：
long limit = 12;
期待される出力：
long expected = 28;解説
The primes below 12 are 2, 3, 5, 7, and 11; their sum is 28.
入力：
limit = 2
期待される出力：
expected = 0入力：
long long limit = 2;
期待される出力：
long long expected = 0;入力：
long limit = 2;
期待される出力：
long expected = 0;解説
There are no primes strictly below 2.
解き方のヒント
まずは自分で考えてから、ヒントを 1 つずつ開いてみましょう。
ヒント 1
The main cost is finding primes efficiently; naive divisibility checks for every number will be too slow.
ヒント 2
Use a sieve-like approach to mark composites, then add the numbers that remain unmarked and below the limit.
ヒント 3
Remember that the limit itself is excluded, even when it is prime, and small limits may contribute nothing.
目安の計算量
O(limit log log limit) time, O(limit) extra space
参考資料
この課題はCodeUtility用に調整されています。上記の説明と制約に従ってください。