三维坐标判共线

#include<vector>
#include<map>
#include<iostream>
using namespace std;
struct Point {
    int x;
    int y;
    int z;
    Point() : x(0), y(0),z(0) {}
    Point(int a, int b,int c) : x(a), y(b),z(c) {}
};
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a%b); }
int gcd(int a, int b, int c) { return gcd(gcd(a, b), c); }
int max(int a, int b) { return a > b ? a : b; }
int maxPoints(vector<Point>& points) 
{
    int ans = 0;
    for (int i = 0; i < points.size(); i++) {
        int cnt = 0,overLap=0;
        map<pair<pair<int, int>, int>,int> line;
        for (int j = i + 1; j < points.size(); j++) {
            int dx = points[i].x - points[j].x;
            int dy = points[i].y - points[j].y;
            int dz = points[i].z - points[j].z;
            //判断两点是否重合
            if (dx == 0 && dy == 0 && dz==0) {
                ++overLap;
                continue;
            }
            //计算最简方向向量并存入map容器中,同时更新cnt
            int g = gcd(dx, dy,dz);
            dx /= g;
            dy /= g;
            dz /= g;

            cnt=max(cnt,++line[pair<pair<int, int>,int>(pair<int,int>(dx, dy),dz)]);
        }
        //统计该基准点下的最大共线点数量
        //cnt+重合点+基准点自身
        ans = max(ans, cnt + overLap + 1);
    }
    return ans;
}
int main()
{
    int n;
    cin >> n;
    vector<Point> points(n);
    for (int i = 0; i < n; i++) 
        cin >> points[i].x >> points[i].y>>points[i].z;
    cout << maxPoints(points) << endl;
}

链接：https://www.nowcoder.com/questionTerminal/7f1490a737024704a3f2b7aad476e3ac

#include<vector>#include<map>#include<iostream>using namespace std;struct Point {int x;int y;int z;Point() : x(0), y(0),z(0) {}Point(int a, int b,int c) : x(a), y(b),z(c) {}};int gcd(int a, int b) { return b == 0 ? a : gcd(b, a%b); }int gcd(int a, int b, int c) { return gcd(gcd(a, b), c); }int max(int a, int b) { return a > b ? a : b; }int maxPoints(vector<Point>& points) {int ans = 0;for (int i = 0; i < points.size(); i++) {int cnt = 0,overLap=0;map<pair<pair<int, int>, int>,int> line;for (int j = i + 1; j < points.size(); j++) {int dx = points[i].x - points[j].x;int dy = points[i].y - points[j].y;int dz = points[i].z - points[j].z;//判断两点是否重合if (dx == 0 && dy == 0 && dz==0) {++overLap;continue;}//计算最简方向向量并存入map容器中,同时更新cntint g = gcd(dx, dy,dz);dx /= g;dy /= g;dz /= g;
cnt=max(cnt,++line[pair<pair<int, int>,int>(pair<int,int>(dx, dy),dz)]);}//统计该基准点下的最大共线点数量//cnt+重合点+基准点自身ans = max(ans, cnt + overLap + 1);}return ans;}int main(){int n;cin >> n;vector<Point> points(n);for (int i = 0; i < n; i++) cin >> points[i].x >> points[i].y>>points[i].z;cout << maxPoints(points) << endl;}