Find prime number K in an array such that (A[i] % K) is maximum

Given an array arr[] of n integers. The task is to find an element from the array K such that

  1. K is prime.
  2. And, arr[i] % K is maximum for all valid i among all possible values of K

if there is no prime number in the array then print -1.

Examples:

Input: arr[] = {2, 10, 15, 7, 6, 8, 13}
Output: 13
2, 7 and 13 are the only prime numbers in the array.
The maximum possible value of arr[i] % 2 is 1 i.e. 15 % 2 = 1.
For 7, it is 6 % 7 = 6
For 13, 10 % 13 = 10 (Maximum possible)

Input: arr[] = {23, 13, 6, 2, 15, 18, 8}
Output: 23



Approach: In order to maximize the value of arr[i] % K, K must be the maximum prime number from the array and arr[i] must be the greatest element from the array which is less than K. So, the problem now gets reduced to finding the maximum prime number from the array. In order to do that,

  1. First find all the prime numbers less than or equal to the maximum element from the array using Sieve.
  2. Then, find the maximum prime number from the array and print it. If there is no prime present in the array then print -1.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the required
// prime number from the array
int getPrime(int arr[], int n)
{
    // Find maximum value in the array
    int max_val = *max_element(arr, arr + n);
  
    // USE SIEVE TO FIND ALL PRIME NUMBERS LESS
    // THAN OR EQUAL TO max_val
    // Create a boolean array "prime[0..n]". A
    // value in prime[i] will finally be false
    // if i is Not a prime, else true.
    vector<bool> prime(max_val + 1, true);
  
    // Remaining part of SIEVE
    prime[0] = false;
    prime[1] = false;
    for (int p = 2; p * p <= max_val; 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 <= max_val; i += p)
                prime[i] = false;
        }
    }
  
    // To store the maximum prime number
    int maximum = -1;
    for (int i = 0; i < n; i++) {
  
        // If current element is prime
        // then update the maximum prime
        if (prime[arr[i]])
            maximum = max(maximum, arr[i]);
    }
  
    // Return the maximum prime
    // number from the array
    return maximum;
}
  
// Driver code
int main()
{
    int arr[] = { 2, 10, 15, 7, 6, 8, 13 };
    int n = sizeof(arr) / sizeof(arr[0]);
  
    cout << getPrime(arr, n);
  
    return 0;
}

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Java














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// Java implementation of the approach 


import java.util.*; 


  


class GFG 


{ 


  


// Function to return the required 


// prime number from the array 


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


{ 


    // Find maximum value in the array 


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


  


    // USE SIEVE TO FIND ALL PRIME NUMBERS LESS 


    // THAN OR EQUAL TO max_val 


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


    // value in prime[i] will finally be false 


    // if i is Not a prime, else true. 


    Vector<Boolean> prime = new Vector<>(max_val + 1); 


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


        prime.add(i,Boolean.TRUE); 


  


    // Remaining part of SIEVE 


    prime.add(1,Boolean.FALSE); 


    prime.add(2,Boolean.FALSE); 


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


    { 


  


        // If prime[p] is not changed, then 


        // it is a prime 


        if (prime.get(p) == true)  


        { 


  


            // Update all multiples of p 


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


                prime.add(i,Boolean.FALSE); 


        } 


    } 


  


    // To store the maximum prime number 


    int maximum = -1; 


    for (int i = 0; i < n; i++)  


    { 


  


        // If current element is prime 


        // then update the maximum prime 


        if (prime.get(arr[i])) 


        { 


            maximum = Math.max(maximum, arr[i]); 


        } 


              


    } 


  


    // Return the maximum prime 


    // number from the array 


    return maximum; 


} 


  


// Driver code 


public static void main(String[] args)  


{ 


    int arr[] = { 2, 10, 15, 7, 6, 8, 13 }; 


    int n = arr.length; 


  


    System.out.println(getPrime(arr, n)); 


} 


} 


  


// This code has been contributed by 29AjayKumar 



















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Python3














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# Python 3 implementation of the approach 


from math import sqrt 


  


