Finds the two closest points from a list of points. — http://ideone.com/NaB5Gb

ClosestPoints.java

import java.util.ArrayList;

class ClosestPoints
{
	public static void main (String[] args) throws java.lang.Exception
	{
		CoordSystem coords = new CoordSystem();
		
		coords.addPoint(new Point(3, 4));
		coords.addPoint(new Point(1, 2));
		coords.addPoint(new Point(-3, 0));
		coords.addPoint(new Point(7, -5));
		coords.addPoint(new Point(1, 0));
		coords.addPoint(new Point(8, -4));
		
		CoordSystem closestPoints = Distance.minimumDistance(coords);
		
		System.out.println("The closest points are:");
		Display.displayPoints(closestPoints);
		System.out.print("The distance between those points is: ");
		System.out.println(Distance.distance(closestPoints.getPoint(0), closestPoints.getPoint(1)));
	}
}

class Display
{
	public static void displayPoints(CoordSystem coords)
	{
		for (int i = 0; i < coords.numberOfPoints(); i++)
			System.out.println(coords.getPoint(i));
	}
}

class Distance
{
	public static double distance(Point pointOne, Point pointTwo)
	{
		int xDiff, yDiff;
		
		xDiff = pointOne.getX() - pointTwo.getX();
		yDiff = pointOne.getY() - pointTwo.getY();
		
		return Math.sqrt(xDiff * xDiff + yDiff * yDiff);
	}
	
	public static CoordSystem minimumDistance(CoordSystem points)
	{
		CoordSystem minDistPoints = new CoordSystem();
		double minDist = Double.MAX_VALUE;
		
		Point pointOne;
		Point pointTwo;
		double dist;
		
		for (int i = 0; i < points.numberOfPoints(); i++)
		{
			pointOne = points.getPoint(i);
			
			for (int j = 0; j < points.numberOfPoints(); j++)
			{
				if (i != j)
				{
					pointTwo = points.getPoint(j);
					dist = distance(pointOne, pointTwo);
					if (dist < minDist) {
						minDistPoints = new CoordSystem();
						minDistPoints.addPoint(pointOne);
						minDistPoints.addPoint(pointTwo);
						minDist = dist;
					}
				}
			}
		}
		return minDistPoints;
	}
}

class CoordSystem
{
	private ArrayList<Point> points;
	
	CoordSystem()
	{
		points = new ArrayList<Point>();
	}
	
	public ArrayList<Point> getAllPoints()
	{ return points; }
	
	public Point getPoint(int i)
	{ return points.get(i); }
	
	public CoordSystem getPointsWithX(int x)
	{
		CoordSystem matches = new CoordSystem();
		
		Point point;
		
		for (int i = 0; i < points.size(); i++)
		{
			point = getPoint(i);
			if (point.getX() == x)
				matches.addPoint(point);
		}
		
		return matches;
	}
	
	public CoordSystem getPointsWithY(int y)
	{
		CoordSystem matches = new CoordSystem();
		
		Point point;
		
		for (int i = 0; i < points.size(); i++)
		{
			point = getPoint(i);
			if (point.getY() == y)
				matches.addPoint(point);
		}
		
		return matches;
	}
	
	public void addPoint(Point point)
	{
		points.add(point);
	}
	
	public boolean hasMatchingPoint(Point other)
	{
		for (int i = 0; i < points.size(); i++)
		{
			if (getPoint(i) == other)
				return true;
		}
		return false;
	}
	
	public int numberOfPoints()
	{ return points.size(); }
}

class Point
{
	private int x;
	private int y;
	
	Point()
	{
		x = 0;
		y = 0;
	}
	
	Point(int x_, int y_)
	{
		x = x_;
		y = y_;
	}
	
	public int getX()
	{ return x; }
	
	public int getY()
	{ return y; }
	
	public boolean equals(Object obj)
	{
		Point other = (Point) obj;
		return x == other.x && y == other.y;
	}
	
	public String toString()
	{ return "(" + x + ", " + y + ")"; }
}