private SkyLine FindSkyline(Building[] building, int low, int high)
{
//here when we divide and seperate recursion there are two possibilities
//low will be equal to high
//if we handle low = high, low won't be greater to high and high won't go lesser than low
if (low == high)
{
//You have one building, get skylines from the building
//eg (1,11,5) will give (1,11) and (5,0)
// update 06/28/2017
// A skyline is a collection of rectangular strips.
// A rectangular strip is represented as a pair (left, ht) where left is x coordinate of left side of strip and ht is height of strip
// here (5, 0) because 5 is the x corordinate of the left side of the strip (2nd strip) of height 0. ..
SkyLine result = new SkyLine(2);
result.append(new Strip(building[low].left, building[low].height));
result.append(new Strip(building[low].right, 0));
return(result);
}
//default case low will be lesser than high
int middle = (low + high) / 2;
SkyLine skyline1 = FindSkyline(building, low, middle);
SkyLine skyline2 = FindSkyline(building, middle + 1, high);
//order is important here merge skyline1 to skyline2
return(MergeTwoSkylines(skyline1, skyline2));
}
//Note: order is important. This function append the skyline2 to skyline1
//same as calling skyline1.merge(skyline2)
public SkyLine MergeTwoSkylines(SkyLine skyline1, SkyLine skyline2)
{
// Create a resultant skyline with capacity as sum of two
// skylines
SkyLine result = new SkyLine(skyline1.GetSize() + skyline2.GetSize());
// The idea is similar to merge of merge sort, start from first strips of two skylines, compare x coordinates.
//Pick the strip with smaller x coordinate and add it to result.
//The height of added strip is considered as maximum of current heights from skyline1 and skyline2.
//Example to show working of merge:
// Height of new Strip is always obtained by takin maximum of following
// (a) Current height from skyline1, say 'h1'.
// (b) Current height from skyline2, say 'h2'
// h1 and h2 are initialized as 0. h1 is updated when a strip from
// SkyLine1 is added to result and h2 is updated when a strip from
// SkyLine2 is added.
int h1 = 0, h2 = 0;
int leftpointer = 0; //left half pointer
int rightpointer = 0; //right half pointer
while (leftpointer < skyline1.GetSize() && rightpointer < skyline2.GetSize())
{
int mergeheight = 0;
if (skyline1.strips[leftpointer].left < skyline2.strips[rightpointer].left)
{
h1 = skyline1.strips[leftpointer].height;
mergeheight = Math.Max(h1, h2);
result.append(new Strip(skyline1.strips[leftpointer].left, mergeheight));
leftpointer++;
}
else
{
//don't worry about equal condition. result.append already has logic to skip skyline if the previous skyline has same height and left
h2 = skyline2.strips[rightpointer].height;
mergeheight = Math.Max(h1, h2);
result.append(new Strip(skyline2.strips[rightpointer].left, mergeheight));
rightpointer++;
}
}
// If there are strips left in this skyline or other
// skyline
while (leftpointer < skyline1.GetSize())
{
result.append(skyline1.strips[leftpointer]);
leftpointer++;
}
while (rightpointer < skyline2.GetSize())
{
result.append(skyline2.strips[rightpointer]);
rightpointer++;
}
return(result);
}
private SkyLine GetSkylinesFromSingleBuilding(Building building)
{
//there are two strips for single building
SkyLine result = new SkyLine(2);
result.append(new Strip(building.left, building.height));
result.append(new Strip(building.right, 0));
return(result);
}
private void button1_Click(object sender, EventArgs e)
{
// Input: Array of buildings
//{ (1,11,5), (2,6,7), (3,13,9), (12,7,16), (14,3,25),
// (19,18,22), (23,13,29), (24,4,28) }
List <Building> buildings = new List <Building>();
Building building1 = new Building(1, 11, 5);
Building building2 = new Building(2, 6, 7);
Building building3 = new Building(3, 13, 9);
Building building4 = new Building(12, 7, 16);
Building building5 = new Building(14, 3, 25);
Building building6 = new Building(19, 18, 22);
Building building7 = new Building(23, 13, 29);
Building building8 = new Building(24, 4, 28);
buildings.Add(building1);
buildings.Add(building2);
//buildings.Add(building3);
//buildings.Add(building4);
//buildings.Add(building5);
//buildings.Add(building6);
//buildings.Add(building7);
//buildings.Add(building8);
SkyLine result = FindSkyline(buildings.ToArray(), 0, buildings.Count - 1);
StringBuilder sb = new StringBuilder();
foreach (Strip s in result.strips)
{
if (s != null)
{
sb.Append("(").Append(s.left).Append(",").Append(s.height).Append(")");
}
}
string output = sb.ToString();
// Skyline for given buildings is
//(1, 11), (3, 13), (9, 0), (12, 7), (16, 3), (19, 18),
//(22, 3), (23, 13), (29, 0),
}
private SkyLine GetSkyline(List <Building> buildings)
{
SkyLine result = null;
foreach (Building building in buildings)
{
SkyLine skyline = GetSkylinesFromSingleBuilding(building);
if (result == null)
{
result = skyline;
}
else
{
result = MergeTwoSkylines(result, skyline);
}
}
return(result);
}
