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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Java














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// Java program to find length of the longest 


// subarray with all primes except possibily 


// one. 


import java.util.*; 


  


class GFG 


{ 


      


static int N = 100000; 


  


static boolean prime[] = new boolean[N]; 


  


static 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. 


    Arrays.fill(prime,true); 


  


    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; 


        } 


    } 


} 


  


  


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


{ 


    int []left = new int[n];int[] right = new int[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 = Math.max(res, left[i] + right[i]); 


      


    return res; 


} 


  


// Driver code 


public static void main(String[] args)  


{ 


    int arr[] = { 2, 8, 5, 7, 9, 5, 7 }; 


  


    // used of SieveOfEratosthenes method to  


    // detect a number prime or not 


    SieveOfEratosthenes(); 


    int n = arr.length; 


  


    System.out.println("largest length of PrimeSubarray "


        + longestPrimeSubarray(arr, n)); 


} 


} 


  


// This code contributed by Rajput-Ji 



















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Python3














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# 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 



















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C#














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// C# program to find length of the longest 


// subarray with all primes except possibily 


// one. 


using System; 


  


class GFG 


{ 


      


    static int N = 100000; 


      


    static bool []prime = new bool[N]; 


      


    static 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. 


        for(int i =0;i<N;i++) 


            prime[i]=true; 


      


        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; 


            } 


        } 


    } 


      


      


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


    { 


        int []left = new int[n];int[] right = new int[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 = Math.Max(res, left[i] + right[i]); 


          


        return res; 


    } 


      


    // Driver code 


    public static void Main(String[] args)  


    { 


        int []arr = { 2, 8, 5, 7, 9, 5, 7 }; 


      


        // used of SieveOfEratosthenes method to  


        // detect a number prime or not 


        SieveOfEratosthenes(); 


        int n = arr.Length; 


      


        Console.WriteLine("largest length of PrimeSubarray "


            + longestPrimeSubarray(arr, n)); 


    } 


} 


  


// This code has been contributed by 29AjayKumar 



















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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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