private static void goRight(ref Treap <Point> current, ref Point currentPoint, ref int toCut)
{
toCut = toCut + Treap <Point> .GetSize(current.Right.Left) + 1;
current = current.Right;
currentPoint = current.Key;
}
private static void goLeft(ref Treap <Point> current, ref Point currentPoint, ref int toCut)
{
toCut = toCut - Treap <Point> .GetSize(current.Left.Right) - 1;
current = current.Left;
currentPoint = current.Key;
}
public void SetConvexHull(bool isLeftHalf, Treap <Point> value)
{
if (isLeftHalf)
{
leftConvexHull = value;
}
else
{
rightConvexHull = value;
}
}
public Treap(T newKey, Treap <T> newLeft = null, Treap <T> newRight = null)
{
Key = newKey;
Left = newLeft;
Right = newRight;
Size = 1;
MaxElement = newKey;
MinElement = newKey;
update();
}
private static void pushSubHullDown(RedBlackNode current, bool isLeftHalf)
{
if (current != null && !current.IsLeaf && current.GetConvexHull(isLeftHalf) != null)
{
Treap <Point> leftHalf;
Treap <Point> rightHalf;
Treap <Point> .SplitBySize(current.GetConvexHull(isLeftHalf), current.GeLowerSubHullSize(isLeftHalf), out leftHalf, out rightHalf);
current.Left.SetConvexHull(isLeftHalf, Treap <Point> .Merge(leftHalf, current.Left.GetConvexHull(isLeftHalf)));
current.Right.SetConvexHull(isLeftHalf, Treap <Point> .Merge(current.Right.GetConvexHull(isLeftHalf), rightHalf));
current.SetConvexHull(isLeftHalf, null);
}
}
private RedBlackNode(Point newPoint = null, RedBlackNode newLeft = null, RedBlackNode newRight = null, RedBlackNode newParent = null)
{
Left = newLeft;
Right = newRight;
Parent = newParent;
MaxPoint = newPoint;
NodeColor = IsRoot ? Color.Black : Color.Red;
leftConvexHull = null;
leftLowerSubHullSize = 0;
rightConvexHull = null;
rightLowerSubHullSize = 0;
}
public static bool IsValid(Treap <Point> hull)
{
if (hull == null)
{
return(true);
}
var list = hull.GetArray();
for (int i = 0; i < list.Count - 2; ++i)
{
if (DeterminePosition(list[i], list[i + 2], list[i + 1]) == PointPosition.Right)
{
return(false);
}
}
return(true);
}
public static void SplitBySize(Treap <T> current, int toCut, out Treap <T> leftHalf, out Treap <T> rightHalf)
{
if (current == null)
{
leftHalf = null;
rightHalf = null;
}
else if (GetSize(current.Left) >= toCut)
{
SplitBySize(current.Left, toCut, out leftHalf, out rightHalf);
current.Left = rightHalf;
current.update();
rightHalf = current;
}
else
{
SplitBySize(current.Right, toCut - GetSize(current.Left) - 1, out leftHalf, out rightHalf);
current.Right = leftHalf;
current.update();
leftHalf = current;
}
}
public static Treap <T> Merge(Treap <T> leftTreap, Treap <T> rightTreap)
{
if (leftTreap == null)
{
return(rightTreap);
}
if (rightTreap == null)
{
return(leftTreap);
}
if (randomGenerator.Next(0, leftTreap.Size + rightTreap.Size) < leftTreap.Size)
{
leftTreap.Right = Merge(leftTreap.Right, rightTreap);
leftTreap.update();
return(leftTreap);
}
else
{
rightTreap.Left = Merge(leftTreap, rightTreap.Left);
rightTreap.update();
return(rightTreap);
}
}
public static int GetSize(Treap <T> treap)
{
return(treap == null ? 0 : treap.Size);
}
private static void recount(RedBlackNode current, bool isLeftHalf)
{
if (current != null && current.Left != null && current.Right != null && current.GetConvexHull(isLeftHalf) == null)
{
