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Count Primes in Ranges

Given a range [L, R], we need to find the count of total numbers of prime numbers in the range [L, R] where 0 <= L <= R < 10000. Consider that there are a large number of queries for different ranges.
Examples: 
 

Input : Query 1 : L = 1, R = 10
        Query 2 : L = 5, R = 10
Output : 4
         2
Explanation
Primes in the range L = 1 to R = 10 are 
{2, 3, 5, 7}. Therefore for query, answer 
is 4 {2, 3, 5, 7}.
For the second query, answer is 2 {5, 7}.

 

Recommended Practice

A simple solution is to do the following for every query [L, R]. Traverse from L to R, check if current number is prime. If yes, increment the count. Finally, return the count.
An efficient solution is to use Sieve of Eratosthenes to find all primes up to the given limit. Then we compute a prefix array to store counts till every value before limit. Once we have a prefix array, we can answer queries in O(1) time. We just need to return prefix[R] – prefix[L-1]. 
 

























Output:  

2
4

Time Complexity: O(n*log(log(n)))

Auxiliary Space: O(n)

Here, n is the size of the prime array, Which is MAX here

 


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