# Function to return the required 


# prime number from the array 


def getPrime(arr, n): 


      


    # Find maximum value in the array 


    max_val = arr[0] 


    for i in range(len(arr)): 


          


        # USE SIEVE TO FIND ALL PRIME NUMBERS LESS 


        # THAN OR EQUAL TO max_val 


        # Create a boolean array "prime[0..n]". A 


        # value in prime[i] will finally be false 


        # if i is Not a prime, else true. 


        if(arr[i] > max_val): 


            max_val = arr[i] 


  


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


   


    # Remaining part of SIEVE 


    prime[0] = False


    prime[1] = False


    for p in range(2, int(sqrt(max_val)) + 1, 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, max_val + 1, p): 


                prime[i] = False


  


    # To store the maximum prime number 


    maximum = -1


    for i in range(n): 


          


        # If current element is prime 


        # then update the maximum prime 


        if (prime[arr[i]]): 


            maximum = max(maximum, arr[i]) 


  


    # Return the maximum prime 


    # number from the array 


    return maximum 


  


# Driver code 


if __name__ == '__main__': 


    arr = [2, 10, 15, 7, 6, 8, 13] 


    n = len(arr) 


  


    print(getPrime(arr, n)) 


      


# This code is contributed by 


# Surendra_Gangwar 



















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C#





// C# implementation of the approach

using System;

using System.Linq;

using System.Collections.Generic; 


class GFG

{


// Function to return the required

// prime number from the array

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

{

	// Find maximum value in the array

	int max_val = arr.Max();


	// USE SIEVE TO FIND ALL PRIME NUMBERS LESS

	// THAN OR EQUAL TO max_val

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

	// value in prime[i] will finally be false

	// if i is Not a prime, else true.

	List prime = new List(max_val + 1);

	for(int i = 0; i < max_val + 1; i++)
		prime.Insert(i, true);

	// Remaining part of SIEVE
	prime.Insert(1, false);
	prime.Insert(2, false);
	for (int p = 2; p * p <= max_val; 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 <= max_val; i += p)
				prime.Insert(i, false);
		}
	}

	// To store the maximum prime number
	int maximum = -1;
	for (int i = 0; i < n; i++) 
	{

		// If current element is prime
		// then update the maximum prime
		if (prime[arr[i]])
		{
			maximum = Math.Max(maximum, arr[i]);
		}
			
	}

	// Return the maximum prime
	// number from the array
	return maximum;
}

// Driver code
public static void Main(String[] args) 
{
	int []arr = { 2, 10, 15, 7, 6, 8, 13 };
	int n = arr.Length;

	Console.WriteLine(getPrime(arr, n));
}
}

// This code contributed by Rajput-Ji



[tabby title = "PHP"]

                











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<?php 


// PHP implementation of the approach  


  


// Function to return the count of primes  


// in the given array  


function getPrime($arr, $n)  


{  


    // Find maximum value in the array  


    $max_val = max($arr);  


  


    // USE SIEVE TO FIND ALL PRIME NUMBERS LESS  


    // THAN OR EQUAL TO max_val  


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


    // value in prime[i] will finally be false  


    // if i is Not a prime, else true.  


    $prime = array_fill(0, $max_val + 1, true);  


  


    // Remaining part of SIEVE  


    $prime[0] = false;  


    $prime[1] = false;  


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


                $prime[$i] = false;  


        }  


    }  


  


    // To store the maximum prime number  


    $maximum = -1;  


      


    for ($i = 0; $i < $n; $i++)  


    {  


  


        // If current element is prime  


        // then update the maximum prime  


        if ($prime[$arr[$i]])  


            $maximum = max($maximum, $arr[$i]);  


    }  


  


    // Return the maximum prime  


    // number from the array  


    return $maximum;  


}  


  


// Driver code  


$arr = array( 2, 10, 15, 7, 6, 8, 13 );  


$n = count($arr) ;  


  


echo getPrime($arr, $n);  


  


// This code is contributed by AnkitRai01 


?> 



















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Output:


13






          
          
          
          

            

    

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