Problem
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.
Constraints
0 ≤ limit ≤ 2,000,000. Return the sum using a signed 64-bit integer.
Examples
Input:
limit = 12
Expected output:
expected = 28Input:
long long limit = 12;
Expected output:
long long expected = 28;Input:
long limit = 12;
Expected output:
long expected = 28;Explanation
The primes below 12 are 2, 3, 5, 7, and 11; their sum is 28.
Input:
limit = 2
Expected output:
expected = 0Input:
long long limit = 2;
Expected output:
long long expected = 0;Input:
long limit = 2;
Expected output:
long expected = 0;Explanation
There are no primes strictly below 2.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
The main cost is finding primes efficiently; naive divisibility checks for every number will be too slow.
Hint 2
Use a sieve-like approach to mark composites, then add the numbers that remain unmarked and below the limit.
Hint 3
Remember that the limit itself is excluded, even when it is prime, and small limits may contribute nothing.
Expected complexity
O(limit log log limit) time, O(limit) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.