Difference Between Largest and 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

 Live Demo

Following is the program in Java to find the required output.

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