public static IEnumerable <SortNodePair <T> > PairOff <T>(IEnumerable <T> items, IComparer <T> comparer)
{
List <SortNodePair <T> > pairs = new List <SortNodePair <T> >(items.Count() / 2);
SortNode <T> previousNode = null;
foreach (T currentItem in items)
{
if (previousNode == null)
{
previousNode = new SortNode <T>(currentItem);
}
else
{
SortNode <T> currentNode = new SortNode <T>(currentItem);
int comparison = comparer.Compare(previousNode.Item, currentItem);
if (comparison >= 0)
{
//previousNode.NumLowerItems = currentNode.NumHigherItems = 1;
pairs.Add(new SortNodePair <T>(currentNode, previousNode));
}
else
{
//previousNode.NumHigherItems = currentNode.NumLowerItems = 1;
pairs.Add(new SortNodePair <T>(previousNode, currentNode));
}
previousNode = null;
}
// Note that if there is an odd number of items then we don't use the last one
}
return(pairs);
}
public static SortNodePair <T> EstimateMedian <T>(IEnumerable <T> items, IComparer <T> comparer)
{
// split into sets of two points
IEnumerable <SortNodePair <T> > currentPairs = PairOff(items, comparer);
List <SortNodePair <T> > nextPairs = new List <SortNodePair <T> >(currentPairs.Count() / 2);
// find some pretty good bounds on the median
while (currentPairs.Count() > 1)
{
SortNodePair <T> previousPair = null;
foreach (SortNodePair <T> currentPair in currentPairs)
{
if (previousPair == null)
{
previousPair = currentPair;
}
else
{
// combine currentPair with previousPair, make a new pair, and add it to nextPairs
SortNode <T> lowestItem, middleItem1, middleItem2, highestItem;
// find the highest and lowest nodes
if (comparer.Compare(previousPair.LowerItem.Item, currentPair.LowerItem.Item) < 0)
{
lowestItem = previousPair.LowerItem;
middleItem1 = currentPair.LowerItem;
}
else
{
lowestItem = currentPair.LowerItem;
middleItem1 = previousPair.LowerItem;
}
if (comparer.Compare(previousPair.UpperItem.Item, currentPair.UpperItem.Item) < 0)
{
middleItem2 = previousPair.UpperItem;
highestItem = currentPair.UpperItem;
}
else
{
middleItem2 = currentPair.UpperItem;
highestItem = previousPair.UpperItem;
}
// make sure middleItem1 < middleItem2
if (comparer.Compare(middleItem1.Item, middleItem2.Item) > 0)
{
SortNode <T> temp = middleItem2;
middleItem2 = middleItem1;
middleItem1 = temp;
}
// make an updated low-middle node
SortNode <T> new_lowMiddle = new SortNode <T>(middleItem1.Item);
new_lowMiddle.NumEqualItems = middleItem1.NumEqualItems;
new_lowMiddle.NumLowerItems = lowestItem.NumLowerItems + middleItem1.NumLowerItems;
if (comparer.Compare(lowestItem.Item, new_lowMiddle.Item) < 0)
{
new_lowMiddle.NumLowerItems += lowestItem.NumEqualItems;
}
else
{
new_lowMiddle.NumEqualItems += lowestItem.NumEqualItems;
}
new_lowMiddle.NumHigherItems = middleItem1.NumHigherItems; // don't need to mark the higher items that new_highMiddle knows about
// make an updated high-middle node
SortNode <T> new_highMiddle = new SortNode <T>(middleItem2.Item);
new_highMiddle.NumEqualItems = middleItem2.NumEqualItems;
new_highMiddle.NumLowerItems = middleItem2.NumLowerItems; // don't need to mark the lower items that new_lowerMiddle knows about
new_highMiddle.NumHigherItems = middleItem2.NumHigherItems + highestItem.NumHigherItems;
if (comparer.Compare(new_highMiddle.Item, highestItem.Item) < 0)
{
new_highMiddle.NumHigherItems += highestItem.NumEqualItems;
}
else
{
new_highMiddle.NumEqualItems += highestItem.NumEqualItems;
}
nextPairs.Add(new SortNodePair <T>(new_lowMiddle, new_highMiddle));
previousPair = null;
}
}
// If a pair remains, we ignore it
//if (previousPair != null)
// nextPairs.AddFirst(previousPair);
currentPairs = nextPairs;
nextPairs = new List <SortNodePair <T> >(currentPairs.Count() / 2);
}
return(currentPairs.First());
}
public SortNodePair(SortNode <T> lowerItem, SortNode <T> upperItem)
{
this.LowerItem = lowerItem;
this.UpperItem = upperItem;
}