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Question

I have a class with the following definition,

class BinomialNode
    {
        public int key; // The key value
        public int x_point; // x co-ordinate for drawing
        public int y_point; // y co-ordinate for drawing
        public int degree;  // number of siblings/children for current node
        public BinomialNode parent;
        public BinomialNode child;
        public BinomialNode sibling;
        ...
    }

We are learning Binomial Heaps in college and I've implemented the merge and insert algorithms in code. At least, when I pause Visual Studio and go over the "Locals" (by hovering the mouse over a variable), I see the data as I expect.

As an experiment, I've added 2 extra variables to the standard "Binomial Node". They are x_point and y_point. Now during program execution I see this,

Please note the area I've indicated above. It's supposed to represent the same node, but as we can see, the value of x_point is different. (In other cases, y_point is different)

Does anyone have a clue why this is happening? As I understand things, if it represents the same node, the data should be identical. But it isn't - which means it's not the same node. How can that be possible? If I ignore my "extra" x_point and y_point variables, the code runs perfectly! In fact, I wouldn't have even know this to be a problem.

It's not visible from my snippet, but x_point & y_point are the only values I EDIT outside the class definition. The others, while public are only read from.

EDIT: Here is the code I've made,

class BinomialNode
{
    public int key; // The key value
    public int x_point; // x co-ordinate for drawing
    public int y_point; // y co-ordinate for drawing
    public int degree;  // number of siblings/children for current node
    public BinomialNode parent;
    public BinomialNode child;
    public BinomialNode sibling;

    // Binomial Link takes the tree rooted at y and makes it a child of z
    private static void Binomial_Link(ref BinomialNode y,ref  BinomialNode z)
    {
        y.parent = z;
        y.sibling = z.child;
        z.child = y;
        z.degree++;
    }

    // This merges the root lists of H1 and H2 into a single linked list that is sorted
    // by degree in increasing order
    private static BinomialNode Binomial_Heap_Merge(BinomialNode H1, BinomialNode H2)
    {
        BinomialNode H = new BinomialNode();
        BinomialNode temp = H;
        if (H1 == null) // if it's the first insert
        {
            return H2;
        }
        while (H1 != null && H2 != null)
        {
            if (H1.degree < H2.degree)
            {
                // insert H1 into position
                temp.key = H1.key;
                temp.x_point = H1.x_point;
                temp.y_point = H1.y_point;
                temp.child = H1.child;
                temp.degree = H1.degree;
                temp.sibling = new BinomialNode();
                temp = temp.sibling;

                // move H1 to the next sibling
                H1 = H1.sibling;
            }
            else
            {
                // insert H2 into position
                temp.key = H2.key;
                temp.x_point = H2.x_point;
                temp.y_point = H2.y_point;
                temp.child = H2.child;
                temp.degree = H2.degree;
                temp.sibling = new BinomialNode();
                temp = temp.sibling;

                // move H2 to next sibling
                H2 = H2.sibling;
            }
        }

        // one of them hit null, so fill in the rest
        while (H1 != null)
        {
            // insert H1 into position
            temp.key = H1.key;
            temp.x_point = H1.x_point;
            temp.y_point = H1.y_point;
            temp.child = H1.child;
            temp.degree = H1.degree;
            temp.sibling = new BinomialNode();
            temp = temp.sibling;

            // move H1 to the next sibling
            H1 = H1.sibling;
        }
        while (H2 != null)
        {
            // insert H2 into position
            temp.key = H2.key;
            temp.x_point = H2.x_point;
            temp.y_point = H2.y_point;
            temp.child = H2.child;
            temp.degree = H2.degree;
            temp.sibling = new BinomialNode();
            temp = temp.sibling;

            // move H2 to the next sibling
            H2 = H2.sibling;
        }

        // To remove the extra node added,
        temp = H;
        while (temp != null)
        {
            if (temp.sibling.key == 0 && temp.sibling.sibling == null && temp.sibling.child == null)
            {
                // found the extra, now to get rid of it!
                temp.sibling = null;
            }
            temp = temp.sibling;
        }
        return H;  // send back the merged heap
    }

    // Unites the binomial heaps H1 & H2 and returns resulting heap
    public static BinomialNode Binomial_Heap_Union(BinomialNode H1, BinomialNode H2)
    {
        BinomialNode prev_x, x, next_x;
        BinomialNode H = new BinomialNode();
        H = Binomial_Heap_Merge(H1, H2);

        // simple checks
        if (H == null)
        {
            return H;
        }
        else
        {
            prev_x = null;
            x = H;
            next_x = x.sibling;
        }

        // now, for the actual merging
        while (next_x != null)
        {
            if ((x.degree != next_x.degree) || (next_x.sibling != null && x.degree == next_x.sibling.degree))
            {
                prev_x = x;
                x = next_x;
            }
            else if (x.key <= next_x.key)
            {
                x.sibling = next_x.sibling;
                Binomial_Link(ref next_x, ref x);
            }
            else
            {
                if (prev_x == null)
                {
                    H = next_x;
                }
                else
                {
                    prev_x.sibling = x.sibling;
                }
                Binomial_Link(ref x, ref next_x);
                x = next_x;
            }
            next_x = x.sibling;
        }

        // now, to return the merged heap
        return H; 
    }

    // inserting a key into a heap
    public static void Binomial_Heap_Insert(ref BinomialNode H, int x)
    {
        BinomialNode H_temp = new BinomialNode();
        H_temp.key = x;
        H_temp.parent = null;
        H_temp.degree = 0;
        H_temp.sibling = null;
        H_temp.child = null;
        H = Binomial_Heap_Union(H, H_temp);
    }
}

I use a form window to get the data from users to fill in the heap. The input is here,

 private void button1_Click(object sender, EventArgs e)
        {
            BinomialNode.Binomial_Heap_Insert(ref B_HEAP1, Int32.Parse(numericUpDown1.Value.ToString()));

            // drawing the heap
            pictureBox1.Refresh();
            int x = 0;
            DrawNodeValue(pictureBox1, ref B_HEAP1, ref x, 0);
        }

I hope the code isn't too badly made?

Answer 1

You're creating a new node, and then copying all the values over. Is that what you want to do? If you expect to be using the same nodes, then use the same nodes.

Instead of:

Node H = new Node();
Node temp = H;
if(node1 > node2)
  temp.values = node1.values
else
  temp.values = node2.values

Just use the actual objects...

Node temp;
if(node1 > node2)
  temp = node1;
else
  temp = node2;

I'm not sure where the values are getting separated, but this is why they're not actually the same node.