current.MaxPoint = Utils.Max(current.Left.MaxPoint, current.Right.MaxPoint);
Treap <Point> lowerCurrent = current.Left.GetConvexHull(isLeftHalf);
Treap <Point> upperCurrent = current.Right.GetConvexHull(isLeftHalf);
Point loweCurrentPoint = lowerCurrent.Key;
Point upperCurrentPoint = upperCurrent.Key;
double mediumY = (lowerCurrent.MaxElement.Y + upperCurrent.MinElement.Y) / 2;
int toCutFromLowerHull = Treap <Point> .GetSize(lowerCurrent?.Left) + 1;
int toLeaveInUpperHull = Treap <Point> .GetSize(upperCurrent?.Left) + 1;
bool bridgeFound = false;
while (!bridgeFound)
{
Point lowerPrevPoint = lowerCurrent?.Left != null ? lowerCurrent.Left.MaxElement : null;
Point lowerNextPoint = lowerCurrent?.Right != null ? lowerCurrent.Right.MinElement : null;
Point upperPrevPoint = upperCurrent?.Left != null ? upperCurrent.Left.MaxElement : null;
Point upperNextPoint = upperCurrent?.Right != null ? upperCurrent.Right.MinElement : null;
bridgeFound = makeDecisionAboutRotation(ref lowerCurrent, ref loweCurrentPoint, lowerPrevPoint, lowerNextPoint, ref toCutFromLowerHull,
ref upperCurrent, ref upperCurrentPoint, upperPrevPoint, upperNextPoint, ref toLeaveInUpperHull,
mediumY, isLeftHalf);
}
// we want to have top point in right treap after split
--toLeaveInUpperHull;
Treap <Point> leftPartOfLowerHull;
Treap <Point> rightPartOfLowerHull;
Treap <Point> leftPartOfUpperHull;
Treap <Point> rightPartOfUpperHull;
if (loweCurrentPoint.Y == upperCurrentPoint.Y)
{
if ((loweCurrentPoint.X < upperCurrentPoint.X && isLeftHalf) ||
(loweCurrentPoint.X > upperCurrentPoint.X && !isLeftHalf))
{
++toLeaveInUpperHull;
}
else if ((loweCurrentPoint.X > upperCurrentPoint.X && isLeftHalf) ||
(loweCurrentPoint.X < upperCurrentPoint.X && !isLeftHalf))
{
--toCutFromLowerHull;
}
else
{
toLeaveInUpperHull++;
}
}
current.SetLowerSubHullSize(isLeftHalf, toCutFromLowerHull);
Treap <Point> .SplitBySize(current.Left.GetConvexHull(isLeftHalf), toCutFromLowerHull, out leftPartOfLowerHull, out rightPartOfLowerHull);
Treap <Point> .SplitBySize(current.Right.GetConvexHull(isLeftHalf), toLeaveInUpperHull, out leftPartOfUpperHull, out rightPartOfUpperHull);
current.SetConvexHull(isLeftHalf, Treap <Point> .Merge(leftPartOfLowerHull, rightPartOfUpperHull));
current.Left.SetConvexHull(isLeftHalf, rightPartOfLowerHull);
current.Right.SetConvexHull(isLeftHalf, leftPartOfUpperHull);
}
}
private static bool makeDecisionAboutRotation(ref Treap <Point> lowerCurrent, ref Point lowerCurrentPoint, Point lowerPrevPoint, Point lowerNextPoint,
ref int toCutFromLowerHull,
ref Treap <Point> upperCurrent, ref Point upperCurrentPoint, Point upperPrevPoint, Point upperNextPoint,
ref int toLeaveInUpperHull,
double mediumY, bool isLeftHalf)
{
PointPosition lowerPrevPos = determinePosition(lowerCurrentPoint, upperCurrentPoint, lowerPrevPoint, isLeftHalf);
PointPosition lowerNextPos = determinePosition(lowerCurrentPoint, upperCurrentPoint, lowerNextPoint, isLeftHalf);
PointPosition upperPrevPos = determinePosition(lowerCurrentPoint, upperCurrentPoint, upperPrevPoint, isLeftHalf);
PointPosition upperNextPos = determinePosition(lowerCurrentPoint, upperCurrentPoint, upperNextPoint, isLeftHalf);
if (lowerPrevPos == PointPosition.Right && lowerNextPos == PointPosition.Right &&
