public static int FindBestRegion(IEnumerable <string> input, int maxDistance)
{
var locations = input.Select((s, i) => Loc.FromString(i + 1, s)).ToList();
// borders
var fromX = locations.Min(l => l.X);
var toX = locations.Max(l => l.X);
var fromY = locations.Min(l => l.Y);
var toY = locations.Max(l => l.Y);
// for each coordinate, compute the sum of the distances to all coordinates
var sumDistanceMap = Enumerable.Range(fromX, toX - fromX + 1)
.SelectMany(x => Enumerable.Range(fromY, toY - fromY + 1)
.Select(y => new { X = x, Y = y, SumOfDistances = locations.Select(l => l.DistanceTo(x, y)).Sum() }));
return(sumDistanceMap.Count(c => c.SumOfDistances < maxDistance));
}
public static int FindBestLocationArea(IEnumerable <string> input)
{
// idea -> iterate over the smallest grid (as defined by (min,max) coordinates)
// for every point compute the closest coord and increase the counter for it
// solution is max of those counters for those who are not infinite
// a location has infinite area when a border point is closest to that location
var locations = input.Select((s, i) => Loc.FromString(i + 1, s)).ToList();
// borders
var fromX = locations.Min(l => l.X);
var toX = locations.Max(l => l.X);
var fromY = locations.Min(l => l.Y);
var toY = locations.Max(l => l.Y);
// helper function
int ClosestLocationFrom(int x, int y)
{
var distances = locations.Select(l => new { l.Id, Distance = l.DistanceTo(x, y) });
var minDistance = distances.Min(d => d.Distance);
var minDistanceLocs = distances.Where(d => d.Distance == minDistance).ToList();
return(minDistanceLocs.Count == 1 ? minDistanceLocs[0].Id : 0); // 0 means: multiple locations closer
}
// compute closest location for each point of the grid
var closestLocations = Enumerable.Range(fromX, toX - fromX + 1)
.SelectMany(x => Enumerable.Range(fromY, toY - fromY + 1)
.Select(y => new { X = x, Y = y, Closest = ClosestLocationFrom(x, y) }));
// find all the "infinite locations" (i.e. they touch the border) and remove them, also remove non-clear locations (0)
var locationsWithInfiniteArea = closestLocations.Where(l => l.Closest == 0 || l.X == fromX || l.X == toX || l.Y == fromY || l.Y == toY).Select(l => l.Closest).ToHashSet();
var closestLocationsWithoutInfinites = closestLocations.Where(l => !locationsWithInfiniteArea.Contains(l.Closest));
// count what's left and select the winner
var areas = closestLocationsWithoutInfinites.GroupBy(l => l.Closest).Select(gl => new { Id = gl.Key, Count = gl.Count() });
var maxArea = areas.Max(a => a.Count);
var maxAreaId = areas.First(a => a.Count == maxArea); // for info only
return(maxArea);
}