[leetcode]給定二維平面上的n個點，找出位於同一直線上的點的最大數目

給定二維平面上的n個點，找出位於同一直線上的點的最大數目。

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) {
        //驗證一下輸入
        if (points == null || points.length == 0){
            return 0;
        }

        //一個點或者兩個點直接返回值
        if (points.length < 3){
            return points.length;
        }

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

        for (int i = 0; i < points.length; i++){
            //初始化一下，剛開始相同點都為零
            samePoint = 0;

            for(int j = i+1; j < points.length; j++){
                sameSlopePoint = 1;//兩點確定一條直線，這個點也應該納入總數
                int XDistance = points[j].x - points[i].x;
                int YDistance = points[j].y - points[i].y;

                if (XDistance == 0 && YDistance ==0){//特殊情況：與第一個點同一位置的點，這時候不用計算后面，因為兩點在同一位置，不能確定一條直線
                    samePoint++;
                }else{
                    sameSlopePoint = 2;
                    for(int k = j+1; k < points.length; k++){//找剩下斜率相同的點，三點的斜率相同則肯定在一條直線上
                        int XDistance2 = points[k].x - points[i].x;
                        int YDistance2 = points[k].y - points[i].y;

                        if(XDistance * YDistance2 == XDistance2 * YDistance){//相乘可以避免斜率為零導致除法異常
                            sameSlopePoint++;
                        }
                    }
                }
                if (max < sameSlopePoint + samePoint){
                    max = sameSlopePoint + samePoint;
                }
            }
        }
        return max;
    }
}