[LeetCode]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.

Analysis:

任意一条直线都可以表述为

y = ax + b

假设，有两个点(x1,y1), (x2,y2)，如果他们都在这条直线上则有

y1 = kx1 +b

y2 = kx2 +b

由此可以得到关系，k = (y2-y1)/(x2-x1)。即如果点c和点a的斜率为k, 而点b和点a的斜率也为k，那么由传递性，可以知道点c和点b也在一条线上。解法就从这里来

取定一个点(xk,yk), 遍历所有节点(xi, yi), 然后统计斜率相同的点数，并求取最大值即可

Java

public int maxPoints(Point[] points) {
        if(points.length<=2) return points.length;
		int maxNum = 0;
        int duplicate = 1;
        HashMap<Float, Integer> slopMap = new HashMap<>();
        for(int i = 0;i<points.length;i++){
        	slopMap.clear();
        	duplicate = 1;
        	for(int j=0;j<points.length;j++){
        		if(i==j) continue;
        		if(points[i].x==points[j].x && points[j].y == points[i].y){
        			duplicate++;
        			continue;
        		}
        		float slop = (points[i].x==points[j].x) ? Integer.MAX_VALUE :(float)(points[j].y-points[i].y)/(points[j].x-points[i].x); 
        		if(slopMap.containsKey(slop)){
        			int temp = slopMap.get(slop);
        			temp++;
        			slopMap.put(slop, temp);
        		}else {
					slopMap.put(slop, 1);
				}
        	}
        	if(slopMap.size()<=0)
        		maxNum = duplicate;
        	for (Iterator<Map.Entry<Float, Integer>> iterator = slopMap.entrySet().iterator(); iterator.hasNext();) {
				Map.Entry<Float, Integer> out=  iterator.next();
				if(out.getValue()+duplicate>maxNum)
					maxNum = out.getValue()+duplicate;
			}
   		}
        return maxNum;
    }

c++

int maxPoints(vector<Point> &points) {
        if(points.size()<=2) return points.size();
    unordered_map<float, int> statistic;
    int maxNum = 0;
    for(int i=0;i<points.size();i++){
        statistic.clear();
        statistic[INT_MIN] = 0;
        int duplicate = 1;
        for(int j=0;j<points.size();j++){
            if(j==i) continue;
            if(points[j].x == points[i].x && points[j].y==points[i].y){
                duplicate++;
                continue;
            }
            float slop = (points[j].x == points[i].x) ?
            INT_MAX: (float)(points[j].y-points[i].y)/(points[j].x-points[i].x);
            statistic[slop]++;
        }
        unordered_map<float, int>::iterator it;
        for(it = statistic.begin();it!=statistic.end();++it){
            if(it->second + duplicate>maxNum)
                maxNum = it->second + duplicate;
        }
    }
    return maxNum;
    }