The Merge-Based Strategy with Matching
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The Merge-based strategy uses the same Merge mechanism as the mergeable strategy does, however it only creates new items if they are needed (i.e. a new node is visited with no previously merged item that matches it). In this case, the created item will be removed from the list and therefore never become an orphan again. The Merge-based strategy is implemented as follows:
public void Merge(int m)
{
int d=m+1;
while(m>0 && list[m].parent!=null)
{
//Create item
if (m>1) //A new node was visited
{
list[m].parent=null;
Item item = new Item(d);
list[m].item = item;
list[m].color = d;
item.color = d;
}
else //The m is the root node and no new item is needed. Remove it
{
list[m].parent=null;
Node temp = list[m];
list[m] = null;
list[m] = temp;
if (m>1) //The root node has no child
return;
}
list[m].color=d;
m--;
}
return;
}
The Merge-based strategy uses an algorithm (Algorithm \[alg-merging\]) based on the classic tree-sorting method [@knuth1998art] to avoid the problems of the mergeable strategy (i.e. orphaned nodes). It works as follows:
int i = 0; //index for list items
int n = n-1; //number of items
int l = 0; //index for list nodes
while(i items[i+1].right)
{
int p = items[i+1];
items[i+1] = items[i];
items[i] = p;
n--;
i++;
}
else if (i items[i+1].left)
{
int p = items[i+1];
items[i+1] = items[i];
items[i] = p;
n--;
i++;
}
else if (i
