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Friday, December 12, 2014

Max points on a line

I don't think this one is a very hard one as long as all the conditions are considered:

1. duplicate points;
2. share lines parallel to y-axis;
3. share lines parallel to x-axis;
4. slopes.

Use a HashMap to store <slope, number of points> pair.


 class Point {
      int x;
      int y;
      Point() { x = 0; y = 0; }
      Point(int a, int b) { x = a; y = b; }
  }
 
public class MaxPointsonALine {
    public int maxPoints(Point[] points) {
        if (points == null || points.length == 0)
            return 0;
        HashMap hm = new HashMap();
        int max = 1;
        
        for (int i = 0; i < points.length; i++)
        {
            //Reinitialize the map since the shared points of each point are different
            hm.clear();
            //put the point itself into the map, use Integer_MIN_VALUE as the key
            hm.put((double)Integer.MIN_VALUE, 1);
            //in case there are duplicates in the array
            int dupli = 0;
            //all the shared points prior to i has been checked in the previous loops, thus we only need to
            //consider shared points after i
            for (int j = i + 1; j < points.length; j++)
            {
                //here comes the duplicates
                if (points[j].x == points[i].x && points[j].y == points[i].y)
                {
                    dupli++;
                    continue;
                }
                double key = 0.0;
                //share a line parallel to y-axis, we know the slop = infinity
               if (points[j].x == points[i].x)
                    key = (double)Integer.MAX_VALUE;
                //just the slope
                // because (double)0/-1 is -0.0, so we should use 0.0+-0.0=0.0 to solve 0.0 !=-0.0
                // problem
                else
                    key = 0.0 + 
                    (double)(points[j].y - points[i].y) / (double)(points[j].x - points[i].x);
                
                if (!hm.containsKey(key))
                    hm.put(key, 2);
                else
                    hm.put(key, hm.get(key) + 1);
                
            }
            //now we add duplicates to the values in the map and compare them with the max
            for (int tmp : hm.values())
            {
                if (tmp + dupli > max)
                    max = tmp + dupli;
            }
        }
        return max;
    }
}

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