149 Max Points on a Line 直线上最多的点数

Posted 2020-10-29 lina2014

给定二维平面上有 n 个点，求最多有多少点在同一条直线上。

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

Java实现：

/**
 * Definition for a point.
 * class Point {
 *     int x;
 *     int y;
 *     Point() { x = 0; y = 0; }
 *     Point(int a, int b) { x = a; y = b; }
 * }
 */
class Solution {
    public int maxPoints(Point[] points) {
        if (points == null || points.length == 0){
            return 0;
        }
        Map<String, List<Point>> slopes = new HashMap<>();
        int res = 0;
        for (int i = 0; i < points.length; i++){
            //starting from different points, could be same slope but they are not in a line
            slopes = new HashMap<String, List<Point>>();
            int samePoints = 1;
            int max = 0;
            for (int j = i + 1; j < points.length; j++){
                int deltaY = points[j].y - points[i].y;
                int deltaX = points[j].x - points[i].x;
                if (deltaY == 0 && deltaX == 0){
                    samePoints++;
                    continue;
                }
                int gcd = getGCD(deltaX, deltaY);
                deltaY /= gcd;
                deltaX /= gcd;
                String slope = deltaY + ":" + deltaX;
                if (!slopes.containsKey(slope)){
                    slopes.put(slope, new ArrayList<Point>());
                }
                slopes.get(slope).add(points[j]);
                max = Math.max(max, slopes.get(slope).size());
            }
            res = Math.max(res, max + samePoints);
        }
        return res;
    }

    private int getGCD(int a, int b){
        if (b == 0){
            return a;
        } else {
            return getGCD(b, a % b);
        }
    }
}

参考：https://www.jianshu.com/p/0073d059687d