Heap.java:
public class Heap <T extends Comparable<T>> {
    public T[] element;
    public Heap(T[] elem) {
        element = elem;
        endIndex = element.length-1;
    }
    private int aktuellerIndex = 0;
    private int endIndex;
    private int root = 0;
    public void heapify() {
        heapify(element, aktuellerIndex, endIndex);
    }
    // Heapify
    public void heapify(T[] element, int aktuellerIndex,int endIndex,int root){
        int largest;
        int left = aktuellerIndex + (root - aktuellerIndex)*2 + 1;
        int right = left + 1;
        if(left <= endIndex && element[left].compareTo(element[root]) > 0)
            largest = left;
        else
            largest = right;
        if(right <= endIndex && element[right].compareTo(element[largest]) > 0)
            largest = right;
        if(largest != root)
            swap(root, largest);
            heapify(element, aktuellerIndex, endIndex,largest);
    }
    // Swap
    public void swap(int root, int largest){
        T temp = element[largest];
        element[largest] = element[root];
        element[root] = temp;
    }
    // Erstellt den Heap
    public void heapify(T[] element, int aktuellerIndex, int endIndex) {
        int length = endIndex - aktuellerIndex +1;
        for(int i = aktuellerIndex + length/2 - 1; i>=aktuellerIndex; i--) {
            heapify(element, aktuellerIndex, endIndex, i);
        }
    }
    // Heapsort
    public void heapSort(T[] element, int aktuellerIndex, int endIndex) {
        for(int i = endIndex; i> aktuellerIndex; i--) {
            swap(aktuellerIndex, i);
            heapify(element, aktuellerIndex, i-1, aktuellerIndex);
        }
    }
    // Print
    void printHeap() {
        for(int i=0; i < element.length; i++) {
            System.out.println(element[i]);
        }
    }
}
TestKlasse.java:
public class TestKlasse {

    public static void main(String [] args) {

        //List<Integer> list = new ArrayList<Integer>(Arrays.asList( new Integer[]{1,2,3,4,5,6,7}));
        Integer[] test;
        test = new Integer[3];
        test[0] = new Integer(1);
        test[1] = new Integer(2);
        test[2] = new Integer(3);

        Heap a = new Heap(test);
        a.printHeap();
        a.heapify();
        a.printHeap();
    }
}

  Errors:
  [lalala]$ java TestKlasse
1
2
3
Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 6
        at Heap.swap(Heap.java:36)
        at Heap.heapify(Heap.java:30)
        at Heap.heapify(Heap.java:31)
        at Heap.heapify(Heap.java:45)
        at Heap.heapify(Heap.java:15)
        at TestKlasse.main(TestKlasse.java:17)