public static int[] kMin(FibonacciHeap H, int k)
    {
        int[] minimums = new int[k];
        int minIndex = 0;
        // add root to new heap
        FibonacciHeap minsHeap = new FibonacciHeap();
        ArrayList<HeapNode> nodes = new ArrayList<>();
        minsHeap.insert(H.getFirst().getKey());
        nodes.add(H.getFirst());

        while (minIndex < k) {
            minimums[minIndex] = minsHeap.findMin().getKey();
            minIndex++;
            HeapNode minNode = null;
            for (HeapNode node : nodes) { // find the pointer of the node in the original tree
                if (node.getKey() == minsHeap.findMin().getKey()) {
                    minNode = node;
                    break;
                }
            }

            // add new minimum's children to the heap and the pointer list
            HeapNode minNodeFirstChild = minNode.getChild();
            if (minNodeFirstChild != null) {
                HeapNode childNode = minNodeFirstChild;
                do {
                    minsHeap.insert(childNode.getKey());
                    nodes.add(childNode);
                    childNode = childNode.getNext();
                }
                while (childNode.getKey() != minNodeFirstChild.getKey());
            }
            minsHeap.deleteMin();
        }
        return minimums;
    }