问题更新后
使用两个 Red-Black Tree 或 Skip_list 映射。两者都是紧凑的自平衡数据结构，为您提供 O(log n) 时间进行搜索、插入和删除操作。一张地图将使用每个点的 X 坐标作为键，将点本身作为值，另一张地图将使用 Y 坐标作为键，将点本身作为值。
作为权衡，我建议最初将光标周围的搜索区域限制为一个正方形。为了完美匹配，正方形边应等于光标周围“敏感圈”的直径。即，如果您只对距离光标 10 像素半径内的最近邻感兴趣，那么正方形边需要为 20px。作为替代，如果你在寻找最近的邻居而不考虑距离，你可以尝试通过评估相对于光标的地板和天花板来动态找到边界。
然后从地图中检索边界内的两个点子集，合并以仅包括两个子集中的点。
遍历结果，计算与每个点的接近度（dx^2+dy^2，避免平方根，因为您对实际距离不感兴趣，只关心接近度），找到最近的邻居。
从邻域图中取平方根来测量到最近邻的距离，看它是否大于“敏感圈”的半径，如果是则表示圆内没有点。
我建议对每种方法都进行一些基准测试；通过优化可以轻松超越两个方面。在我的普通硬件 (Duo Core 2) 上，在 Java 中重复 1000 次重复 1000 次的简单单线程搜索最近的邻居需要 350 毫秒。只要整体 UI 响应时间低于 100 毫秒，用户就会觉得它是即时的，请记住，即使是简单的搜索也可能会给您足够快的响应。
通用解决方案
最有效的数据结构取决于您计划使用的算法、时空权衡和预期的点相对分布：
因此，评估数据结构与算法的隔离是不可能的，如果没有对任务约束和优先级的良好了解，就很难评估。
Java 实现示例
import java.util.*;
import java.util.concurrent.ConcurrentSkipListMap;
class Test
{
public static void main (String[] args)
{
Drawing naive = new NaiveDrawing();
Drawing skip = new SkipListDrawing();
long start;
start = System.currentTimeMillis();
testInsert(naive);
System.out.println("Naive insert: "+(System.currentTimeMillis() - start)+"ms");
start = System.currentTimeMillis();
testSearch(naive);
System.out.println("Naive search: "+(System.currentTimeMillis() - start)+"ms");
start = System.currentTimeMillis();
testInsert(skip);
System.out.println("Skip List insert: "+(System.currentTimeMillis() - start)+"ms");
start = System.currentTimeMillis();
testSearch(skip);
System.out.println("Skip List search: "+(System.currentTimeMillis() - start)+"ms");
}
public static void testInsert(Drawing d)
{
Random r = new Random();
for (int i=0;i<100000;i++)
d.addPoint(new Point(r.nextInt(4096),r.nextInt(2048)));
}
public static void testSearch(Drawing d)
{
Point cursor;
Random r = new Random();
for (int i=0;i<1000;i++)
{
cursor = new Point(r.nextInt(4096),r.nextInt(2048));
d.getNearestFrom(cursor,10);
}
}
}
// A simple point class
class Point
{
public Point (int x, int y)
{
this.x = x;
this.y = y;
}
public final int x,y;
public String toString()
{
return "["+x+","+y+"]";
}
}
// Interface will make the benchmarking easier
interface Drawing
{
void addPoint (Point p);
Set<Point> getNearestFrom (Point source,int radius);
}
class SkipListDrawing implements Drawing
{
// Helper class to store an index of point by a single coordinate
// Unlike standard Map it's capable of storing several points against the same coordinate, i.e.
// [10,15] [10,40] [10,49] all can be stored against X-coordinate and retrieved later
// This is achieved by storing a list of points against the key, as opposed to storing just a point.
private class Index
{
final private NavigableMap<Integer,List<Point>> index = new ConcurrentSkipListMap <Integer,List<Point>> ();
void add (Point p,int indexKey)
{
List<Point> list = index.get(indexKey);
if (list==null)
{
list = new ArrayList<Point>();
index.put(indexKey,list);
}
list.add(p);
}
HashSet<Point> get (int fromKey,int toKey)
{
final HashSet<Point> result = new HashSet<Point> ();
// Use NavigableMap.subMap to quickly retrieve all entries matching
// search boundaries, then flatten resulting lists of points into
// a single HashSet of points.
for (List<Point> s: index.subMap(fromKey,true,toKey,true).values())
for (Point p: s)
result.add(p);
return result;
}
}
// Store each point index by it's X and Y coordinate in two separate indices
final private Index xIndex = new Index();
final private Index yIndex = new Index();
public void addPoint (Point p)
{
xIndex.add(p,p.x);
yIndex.add(p,p.y);
}
public Set<Point> getNearestFrom (Point origin,int radius)
{
final Set<Point> searchSpace;
// search space is going to contain only the points that are within
// "sensitivity square". First get all points where X coordinate
// is within the given range.
searchSpace = xIndex.get(origin.x-radius,origin.x+radius);
// Then get all points where Y is within the range, and store
// within searchSpace the intersection of two sets, i.e. only
// points where both X and Y are within the range.
searchSpace.retainAll(yIndex.get(origin.y-radius,origin.y+radius));
// Loop through search space, calculate proximity to each point
// Don't take square root as it's expensive and really unneccessary
// at this stage.
//
// Keep track of nearest points list if there are several
// at the same distance.
int dist,dx,dy, minDist = Integer.MAX_VALUE;
Set<Point> nearest = new HashSet<Point>();
for (Point p: searchSpace)
{
dx=p.x-origin.x;
dy=p.y-origin.y;
dist=dx*dx+dy*dy;
if (dist<minDist)
{
minDist=dist;
nearest.clear();
nearest.add(p);
}
else if (dist==minDist)
{
nearest.add(p);
}
}
// Ok, now we have the list of nearest points, it might be empty.
// But let's check if they are still beyond the sensitivity radius:
// we search area we have evaluated was square with an side to
// the diameter of the actual circle. If points we've found are
// in the corners of the square area they might be outside the circle.
// Let's see what the distance is and if it greater than the radius
// then we don't have a single point within proximity boundaries.
if (Math.sqrt(minDist) > radius) nearest.clear();
return nearest;
}
}
// Naive approach: just loop through every point and see if it's nearest.
class NaiveDrawing implements Drawing
{
final private List<Point> points = new ArrayList<Point> ();
public void addPoint (Point p)
{
points.add(p);
}
public Set<Point> getNearestFrom (Point origin,int radius)
{
int prevDist = Integer.MAX_VALUE;
int dist;
Set<Point> nearest = Collections.emptySet();
for (Point p: points)
{
int dx = p.x-origin.x;
int dy = p.y-origin.y;
dist = dx * dx + dy * dy;
if (dist < prevDist)
{
prevDist = dist;
nearest = new HashSet<Point>();
nearest.add(p);
}
else if (dist==prevDist) nearest.add(p);
}
if (Math.sqrt(prevDist) > radius) nearest = Collections.emptySet();
return nearest;
}
}