Longest Prime Subarray after removing one element

Given an array A of integers. We can remove at most one index from the array. Our goal is to maximize the length of the subarray that contains all primes. Print the largest length subarray that you can achieve by removing exactly one element from the array .

Examples:

Input : arr[] = { 2, 8, 5, 7, 9, 5, 7 }
Output : 4
Explanation :If we remove the number 9 which is at index 5 then the remaining array contains a subarray whose length is 4 which is maximum.

Input : arr[] = { 2, 3, 5, 7 }
Output : 3
If we remove the number 3 which is at index 1 then the remaining array contains a subarray whose length is 3 which is maximum.


The idea is to count contiguous primes just before every index and just after every index. Now traverse the array again and find an index for which sum counts of primes after and before is maximum.

C++

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// CPP program to find length of the longest
// subarray with all primes except possibily
// one.
#include <bits/stdc++.h>
using namespace std;
#define N 100000
  
bool prime[N];
  
void SieveOfEratosthenes()
{
    // Create a boolean array "prime[0..n]" and 
    // initialize all entries it as true. A value
    // in prime[i] will finally be false if i is 
    // Not a prime, else true.
    memset(prime, true, sizeof(prime));
  
    for (int p = 2; p * p <= N; p++) {
  
        // If prime[p] is not changed, 
        // then it is a prime
        if (prime[p] == true) {
             
            // Update all multiples of p
            for (int i = p * 2; i <= N; i += p)
                prime[i] = false;
        }
    }
}
  
  
int longestPrimeSubarray(int arr[], int n)
{
    int left[n], right[n];
    int primecount = 0, res = 0;
  
    // left array used to count number of 
    // continuous prime numbers starting 
    // from left of current element
    for (int i = 0; i < n; i++) {
        left[i] = primecount;
        if (prime[arr[i]]) {
            primecount++;
        }
        else
            primecount = 0;
    }
  
    // right array used to count number of 
    // continuous prime numbers starting from 
    // right of current element
    primecount = 0;
    for (int i = n - 1; i >= 0; i--) {
        right[i] = primecount;
        if (prime[arr[i]]) {
            primecount++;
        }
        else
            primecount = 0;
    }
  
    for (int i = 0; i < n; i++) 
        res = max(res, left[i] + right[i]);
      
    return res;
}
  
// Driver code
int main()
{
    int arr[] = { 2, 8, 5, 7, 9, 5, 7 };
  
    // used of SieveOfEratosthenes method to 
    // detect a number prime or not
    SieveOfEratosthenes();
    int n = sizeof(arr) / sizeof(arr[0]);
  
    cout << "largest length of PrimeSubarray " 
         << longestPrimeSubarray(arr, n) << endl;
  
    return 0;
}

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Python3





# Python 3 program to find length of the

# longest subarray with all primes except

# possibily one.

from math import sqrt

N = 100000


prime = [True for i in range(N + 1)]


def SieveOfEratosthenes():


	# Create a boolean array “prime[0..n]”

	# and initialize all entries it as true.

	# A value in prime[i] will finally be

	# false if i is Not a prime, else true.

	k = int(sqrt(N)) + 1

	for p in range(2, k, 1):


		# 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, N + 1, p):

				prime[i] = False


def longestPrimeSubarray(arr, n):

	left = [0 for i in range(n)]

	right = [0 for i in range(n)]

	primecount = 0

	res = 0


	# left array used to count number of

	# continuous prime numbers starting

	# from left of current element

	for i in range(n):

		left[i] = primecount

		if (prime[arr[i]]):

			primecount += 1


		else:

			primecount = 0


	# right array used to count number of

	# continuous prime numbers starting

	# from right of current element

	primecount = 0

	i = n – 1

	while(i >= 0):

		right[i] = primecount

		if (prime[arr[i]]):

			primecount += 1


		else:

			primecount = 0


		i -= 1


	for i in range(n):

		res = max(res, left[i] + right[i])


	return res


# Driver code

if __name__ == ‘__main__’:

	arr = [2, 8, 5, 7, 9, 5, 7]


	# used of SieveOfEratosthenes method

	# to detect a number prime or not

	SieveOfEratosthenes()

	n = len(arr)

	print(“largest length of PrimeSubarray”,

	           longestPrimeSubarray(arr, n))


# This code is contributed by

# Surendra_Gangwar



PHP














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<?php 


// PHP program to find length of  


// the longest subarray with all at most 


// primes except possibily one. 


$N = 100000; 


$prime = array_fill(0, $N, true); 


  


function SieveOfEratosthenes() 


{ 


    // Create a boolean array "prime[0..n]"  


    // and initialize all entries it as  


    // true. A value in prime[i] will   


    // finally be false if i is Not a  


    // prime, else true. 


    global $prime, $N; 


  


    for ($p = 2; $p * $p <= $N; $p++)  


    { 


  


        // If prime[p] is not changed,  


        // then it is a prime 


        if ($prime[$p] == true)  


        { 


              


            // Update all multiples of p 


            for ($i = $p * 2; $i <= $N; $i += $p) 


                $prime[$i] = false; 


        } 


    } 


} 


  


function longestPrimeSubarray($arr, $n) 


{ 


    global $prime, $N; 


    $left = array($n); 


    $right = array($n); 


    $primecount = 0; 


    $res = 0; 


  


    // left array used to count number of  


    // continuous prime numbers starting  


    // from left of current element 


    for ($i = 0; $i < $n; $i++)  


    { 


        $left[$i] = $primecount; 


        if ($prime[$arr[$i]])  


        { 


            $primecount++; 


        } 


        else


            $primecount = 0; 


    } 


  


    // right array used to count number 


    // of continuous prime numbers starting 


    // from right of current element 


    $primecount = 0; 


    for ($i = $n - 1; $i >= 0; $i--)  


    { 


        $right[$i] = $primecount; 


        if ($prime[$arr[$i]]) 


        { 


            $primecount++; 


        } 


        else


            $primecount = 0; 


    } 


  


    for ($i = 0; $i < $n; $i++)  


        $res = max($res, $left[$i] +     


                         $right[$i]); 


      


    return $res; 


} 


  


// Driver Code 


$arr = array(2, 8, 5, 7, 9, 5, 7); 


  


// used of SieveOfEratosthenes method  


// to detect a number prime or not 


SieveOfEratosthenes(); 


$n = count($arr); 


  


echo "largest length of PrimeSubarray " .  


      longestPrimeSubarray($arr, $n); 


  


// This code is contributed by mits 


?> 



















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Output:


largest length of PrimeSubarray 4






          
          
          
          

            

    

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