Given an array of integers (less than 10^6), the task is to find the sum of all the prime numbers which appear after every (k-1) prime numbers
i.e. every K’th prime number in the array.
Input : Array : 2, 3, 5, 7, 11 ; n=5; k=2 Output : Sum = 10 Explanation: All the elements of the array are prime. So, the prime numbers after every K intervals are 3, 7 and their sum is 10. Input : Array : 41, 23, 12, 17, 18, 19 ; n=6; k=2 Output : Sum = 42
A simple approach
We have to traverse the array and find the prime numbers after every (k-1) prime numbers. In this way, we’ll have to check every element of the array whether it is prime or not which will take more time as the size of the array increases.
We will create a sieve which will store whether a number is prime or not. Then, it can be used to check a number against prime in O(1) time. In this way, we only have to keep track of every K’th prime number and maintain the running sum.
Below is the implementation of the above approach:
# Python3 implementation of the approach
# 0 and 1 are not prime numbers
prime = False
prime = False
p = 2
while p * p <= MAX: # If prime[p] is not changed, # then it is a prime if prime[p] == True: # Update all multiples of p for i in range(p * 2, MAX + 1, p): prime[i] = False p += 1 # Compute the answer def solve(arr, n, k): # count of primes c = 0 # sum of the primes Sum = 0 # Traverse the array for i in range(0, n): # if the number is a prime if prime[arr[i]]: # increase the count c += 1 # if it is the K'th prime if c % k == 0: Sum += arr[i] c = 0 print(Sum) # Driver code if __name__ == "__main__": MAX = 1000000 prime = [True] * (MAX + 1) # Create the sieve SieveOfEratosthenes() n, k = 5, 2 arr = [2, 3, 5, 7, 11] solve(arr, n, k) # This code is contributed by Rituraj Jain [tabby title="C#"]
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