leetcode149

   /*
      *  A line is determined by two factors,say y=ax+b
      *
      *  If two points(x1,y1) (x2,y2) are on the same line(Of course). 

      *  Consider the gap between two points.

      *  We have (y2-y1)=a(x2-x1),a=(y2-y1)/(x2-x1) a is a rational, b is canceled since b is a constant

      *  If a third point (x3,y3) are on the same line. So we must have y3=ax3+b

      *  Thus,(y3-y1)/(x3-x1)=(y2-y1)/(x2-x1)=a

      *  Since a is a rational, there exists y0 and x0, y0/x0=(y3-y1)/(x3-x1)=(y2-y1)/(x2-x1)=a

      *  So we can use y0&x0 to track a line;
      */

     public class Solution{
         public int maxPoints(Point[] points) {
             if (points==null) return 0;
             if (points.length<=2) return points.length;

             Map<Integer,Map<Integer,Integer>> map = new HashMap<Integer,Map<Integer,Integer>>();
             int result=0;
             for (int i=0;i<points.length;i++){
                 map.clear();
                 int overlap=0,max=0;
                 for (int j=i+1;j<points.length;j++){
                     int x=points[j].x-points[i].x;
                     int y=points[j].y-points[i].y;
                     if (x==0&&y==0){
                         overlap++;
                         continue;
                     }
                     int gcd=generateGCD(x,y);
                     if (gcd!=0){
                         x/=gcd;
                         y/=gcd;
                     }

                     if (map.containsKey(x)){
                         if (map.get(x).containsKey(y)){
                             map.get(x).put(y, map.get(x).get(y)+1);
                         }else{
                             map.get(x).put(y, 1);
                         }
                     }else{
                         Map<Integer,Integer> m = new HashMap<Integer,Integer>();
                         m.put(y, 1);
                         map.put(x, m);
                     }
                     max=Math.max(max, map.get(x).get(y));
                 }
                 result=Math.max(result, max+overlap+1);
             }
             return result;

         }
         private int generateGCD(int a,int b){

             if (b==0) return a;
             else return generateGCD(b,a%b);

         }
     }

参考：https://leetcode.com/problems/max-points-on-a-line/discuss/47113/A-java-solution-with-notes