public static void TestClosestPairOfPoints()
{
Point[] allPoints = new Point[] { new Point(2, 3), new Point(12, 30), new Point(40, 50), new Point(5, 1), new Point(12, 10), new Point(3, 4) };
ClosestPairOfPoints cp = new ClosestPairOfPoints();
PairOfPoints pair = cp.GetTheClosestPoint(allPoints);
Console.WriteLine("The closest pair of points are {0} and {1} and the minDistance is {2}", pair.PointA.ToString(), pair.PointB.ToString(), pair.Distance);
}
/// <summary>
/// this the merge subroutine of the divide and conquer approach
/// </summary>
/// <param name="pointsInStrip">this is the points present in the strip. These points are sorted wrt y axis</param>
/// <param name="min">the current pair of points with minimum distance</param>
/// <returns>pair of points with minimum distance after merging the 2 space</returns>
private PairOfPoints Combine(List <Point> pointsInStrip, PairOfPoints min)
{
// Note this operations should take O(n) running time
// it can be geometrically proven that each point in the strip needs to be compared with atmost 6 other points
for (int i = 0; i < pointsInStrip.Count; i++)
{
for (int j = i + 1; j < pointsInStrip.Count; j++)
{
if (pointsInStrip[j].Ycoordinate - pointsInStrip[i].Ycoordinate > min.Distance)
{
// there is no point in checking more than j cause the distance will always ne greater than min.Distance
break;
}
PairOfPoints currentPair = new PairOfPoints(pointsInStrip[i], pointsInStrip[j]);
if (currentPair.Distance < min.Distance)
{
min = currentPair;
}
}
}
return(min);
}
/// <summary>
/// This is the divide subroutine in divide and conquer approach
/// Here we divide the space into left and right and get the pair of points with minimum distance
/// and then call the combine subroutine and return the pair of points with minimum distance
/// </summary>
/// <param name="ptsSortedByX">points sorted wrt x axis</param>
/// <param name="ptsSortedByY">points sorted wrt y axis</param>
/// <returns>pair of points with minimum distance</returns>
private PairOfPoints GetClosestPointsSubroutine(Point[] ptsSortedByX, Point[] ptsSortedByY)
{
//Base case
if (ptsSortedByX.Length < 2)
{
return(new PairOfPoints());
}
else if (ptsSortedByX.Length == 2)
{
return(new PairOfPoints(ptsSortedByX[0], ptsSortedByX[1]));
}
int midIndex = ptsSortedByX.Length / 2;
Point[] pointsOnLeftSideSortedByY = new Point[midIndex];
Point[] pointsOnRightSideSortedByY = new Point[ptsSortedByX.Length - (midIndex)]; // Element at the midIndex will lie on the right side
Point[] pointsOnLeftSideSortedByX = new Point[midIndex];
Point[] pointsOnRightSideSortedByX = new Point[ptsSortedByX.Length - (midIndex)]; // Element at the midIndex will lie on the right side
int leftIndex = 0;
int rightIndex = 0;
// Divide the ptsSortedByY into left and right of the line perpendicular to the x-axis and passing from the midIndex
for (int i = 0; i < ptsSortedByY.Length; i++)
{
if (ptsSortedByY[i].Xcoordinate <= ptsSortedByX[midIndex].Xcoordinate && leftIndex < midIndex)
{
// this condition is used in case where there are duplicate Points with same Xcoordinates
// and one point is the one in midIndex
pointsOnLeftSideSortedByY[leftIndex++] = ptsSortedByY[i];
}
else
{
pointsOnRightSideSortedByY[rightIndex++] = ptsSortedByY[i];
}
if (i < midIndex)
{
pointsOnLeftSideSortedByX[i] = ptsSortedByX[i];
}
else
{
pointsOnRightSideSortedByX[i - midIndex] = ptsSortedByX[i];
}
}
// Now solve the subproblem
PairOfPoints leftMinPair = GetClosestPointsSubroutine(pointsOnLeftSideSortedByX, pointsOnLeftSideSortedByY);
PairOfPoints rightMinPair = GetClosestPointsSubroutine(pointsOnRightSideSortedByX, pointsOnRightSideSortedByY);
//get the min
PairOfPoints min = leftMinPair;
if (min.Distance > rightMinPair.Distance)
{
min = rightMinPair;
}
//Create the list with all the points in the strip
List <Point> pointsInStrip = new List <Point>();
for (int i = 0; i < ptsSortedByY.Length; i++)
{
if (Math.Abs(ptsSortedByX[midIndex].Xcoordinate - ptsSortedByY[i].Xcoordinate) <= min.Distance)
{
pointsInStrip.Add(ptsSortedByY[i]);
}
}
//Combine the left and right
return(Combine(pointsInStrip, min));
}