[leetcode]给定二维平面上的n个点，找出位于同一直线上的点的最大数目

给定二维平面上的n个点，找出位于同一直线上的点的最大数目。

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

public class Solution {
    public int maxPoints(Point[] points) {
        //验证一下输入
        if (points == null || points.length == 0){
            return 0;
        }

        //一个点或者两个点直接返回值
        if (points.length < 3){
            return points.length;
        }

        int max = 2;
        int sameSlopePoint;//相同斜率的点
        int samePoint;//相同的点

        for (int i = 0; i < points.length; i++){
            //初始化一下，刚开始相同点都为零
            samePoint = 0;

            for(int j = i+1; j < points.length; j++){
                sameSlopePoint = 1;//两点确定一条直线，这个点也应该纳入总数
                int XDistance = points[j].x - points[i].x;
                int YDistance = points[j].y - points[i].y;

                if (XDistance == 0 && YDistance ==0){//特殊情况：与第一个点同一位置的点，这时候不用计算后面，因为两点在同一位置，不能确定一条直线
                    samePoint++;
                }else{
                    sameSlopePoint = 2;
                    for(int k = j+1; k < points.length; k++){//找剩下斜率相同的点，三点的斜率相同则肯定在一条直线上
                        int XDistance2 = points[k].x - points[i].x;
                        int YDistance2 = points[k].y - points[i].y;

                        if(XDistance * YDistance2 == XDistance2 * YDistance){//相乘可以避免斜率为零导致除法异常
                            sameSlopePoint++;
                        }
                    }
                }
                if (max < sameSlopePoint + samePoint){
                    max = sameSlopePoint + samePoint;
                }
            }
        }
        return max;
    }
}