public PointList Merge(PointList lhs, PointList rhs)
{
// the base case
PointList p = null;
if (lhs.Length == 1 && rhs.Length == 1)
{
p = new PointList(lhs, rhs);
return(p);
}
// finding the top connecting nodes
/*
* O(n) because you will visit each node a maximum of one time within the while loop
* (with the possible exception of the first node checked, which may get visited twice, at most)
* where n is the number of nodes given before they are split in the Divide function
*/
// Finding the rightmost of the lhs and the leftmost of the rhs are a combined O(n)
PointF lpt_top = lhs.Rightmost(), rpt_top = rhs.Leftmost();
PointF current;
bool changed = true;
bool growing = true;
while (changed)
{
changed = false;
growing = true;
while (growing)
{
current = lhs.prev();
if (Slope(current, rpt_top) > Slope(lpt_top, rpt_top))
{
lpt_top = current;
changed = true;
}
else
{
growing = false;
lhs.next();
}
}
growing = true;
while (growing)
{
current = rhs.next();
if (Slope(lpt_top, current) < Slope(lpt_top, rpt_top))
{
rpt_top = current;
changed = true;
}
else
{
growing = false;
rhs.prev();
}
}
}
// finding the bottom connecting nodes
/*
* O(n) because you will visit each node a maximum of one time within the while loop
* (with the possible exception of the first node checked, which may get visited twice, at most)
* where n is the number of nodes given before they are split in the Divide function
*/
// Finding the rightmost of the lhs and the leftmost of the rhs are a combined O(n)
PointF lpt_bot = lhs.Rightmost(), rpt_bot = rhs.Leftmost();
changed = true;
growing = true;
while (changed)
{
changed = false;
growing = true;
while (growing)
{
current = lhs.next();
if (Slope(current, rpt_bot) < Slope(lpt_bot, rpt_bot))
{
lpt_bot = current;
changed = true;
}
else
{
growing = false;
lhs.prev();
}
}
growing = true;
while (growing)
{
current = rhs.prev();
if (Slope(lpt_bot, current) > Slope(lpt_bot, rpt_bot))
{
rpt_bot = current;
changed = true;
}
else
{
growing = false;
rhs.next();
}
}
}
// forming the new list with only the convex hull nodes
/*
* O(n) because you might have to add all n nodes from the lhs and rhs
* bounding lists to the new bounding list.
* Usually this will only be a fraction of the actual number of nodes given to Divide()
*/
List <PointF> list = new List <PointF>();
growing = true;
current = lpt_bot;
lhs.SetIndex(lpt_bot);
while (growing)
{
if (current == lpt_top)
{
growing = false;
}
list.Add(current);
current = lhs.next();
}
growing = true;
current = rpt_top;
rhs.SetIndex(rpt_top);
while (growing)
{
if (current == rpt_bot)
{
growing = false;
}
list.Add(current);
current = rhs.next();
}
p = new PointList(list);
return(p);
// Total Time: O(5n) = O(n)
// Total Space: O(n) for the new list allocated at the end
}
public PointList Merge(PointList lhs, PointList rhs)
{
// the base case
if (lhs.Length == 1 || rhs.Length == 1)
{
return(new PointList(lhs, rhs));
}
// finding the top connecting nodes
PointF lpt_top = lhs.Rightmost(), rpt_top = rhs.Leftmost();
PointF current;
bool changed = true;
bool growing = true;
while (changed)
{
changed = false;
growing = true;
while (growing)
{
current = lhs.prev();
if (Slope(current, rpt_top) > Slope(lpt_top, rpt_top))
{
lpt_top = current;
changed = true;
}
else
{
growing = false;
lhs.next();
}
}
growing = true;
while (growing)
{
current = rhs.next();
if (Slope(lpt_top, current) < Slope(lpt_top, rpt_top))
{
rpt_top = current;
changed = true;
}
else
{
growing = false;
rhs.prev();
}
}
}
// finding the bottom connecting nodes
PointF lpt_bot = lhs.Rightmost(), rpt_bot = rhs.Leftmost();
bool changed = true;
bool growing = true;
while (changed)
{
changed = false;
growing = true;
while (growing)
{
current = lhs.next();
if (Slope(current, rpt_bot) < Slope(lpt_bot, rpt_bot))
{
lpt_bot = current;
changed = true;
}
else
{
growing = false;
lhs.prev();
}
}
growing = true;
while (growing)
{
current = rhs.prev();
if (Slope(lpt_bot, current) > Slope(lpt_bot, rpt_bot))
{
rpt_bot = current;
changed = true;
}
else
{
growing = false;
rhs.next();
}
}
}
// forming the new list with only the convex hull nodes
List <PointF> list = new List <>();
growing = true;
current = lpt_bot;
lhs.SetIndex(lpt_bot);
while (growing)
{
if (current == lpt_top)
{
growing = false;
}
list.Add(current);
current = lhs.next();
}
growing = true;
current = rpt_top;
rhs.SetIndex(rpt_top);
while (growing)
{
if (current == rpt_bot)
{
growing = false;
}
list.Add(current);
current = rhs.next();
}
return(new PointList(list));
}
public PointList(PointList pts1, PointList pts2)
{
points = new PointF[pts1.Length + pts2.Length];
Array.Copy(pts1.points, 0, points, 0, pts1.Length);
Array.Copy(pts2.points, 0, points, pts1.Length, pts1.Length + pts2.Length);
}