समस्या
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.
सीमाएँ
0 ≤ limit ≤ 2,000,000. Return the sum using a signed 64-bit integer.
उदाहरण
इनपुट:
limit = 12
अपेक्षित आउटपुट:
expected = 28इनपुट:
long long limit = 12;
अपेक्षित आउटपुट:
long long expected = 28;इनपुट:
long limit = 12;
अपेक्षित आउटपुट:
long expected = 28;व्याख्या
The primes below 12 are 2, 3, 5, 7, and 11; their sum is 28.
इनपुट:
limit = 2
अपेक्षित आउटपुट:
expected = 0इनपुट:
long long limit = 2;
अपेक्षित आउटपुट:
long long expected = 0;इनपुट:
long limit = 2;
अपेक्षित आउटपुट:
long expected = 0;व्याख्या
There are no primes strictly below 2.
कैसे हल करें
पहले खुद कोशिश करें, फिर एक-एक करके संकेत खोलें।
संकेत 1
The main cost is finding primes efficiently; naive divisibility checks for every number will be too slow.
संकेत 2
Use a sieve-like approach to mark composites, then add the numbers that remain unmarked and below the limit.
संकेत 3
Remember that the limit itself is excluded, even when it is prime, and small limits may contribute nothing.
अपेक्षित जटिलता
O(limit log log limit) time, O(limit) extra space
संदर्भ
यह चुनौती CodeUtility के लिए अनुकूलित की गई है। ऊपर दिए गए स्टेटमेंट और सीमाओं का पालन करें।