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splaying elements to the root..

DrJones (156)
I am having some difficulties splaying this element to the root..
considering i have this splay tree . 

1
2
3
4
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8
9
 
0
 \
  1
   \
    2
     \
      3
       \
        4


Could anyone show me the steps to get it 4 to the root?
Last edited on
tcs (519)
A recursive implementation:

1. After reaching 4 you've the item to be looked up returning it to the previous level.
2. When returning to 3 you'll detect the returned 4 as your right node - but because 3 isn't the root node, there's nothing else to do than returning node 4 to node 2.
3. At node 2 you'll detect node 4 as your rightmost grandchild. Now you've to rotate left two times: At first at node 2 and than at the new top node of the resulting subtree namely node 3. You'll get 4-3-2 where 4 is the root of this subtree. Now you'll return this subtree to node 1.
4. Node 1 just points to node 2 as its right node. Because we don't detect the returned subtrees top level node 4 as our right child nor grandchild, we've to replace our right child pointer by this subtree. Then we'll return to 0 with our right subtree (with 4 as top level node).
At this moment our tree should look like:
0
 \
   1
    \
      \
        \
         4
        /
       3
     /
    2

5. At level 0 we'll detect the returned top level node, namely 4, as our right most grandchild. So we've to do two more rotation to the left like before. That's it!

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template <typename ItemType>
class BstNode
{
private:
    typedef BstNode<ItemType> BstItemNode;

private:
    ItemType      _data;
    BstItemNode  *_left, *_right;    // May be left undefined before Dest

private:
    BstItemNode &rotateLeft();
    BstItemNode &rotateRight();
    BstItemNode *splay(const ItemType &val, bool isRootLevel);
//...
} /* BstNode */;


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template <typename ItemType>
BstNode<ItemType> *BstNode<ItemType>::splay(const ItemType &val, bool isRootLevel)
{
    BstItemNode *nodeFound;

    if      (val < _data)
    {
        if      (_left == nullptr)
        {
            nodeFound = this;
        }
        else
        {
            nodeFound = _left->splay(val, false);

            if (nodeFound != _left)
                // zig - ...
            {
                if (nodeFound == _left->_left)
                    // ... - zig
                {
                    rotateRight().rotateRight();
                }
                else if (nodeFound == _left->_right)
                    // ... - zag
                {
                    _left = &_left->rotateLeft();
                    rotateRight();
                }
                else
                {
                    _left = nodeFound;
                }
            }
            if (nodeFound == _left)
                // zig
            {
                if (isRootLevel)
                {
                    rotateRight();
                }
            }
        }
    }
    else if (_data < val)
    {
        if (_right == nullptr)
        {
            nodeFound = this;
        }
        else
        {
            nodeFound = _right->splay(val, false);

            if (nodeFound != _right)
                // zig - ...
            {
                if (nodeFound == _right->_right)
                    // ... - zig
                {
                    rotateLeft().rotateLeft();
                }
                else if (nodeFound == _right->_left)
                    // ... - zag
                {
                    _right = &_right->rotateRight();
                    rotateLeft();
                }
                else
                {
                    _right = nodeFound;
                }
            }
            if (nodeFound == _right)
                // zig
            {
                if (isRootLevel)
                {
                    rotateLeft();
                }
            }
        }
    }
    else // (_data == val)
    {
        nodeFound = this;
    }

    assert(nodeFound != nullptr);
    return nodeFound;

} /* splay() */
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