# Java Data Types Structures and Operations

## Let see what we can do with the datatypes we have

### List

Let's start with a simple program:
```Java
public class Sets {
  public static void main(String[] args) {
    Set<Integer> a = new HashSet<Integer>();
    Set<Integer> b = new HashSet<Integer>();

    a.addAll(Arrays.asList(2,4,6,8,10));
    b.addAll(Arrays.asList(1,2,3,4,5));

    System.out.println("A: "+a);
    System.out.println("B: "+b);
  }
}
```
---
What is a union?

Can we find the union between two Lists?

```Java
Set<Integer> union = new HashSet<Integer>();
union.addAll(a);
union.addAll(b);
System.out.println("Union: "+union);
```

The set will have the combined value of the lists.

---

What is an intersection?

What is the intersection of two lists?
---

```Java
Set<Integer> intersection = new HashSet<Integer>();
intersection.addAll(a);
intersection.retainAll(b);
System.out.println("Intersection: "+intersection);
```
---
What is a difference?

What is the difference between the two lists?
---

```Java
Set<Integer> difference = new HashSet<Integer>();
difference.addAll(a);
difference.removeAll(b);
System.out.println("Difference: " + difference);
```

---
What is the complement?

What is the complement between the two lists?
---

```Java
Set<Integer> complement = new HashSet<Integer>();
complement.addAll(B);
complement.removeAll(A);
System.out.println("Complement: " + complement);
```
---
Sieve Of Eratosthenes

What is it?
It is a fast way of finding primes. In the original Greek, `κόσκινον Ἐρατοσθένους` it was found by Eratosthenes of Cyrene.

---
```Java
public class SieveOfEratosthenes {

   public static List<Integer> calculate(int n) {

      boolean[] prime = new boolean[n + 1];

      List<Integer> list = new ArrayList<Integer>();
      for (int i = 2; i < n; i++) {
         prime[i] = true;
      }
      for (int i = 2; i < n; i++) {
         if (prime[i]) {
            list.add(i);
            for (int j = i; j * i <= n; j++) {
              prime[i * j] = false;
            }
         }
      }
      return list;
   }

   public static void main(String[] args) {
      List<Integer> list = calculate(100);
      for (Integer prime : list) {
         System.out.println(prime);
      }
   }
}
```