CareerCup

O(nlogn) Solution.
1. consider the given view point as center of axis and calculate the angle of each point.
2. sort the angles
3. find the maximum window in the sorted list with max difference of given viewing angle.

import java.util.Collections;
import java.util.LinkedList;
import java.util.List;

/**
 * Created by paras.mal on 14/11/16.
 */
public class A2 {


    static class Point{

        int x,  y;
        public Point(int x, int y){
            this.x = x;
            this.y = y;
        }

    }
    public static double getAngle(int x, int y, int x1, int y1){

        x = x1-x;
        y = y1-y;

        if(x > 0 && y >= 0){
            return Math.toDegrees(Math.asin(Math.abs(y) / Math.sqrt(x * x + y * y)));
        }

        if(x<=0 && y>0){
            return Math.toDegrees(Math.asin(Math.abs(x)/Math.sqrt(x*x + y*y))) + 90;
        }

        if( x < 0 && y<=0){
            return Math.toDegrees(Math.asin(Math.abs(y)/Math.sqrt(x*x + y*y))) + 180;
        }
        if( x >= 0 && y<0){
            return Math.toDegrees(Math.asin(Math.abs(x)/Math.sqrt(x*x + y*y))) + 270;
        }


        throw new RuntimeException();



    }

    public static void main(String s[]){
        List<Point> points = new LinkedList<>();

        points.add(new Point(2,1));
        points.add(new Point(2,2));
        points.add(new Point(1,2));
        points.add(new Point(0,2));
        points.add(new Point(0,1));
        points.add(new Point(0,0));
        points.add(new Point(1,0));
        points.add(new Point(2,0));

        List<Double> d= new LinkedList<>();
        int x1 = 1,y1 = 1;
        points.stream().forEach((x) -> d.add(getAngle(x1, y1, x.x, x.y)));
        Collections.sort(d);
        int i = 0, j = 0;
        int diff = 0;
        int check = 90;
        int i1 =0, j1 =0;
        while(j<d.size() && i<d.size()){
            while(j<d.size() && d.get(j)-d.get(i) <= check){
                if(j1-i1 < j-i && d.get(j)-d.get(i) <= check){
                    j1 = j;
                    i1 = i;
                }
                j++;
            }
            while( i <= j && j < d.size() && d.get(j)-d.get(i) > check){
                i++;
            }
        }
    }

}

1. make the points angle based = angleArray
2. sort angleArray nlogn
3. for i in range(0,len(angleArray):
count how many enter in you window. = tempSum = max
4. move to next point where the is tempSum = tempSum-1 + count untill you exeed the window (you continue from the index you stopped you dont go back) so you just do here O(n)
5. if tempSum > max then max = tempSum