upperPrevPos == PointPosition.Right && upperNextPos == PointPosition.Right) // A - found
{
return(true); // answer found
}
else if (lowerPrevPos == PointPosition.Left && lowerNextPos == PointPosition.Right &&
upperPrevPos == PointPosition.Right && upperNextPos == PointPosition.Right) // B
{
goLeft(ref lowerCurrent, ref lowerCurrentPoint, ref toCutFromLowerHull);
//goRight(ref rightTop, ref rightTopPoint, ref rightMinPoint, ref rightMaxPoint,
// ref toLeaveInRightHull, ref minPointLeaveInRight, ref maxPointLeaveInRight);
}
else if (lowerPrevPos == PointPosition.Right && lowerNextPos == PointPosition.Left &&
upperPrevPos == PointPosition.Right && upperNextPos == PointPosition.Right) // C
{
goRight(ref lowerCurrent, ref lowerCurrentPoint, ref toCutFromLowerHull);
//goRight(ref rightTop, ref rightTopPoint, ref rightMinPoint, ref rightMaxPoint,
// ref toLeaveInRightHull, ref minPointLeaveInRight, ref maxPointLeaveInRight);
}
else if (lowerPrevPos == PointPosition.Right && lowerNextPos == PointPosition.Right &&
upperPrevPos == PointPosition.Right && upperNextPos == PointPosition.Left) // D
{
//goLeft(ref leftTop, ref leftTopPoint, ref leftMinPoint, ref leftMaxPoint,
// ref toCutFromLeftHull, ref minPointCutFromLeft, ref maxPointCutFromLeft);
goRight(ref upperCurrent, ref upperCurrentPoint, ref toLeaveInUpperHull);
}
else if (lowerPrevPos == PointPosition.Right && lowerNextPos == PointPosition.Right &&
upperPrevPos == PointPosition.Left && upperNextPos == PointPosition.Right) // E
{
//goLeft(ref leftTop, ref leftTopPoint, ref leftMinPoint, ref leftMaxPoint,
// ref toCutFromLeftHull, ref minPointCutFromLeft, ref maxPointCutFromLeft);
goLeft(ref upperCurrent, ref upperCurrentPoint, ref toLeaveInUpperHull);
}
else if (lowerPrevPos == PointPosition.Left && lowerNextPos == PointPosition.Right &&
upperPrevPos == PointPosition.Right && upperNextPos == PointPosition.Left) // F
{
goLeft(ref lowerCurrent, ref lowerCurrentPoint, ref toCutFromLowerHull);
goRight(ref upperCurrent, ref upperCurrentPoint, ref toLeaveInUpperHull);
}
else if (lowerPrevPos == PointPosition.Left && lowerNextPos == PointPosition.Right &&
upperPrevPos == PointPosition.Left && upperNextPos == PointPosition.Right) // G
{
goLeft(ref lowerCurrent, ref lowerCurrentPoint, ref toCutFromLowerHull);
}
else if (lowerPrevPos == PointPosition.Right && lowerNextPos == PointPosition.Left &&
upperPrevPos == PointPosition.Right && upperNextPos == PointPosition.Left) // H
{
goRight(ref upperCurrent, ref upperCurrentPoint, ref toLeaveInUpperHull);
}
else if (lowerPrevPos == PointPosition.Right && lowerNextPos == PointPosition.Left &&
upperPrevPos == PointPosition.Left && upperNextPos == PointPosition.Right) // I - the hardest
{
if (isIntersectLoverY(lowerCurrentPoint, lowerNextPoint, upperCurrentPoint, upperPrevPoint, mediumY, isLeftHalf))
{
goRight(ref lowerCurrent, ref lowerCurrentPoint, ref toCutFromLowerHull);
}
else
{
goLeft(ref upperCurrent, ref upperCurrentPoint, ref toLeaveInUpperHull);
}
}
else
{
throw new Exception("something wrong");
}
return(false); // answer not found
}
public RedBlackNode(Point newPoint, RedBlackNode newParent = null) : this(newPoint, null, null, newParent)
{
leftConvexHull = new Treap <Point>(newPoint);
rightConvexHull = new Treap <Point>(newPoint);
}
