Max Points on a Line

Given n points on a 2D plane, find the maximum number of points that lie on the same straight line.

难度：hard

Solution: Hashtable

/**
 * Definition for a point.
 * class Point {
 *     int x;
 *     int y;
 *     Point() { x = 0; y = 0; }
 *     Point(int a, int b) { x = a; y = b; }
 * }
 */
public class Solution {
    public int maxPoints(Point[] points) {
        int maxNumPoints = 0;
        for(int i = 0; i < points.length; ++i) {
            Map<String, Integer> map = new HashMap<>();
            int duplicates = 0, maxCount = 0;
            for(int j = 0; j < points.length; ++j) {
                int x = points[i].x - points[j].x;
                int y = points[i].y - points[j].y;
                if(x == 0 && y == 0) {
                    ++duplicates;
                } else if(x == 0 && y != 0) {
                    String key = 0 + " " + 1;
                    int count = map.containsKey(key) ? map.get(key) + 1 : 1;
                    map.put(key, count);
                    maxCount = Math.max(maxCount, count);
                } else if(x != 0 && y == 0) {
                    String key = 1 + " " + 0;
                    int count = map.containsKey(key) ? map.get(key) + 1 : 1;
                    map.put(key, count);
                    maxCount = Math.max(maxCount, count);
                } else {
                    int r = gcd(x, y);
                    x /= r;
                    y /= r;
                    String key = x + " " + y;
                    int count = map.containsKey(key) ? map.get(key) + 1 : 1;
                    map.put(key, count);
                    maxCount = Math.max(maxCount, count);
                }
            }
            maxNumPoints = Math.max(maxNumPoints, maxCount + duplicates);
        }
        return maxNumPoints;
    }
    private int gcd(int p, int q) {
        if(q == 0) {
            return p;
        }
        int r = p % q;
        return gcd(q, r);
    }
}