我写了这个算法。在我的短测试用例中它可以工作,但是对于更大的输入太慢了。我该如何让它更快?
// Returns an array of length 2 with the two closest points to each other from the
// original array of points "arr"
private static Point2D[] getClosestPair(Point2D[] arr)
{
int n = arr.length;
float min = 1.0f;
float dist = 0.0f;
Point2D[] ret = new Point2D[2];
// If array only has 2 points, return array
if (n == 2) return arr;
// Algorithm says to brute force at 3 or lower array items
if (n <= 3)
{
for (int i = 0; i < arr.length; i++)
{
for (int j = 0; j < arr.length; j++)
{
// If points are identical but the point is not looking
// at itself, return because shortest distance is 0 then
if (i != j && arr[i].equals(arr[j]))
{
ret[0] = arr[i];
ret[1] = arr[j];
return ret;
}
// If points are not the same and current min is larger than
// current stored distance
else if (i != j && dist < min)
{
dist = distanceSq(arr[i], arr[j]);
ret[0] = arr[i];
ret[1] = arr[j];
min = dist;
}
}
}
return ret;
}
int halfN = n/2;
// Left hand side
Point2D[] LHS = Arrays.copyOfRange(arr, 0, halfN);
// Right hand side
Point2D[] RHS = Arrays.copyOfRange(arr, halfN, n);
// Result of left recursion
Point2D[] LRes = getClosestPair(LHS);
// Result of right recursion
Point2D[] RRes = getClosestPair(RHS);
float LDist = distanceSq(LRes[0], LRes[1]);
float RDist = distanceSq(RRes[0], RRes[1]);
// Calculate minimum of both recursive results
if (LDist > RDist)
{
min = RDist;
ret[0] = RRes[0];
ret[1] = RRes[1];
}
else
{
min = LDist;
ret[0] = LRes[0];
ret[1] = LRes[1];
}
for (Point2D q : LHS)
{
// If q is close to the median line
if ((halfN - q.getX()) < min)
{
for (Point2D p : RHS)
{
// If p is close to q
if ((p.getX() - q.getX()) < min)
{
dist = distanceSq(q, p);
if (!q.equals(p) && dist < min)
{
min = dist;
ret[0] = q;
ret[1] = p;
}
}
}
}
}
return ret;
}
private static float distanceSq(Point2D p1, Point2D p2)
{
return (float)Math.pow((p1.getX() - p2.getX()) + (p1.getY() - p2.getY()), 2);
}
我大致遵循这里解释的算法: http://www.cs.mcgill.ca/~cs251/ClosestPair/ClosestPairDQ.html以及一个不同的伪代码资源:
http://i.imgur.com/XYDTfBl.png
我无法更改函数的返回类型或添加任何新的参数。
感谢您的帮助!
if ((p.getX() - q.getX()) < min)
我已经在min = 0
时添加了早期退出,并实现了您的建议,但最多只能节省几毫秒。还有其他想法吗? - Dan