public int DistToSqrd(Point3d other)
{
int dx = X - other.X;
int dy = Y - other.Y;
int dz = Z - other.Z;
return dx*dx + dy*dy + dz*dz;
}
static List<Range> ProjectBombs(int x, int y, Point3d[] bombsByZ, int radSqr)
{
var result = new List<Range>();
foreach (var b in bombsByZ)
{
int dx = b.X - x;
int dy = b.Y - y;
int xYDistSqr = dx*dx + dy*dy;
if (radSqr >= xYDistSqr)
{
int maxDz = (int)Math.Sqrt(radSqr - xYDistSqr);
var newRange = new Range(b.Z - maxDz, b.Z + maxDz + 1);
// The intersection of a bomb is symetric around its Z
// Also, each bomb has Z >= all previous ones
// Thus, if the Begin of the range is less than a previous Begin, the new range totally superceeds the previous range,
// and the previous range can be removed
for (int iExisting = result.Count - 1; iExisting >= 0; iExisting--)
{
if (newRange.Begin <= result[iExisting].Begin)
{
result.RemoveAt(iExisting);
}
else
{
// result is build up sorted by Begin
// Thus, if Begin at iExisting is too small, there is no point continuing back through the list
break;
}
}
result.Add(newRange);
}
}
return result;
}
private static int FindMinRadius(Point3d p, List<Point3d> bombs)
{
var result = bombs.Select(b => b.DistToSqrd(p)).Min();
return result;
}
static void Main()
{
var bombs = new List<Point3d>();
var rand = new Random();
while (bombs.Count < 200)
{
int x = rand.Next(CubeSize);
int y = rand.Next(CubeSize);
int z = rand.Next(CubeSize);
var next = new Point3d(x, y, z);
if (!bombs.Contains(next))
{
bombs.Add(next);
}
}
// Add in Corner bombs, as otherwise the corners tend to be the safest spots, which isn't very interesting
bombs.Add(new Point3d(0, 0, 0));
bombs.Add(new Point3d(0, 0, 1000));
bombs.Add(new Point3d(0, 1000, 0));
bombs.Add(new Point3d(0, 1000, 1000));
bombs.Add(new Point3d(1000, 0, 0));
bombs.Add(new Point3d(1000, 0, 1000));
bombs.Add(new Point3d(1000, 1000, 0));
bombs.Add(new Point3d(1000, 1000, 1000));
// Add the center of each face
bombs.Add(new Point3d(0, 500, 500));
bombs.Add(new Point3d(1000, 500, 500));
bombs.Add(new Point3d(500, 0, 500));
bombs.Add(new Point3d(500, 1000, 500));
bombs.Add(new Point3d(500, 500, 0));
bombs.Add(new Point3d(500, 500, 1000));
Console.WriteLine("{0} bombs - eg {1}", bombs.Count, bombs.First());
Console.WriteLine();
FindSafest(bombs);
}
static void FindSafest(List<Point3d> bombs)
{
var bombsByZ = bombs.OrderBy(b => b.Z).ToArray();
int bestRad = 0;
var bestPlace = new Point3d();
// Basic algorithm - each x = x1, y = y1 defines a line of CubeSize points for each Z
// Project each bomb with current best radius onto this line to find
// section where the sphere around each bomb intersects
// Then, only need to check Z values not in these intersections
for (int x = 0; x < CubeSize; x++)
{
for (int y = 0; y < CubeSize; y++)
{
var exclusions = ProjectBombs(x, y, bombsByZ, bestRad);
int oldRad = bestRad;
foreach (int z in ValuesLeft(exclusions))
{
var p = new Point3d(x, y, z);
int candidate = FindMinRadius(p, bombs);
if (candidate > bestRad)
{
bestRad = candidate;
bestPlace = p;
}
}
if (bestRad > oldRad)
{
Console.WriteLine("{0,20} : Cursor : {1} : Found new radius of {2}", TimeStamp(), bestPlace, bestRad);
}
}
}
Console.WriteLine("Total Time = {0}", s_timer.Elapsed);
Console.WriteLine("Safest radius {0} @ {1}", bestRad, bestPlace);
}
