LeetCode 149. Max Points on a Line

Description

https://leetcode.com/problems/max-points-on-a-line/

给定平面内n个点，求同一直线上的点的最大个数。

Solving Ideas

https://blog.csdn.net/qq_32767041/article/details/88386459

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

时间复杂度：$O(n^2)$
空间复杂度：$O(n)$

Solution

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<>();
        int res = 0;
        for (int i = 0; i < points.length; i++) {
            int overlap = 0, count = 0;
            for (int j = i + 1; j < points.length; j++) {
                int dx = points[j].x - points[i].x;
                int dy = points[j].y - points[i].y;

                if (dx == 0 && dy == 0) {
                    overlap++;
                    continue;
                }

                int gcd = gcd(dx, dy);
                dx /= gcd;
                dy /= gcd;

                if (map.containsKey(dx)) {
                    if (map.get(dx).containsKey(dy)) {
                        map.get(dx).put(dy, map.get(dx).get(dy) + 1);
                    } else {
                        map.get(dx).put(dy, 1);
                    }
                } else {
                    Map<Integer, Integer> m = new HashMap<>();
                    m.put(dy, 1);
                    map.put(dx, m);
                }
                count = Math.max(count, map.get(dx).get(dy));
            }
            res = Math.max(res, count + 1 + overlap);
            map.clear();
        }
        return res;
    }

    private int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }
}