Maximum no. of contiguous Prime Numbers in an array

Given an array arr[] of N elements. The task is to find the maximum number of the contiguous prime numbers in the given array.

Examples:

Input: arr[] = {3, 5, 2, 66, 7, 11, 8}
Output: 3
Maximum contiguous prime number sequence is {2, 3, 5}

Input: arr[] = {1, 0, 2, 11, 32, 8, 9}
Output: 2
Maximum contiguous prime number sequence is {2, 11}

Approach:
->Create a sieve to check whether an element is prime or not in O(1).
->Traverse the array with two variables named current_max and max_so_far.
->If a prime number is found then increment current_max and compare it with max_so_far.
->If current_max is greater than max_so_far, then assign max_so_far with current_max
->Every time a non-prime element is found reset current_max to 0.



C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
void SieveOfEratosthenes(bool prime[], int p_size)
{
    // false here indicates
    // that it is not prime
    prime[0] = false;
    prime[1] = false;
  
    for (int p = 2; p * p <= p_size; p++) {
  
        // If prime[p] is not changed,
        // then it is a prime
        if (prime[p]) {
  
            // Update all multiples of p,
            // set them to non-prime
            for (int i = p * 2; i <= p_size; i += p)
                prime[i] = false;
        }
    }
}
  
// Function that finds
// maximum contiguous subarray of prime numbers
int maxPrimeSubarray(int arr[], int n)
{
    int max_ele = *max_element(arr, arr+n);
    bool prime[max_ele + 1];
    memset(prime, true, sizeof(prime));
  
    SieveOfEratosthenes(prime, max_ele);
  
    int current_max = 0, max_so_far = 0;
  
    for (int i = 0; i < n; i++) {
  
        // check if element is non-prime
        if (prime[arr[i]] == false)
            current_max = 0;
  
        // If element is prime, than update
        // current_max and max_so_far accordingly.
        else {
            current_max++;
            max_so_far = max(current_max, max_so_far);
        }
    }
  
    return max_so_far;
}
  
// Driver code
int main()
{
  
    int arr[] = { 1, 0, 2, 4, 3, 29, 11, 7, 8, 9 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << maxPrimeSubarray(arr, n);
  
    return 0;
}

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Java














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// Java implementation of the approach 


import java.util.*; 


  


class GFG  


{ 


  


static void SieveOfEratosthenes(boolean prime[], 


                                int p_size) 


{ 


    // false here indicates 


    // that it is not prime 


    prime[0] = false; 


    prime[1] = false; 


  


    for (int p = 2; p * p <= p_size; p++)  


    { 


  


        // If prime[p] is not changed, 


        // then it is a prime 


        if (prime[p])  


        { 


  


            // Update all multiples of p, 


            // set them to non-prime 


            for (int i = p * 2; i <= p_size; i += p) 


                prime[i] = false; 


        } 


    } 


} 


  


// Function that finds 


// maximum contiguous subarray of prime numbers 


static int maxPrimeSubarray(int arr[], int n) 


{ 


    int max_ele = Arrays.stream(arr).max().getAsInt(); 


    boolean prime[] = new boolean[max_ele + 1]; 


    Arrays.fill(prime, true); 


  


    SieveOfEratosthenes(prime, max_ele); 


  


    int current_max = 0, max_so_far = 0; 


  


    for (int i = 0; i < n; i++) 


    { 


        // check if element is non-prime 


        if (prime[arr[i]] == false) 


            current_max = 0; 


  


        // If element is prime, than update 


        // current_max and max_so_far accordingly. 


        else 


        { 


            current_max++; 


            max_so_far = Math.max(current_max, max_so_far); 


        } 


    } 


    return max_so_far; 


} 


  


// Driver code 


public static void main(String[] args)  


{ 


    int arr[] = { 1, 0, 2, 4, 3, 29, 11, 7, 8, 9 }; 


    int n = arr.length; 


    System.out.print(maxPrimeSubarray(arr, n)); 


} 


} 


  


/* This code contributed by PrinciRaj1992 */



















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Python 3














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# Python3 implementation of  


# the approach  


  


def SieveOfEratosthenes( prime, p_size): 


  


    # false here indicates  


    # that it is not prime  


    prime[0] = False


    prime[1] = False


    for p in range(2,p_size+1): 


        if(p*p>p_size): 


            break


  


        # If prime[p] is not changed,  


        # then it is a prime  


        if (prime[p]):  


  


            # Update all multiples of p,  


            # set them to non-prime 


            i=p*2


            while(i<=p_size): 


                prime[i] = False


                i = i + p  


          


# Function that finds  


# maximum contiguous subarray of prime numbers  


def maxPrimeSubarray( arr, n):  


  


    max_ele = max(arr)  


    prime=[True]*(max_ele + 1)  


  


    SieveOfEratosthenes(prime, max_ele)  


  


    current_max = 0


    max_so_far = 0


    for i in range(n): 


  


        # check if element is non-prime  


        if (prime[arr[i]] == False):  


            current_max = 0


  


        # If element is prime, than update  


        # current_max and max_so_far accordingly.  


        else:  


            current_max=current_max + 1


            max_so_far = max(current_max, max_so_far)  


          


    return max_so_far  


  


# Driver code  


if __name__=='__main__': 


    arr = [ 1, 0, 2, 4, 3, 29, 11, 7, 8, 9 ]  


    n = len(arr)  


    print(maxPrimeSubarray(arr, n)) 


  


# this code is contributed by  


# ash264 



















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C#














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// C# implementation of the approach 


using System;  


using System.Linq; 


  


class GFG  


{ 


  


static void SieveOfEratosthenes(bool []prime, 


                                int p_size) 


{ 


    // false here indicates 


    // that it is not prime 


    prime[0] = false; 


    prime[1] = false; 


  


    for (int p = 2; p * p <= p_size; p++)  


    { 


  


        // If prime[p] is not changed, 


        // then it is a prime 


        if (prime[p])  


        { 


  


            // Update all multiples of p, 


            // set them to non-prime 


            for (int i = p * 2; i <= p_size; i += p) 


                prime[i] = false; 


        } 


    } 


} 


  


// Function that finds maximum  


// contiguous subarray of prime numbers 


static int maxPrimeSubarray(int []arr, int n) 


{ 


    int max_ele = arr.Max(); 


    bool []prime = new bool[max_ele + 1]; 


    for(int i = 0; i < max_ele + 1; i++) 


        prime[i]=true; 


  


    SieveOfEratosthenes(prime, max_ele); 


  


    int current_max = 0, max_so_far = 0; 


  


    for (int i = 0; i < n; i++) 


    { 


        // check if element is non-prime 


        if (prime[arr[i]] == false) 


            current_max = 0; 


  


        // If element is prime, than update 


        // current_max and max_so_far accordingly. 


        else


        { 


            current_max++; 


            max_so_far = Math.Max(current_max, max_so_far); 


        } 


    } 


    return max_so_far; 


} 


  


// Driver code 


public static void Main(String[] args)  


{ 


    int []arr = { 1, 0, 2, 4, 3, 29, 11, 7, 8, 9 }; 


    int n = arr.Length; 


    Console.Write(maxPrimeSubarray(arr, n)); 


} 


} 


  


// This code contributed by Rajput-Ji 



















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Output:


4








    

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