@Override
public int compare(PointInt o1, PointInt o2) {
return ComparisonChain.start()
.compare(o1.getX(), o2.getX())
.compare(o1.getY(), o2.getY())
.result();
}
public double findMinPerim(int leftIndex, int rightIndex, List<PointInt> listPointsSortedY) {
int numberOfPoints = rightIndex - leftIndex + 1;
Preconditions.checkArgument(listPointsSortedY.size() == numberOfPoints);
if (numberOfPoints < 3) {
return Double.MAX_VALUE;
}
int leftHalfEndIndex = leftIndex + numberOfPoints / 2 - 1;
int rightHalfStartIndex = leftHalfEndIndex + 1;
Preconditions.checkState(rightHalfStartIndex <= rightIndex);
double min = Double.MAX_VALUE;
/*
* In order to avoid having to do another sort by y, (taking n log n), we just split using the sortedY list
*/
List<PointInt> leftList = new ArrayList<>(leftHalfEndIndex - leftIndex + 1);
List<PointInt> rightList = new ArrayList<>(rightIndex - rightHalfStartIndex + 1);
// We must compare x and y because though we are partitioning by a vertical line, we must also
// be able to partition if all points have the same x
// Because the partition is strictly less and due to rounding error from longs,
// we use this as the division point
PointInt midPoint = list.get(rightHalfStartIndex);
for (PointInt pl : listPointsSortedY) {
// Verify the points are still between left and right index
Preconditions.checkState(list.get(leftIndex).getX() <= pl.getX());
Preconditions.checkState(list.get(rightIndex).getX() >= pl.getX());
if (compX.compare(pl, midPoint) < 0) {
leftList.add(pl);
} else {
rightList.add(pl);
}
}
Preconditions.checkState(leftList.size() == numberOfPoints / 2);
Preconditions.checkState(leftList.size() > 0);
Preconditions.checkState(rightList.size() > 0);
Preconditions.checkState(leftHalfEndIndex != rightIndex);
Preconditions.checkState(rightHalfStartIndex != leftIndex);
Preconditions.checkState(numberOfPoints == leftList.size() + rightList.size());
// Divide
double minLeft = findMinPerim(leftIndex, leftHalfEndIndex, leftList);
double minRight = findMinPerim(rightHalfStartIndex, rightIndex, rightList);
min = Math.min(minLeft, minRight);
/*
* For the combine, we make a box.
* Left bound is min / 2 from vertical line, right bound is min / 2.
*
* Reason being that any triangle covering the vertical line and with a
* point greater than min / 2 would have a perimeter > min.
*/
int boxMargin =
DoubleMath.roundToInt(
(min > Double.MAX_VALUE / 2 ? Integer.MAX_VALUE : min) / 2d, RoundingMode.UP);
Preconditions.checkState(min > Integer.MAX_VALUE || boxMargin < min);
Preconditions.checkState(min > Integer.MAX_VALUE || boxMargin * 2 >= min);
List<PointInt> boxPoints = new ArrayList<>();
int startBox = 0;
for (int i = 0; i < listPointsSortedY.size(); ++i) {
PointInt point = listPointsSortedY.get(i);
if (Math.abs(point.getX() - midPoint.getX()) > boxMargin) {
continue;
}
// Calculate start of the box to consider. Should be at most
// boxMargin away from currenty point. End of box is the last point added
while (startBox < boxPoints.size()
&& point.getY() - boxPoints.get(startBox).getY() > boxMargin) {
startBox++;
}
/**
* To explain this, the box goes from -minP / 2 to + minP / 2 from the dividing vertical line.
* Its height is also minP / 2.
*
* <p>Because we have the minimum with respect to the left and right sides, all triangles to
* the left and right have max perimiter <= minP.
*
* <p>The only way to cram 16 points is to have 2 points on each corner and in the middle
*
* <p>PP-------PP--------PP
*
* <p>PP PP
*
* <p>PP-------PP--------PP
*
* <p>The perim of any triangle is >= minP. Any other point would be a triangle of perim <
* minP.
*/
Preconditions.checkState(boxPoints.size() - startBox <= 16);
// Consider all points in box (can be proved <= 16...Similar to most 6 for closest 2 points
// algorithm
for (int bi = startBox; bi < boxPoints.size(); ++bi) {
for (int j = bi + 1; j < boxPoints.size(); ++j) {
double perim =
point.distance(boxPoints.get(bi))
+ point.distance(boxPoints.get(j))
+ boxPoints.get(bi).distance(boxPoints.get(j));
min = Math.min(min, perim);
}
}
boxPoints.add(point);
}
return min;
}
