LeetCode: 149. Max Points on a Line

题目描述

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

Example 1:

Input: [[1,1],[2,2],[3,3]]
Output: 3
Explanation:
^
|
|        o
|     o
|  o  
+------------->
0  1  2  3  4

Example 2:

Input: [[1,1],[3,2],[5,3],[4,1],[2,3],[1,4]]
Output: 4
Explanation:
^
|
|  o
|     o        o
|        o
|  o        o
+------------------->
0  1  2  3  4  5  6

解题思路

用 map 统计所有直线上的 点的个数

AC 代码

/** * Definition for a point. * struct Point { * int x; * int y; * Point() : x(0), y(0) {} * Point(int a, int b) : x(a), y(b) {} * }; */
class Solution {
    // 用 Ax + By + C = 0 的形式表示点 pt1 和点 pt2 构成的直线
    // 返回值是三元组 <A, B, C>
    tuple<int, int, int> MakeLine(Point pt1, Point pt2)
    {
        int A = 0, B = 0, C = 0;

        // x = b 类型
        if(pt1.x == pt2.x)
        {
            A = 1;
            B = 0;
            C = -pt1.x;
        }
        else if(pt1.y == pt2.y) 
        {
            A = 0;
            B = 1;
            C = -pt2.y;
        }
        else // 否则是 y = kx + b 类型
        {
            // 两点式直线方程：(x-x1)/(x2-x1) = (y-y1)/(y2-y1)
            // 即 (y2-y1)x -(x2-x1)y -(y2-y1)x1+(x2-x1)y1 = 0
            // A = y2-y1; B = -(x2-x1); C = -(y2-y1)x1+(x2-x1)y1
            A = pt2.y - pt1.y;
            B = -(pt2.x - pt1.x);
            C = -(pt2.y - pt1.y)*pt1.x + (pt2.x - pt1.x)*pt1.y;
        }

        return {A, B, C};
    }

    // 判断点 pt 是否在直线 line 上
    bool PtOnLine(Point pt, const tuple<int, int, int>& line)
    {
        int A = get<0>(line);
        int B = get<1>(line);
        int C = get<2>(line);
        return ((long long)A*pt.x+B*pt.y+C == 0);
    }
public:
    int maxPoints(vector<Point>& points) {

        if(points.empty()) return 0;
        // 统计线上的点数
        map<tuple<int, int, int>, int> pointsInLine;

        for(size_t i = 0; i < points.size(); ++i)
        {
            for(size_t j = i+1; j < points.size(); ++j)
            {
                auto line = MakeLine(points[i], points[j]);
                if(pointsInLine.find(line) == pointsInLine.end()) pointsInLine[line] = 0; 
            }
        }

        int maxCnt = 1;
        // 统计
        for(size_t i = 0; i < points.size(); ++i)
        {
            for(auto& line : pointsInLine)
            {
                if(PtOnLine(points[i], line.first) == true)
                {
                    if(++pointsInLine[line.first] > maxCnt)
                    {
                        maxCnt = pointsInLine[line.first] ;
                    }
                }
            }
        }


        return maxCnt;
    }
};