Difference between the largest and the smallest primes in an array in Java

Problem Statement

With a given array of integers where all elements are less than 1000000. Find the difference between the largest and the smallest primes in an array.

Example

Array: [ 1, 2, 3, 4, 5 ]

Largest Prime Number = 5
Smallest Prime Number = 2

Difference = 5 - 3 = 2.

Solution

Use Sieve of Eratosthenes approach, which is an efficient way to find out all prime numbers smaller than a given number. Then we will figure out the largest and smallest prime number to get the required difference.

Example

public class JavaTester {

   static int MAX = 1000000;
   static boolean prime[] = new boolean[MAX + 1];

   public static void runSieveOfEratosthenes(){
      //reset prime flags to be true
      for(int i=0; i< MAX+1; i++) prime[i] = true;
      //set 1 as non-prime
      prime[1] = false;

      for (int p = 2; p * p <= MAX; p++) {
         // If prime[p] is not modified, then it is a prime
         if (prime[p]) {
            // Update all multiples of p
            for (int i = p * 2; i <= MAX; i += p) prime[i] = false;
         }
      }
   }

   public static int difference(int arr[]){
      int min = MAX + 2;
      int max = -1;
      for (int i = 0; i < arr.length; i++) {
         // check if the number is prime or not
         if (prime[arr[i]] == true) {
            // set the max and min values
            if (arr[i] > max) max = arr[i];
            if (arr[i] < min) min = arr[i];
         }
      }
      return max - min;
   }

   public static void main(String args[]){
      // run the sieve
      runSieveOfEratosthenes();
      int arr[] = { 1, 2, 3, 4, 5 };
      System.out.println(difference(arr));
   }
}

Output

3