2020牛客暑期多校训练营（第二场）B三点确定圆心

 

 

 

 题意：给定原点及n个点，找到一个圆使得尽可能多的点在圆上
题解：三点可以确定一个圆，原点固定，遍历两个点去确定圆心，并用map保存圆心，当再次得到一个相同的圆心时，map++（圆心相同，且有共点必定为同一个圆）

#include<iostream>
#include<stdio.h>
#include<math.h>
#include<map>
using namespace std;
const int maxn = 2e3+10;
const double eps=1e-5;
struct Point{
    double x,y;
}a[maxn];
map<pair<double,double>,int> mp; 
int main(){
    int n;
    cin>>n;
    for(int i=1;i<=n;i++){
        scanf("%lf %lf",&a[i].x,&a[i].y);
    }
    int ans = 0;
    for(int i=1;i<=n;i++){
        mp.clear();
        for(int j=i+1;j<=n;j++){
            double x1 = a[i].x,x2 = a[j].x,y1 = a[i].y,y2 = a[j].y;
            double x3=0,y3=0;
            double a = x1-x2;
            double b = y1-y2;
            double c = x1-x3;
            double d = y1-y3;
            double e = ((x1*x1-x2*x2)+(y1*y1-y2*y2))/2.0;
            double f = ((x1*x1-x3*x3)+(y1*y1-y3*y3))/2.0;
            double det = b*c-a*d;
            if(fabs(det)<eps){
                continue;
            }
            double x = -(d*e-b*f)/det;
            double y = -(a*f-c*e)/det;
            ans = max(ans,++mp[{x,y}]);
            
        }
    }
    cout<<ans+1<<endl;//自己这个点要算进去
    return 0;
}

 三点确定圆心模板：

#include <bits/stdc++.h>
using namespace std;
#define db double
#define pdd pair<db, db>
const db eps = 1e-5;

pdd Circle_center(db x1, db x2, db x3, db y1, db y2, db y3) {
    db a = x1 - x2;
    db b = y1 - y2;
    db c = x1 - x3;
    db d = y1 - y3;
    db e = ((x1 * x1 - x2 * x2) + (y1 * y1 - y2 * y2)) / 2.0;
    db f = ((x1 * x1 - x3 * x3) + (y1 * y1 - y3 * y3)) / 2.0;
    db det = b * c - a * d;
    if (fabs(det) < eps)  //三点共线
        return {0, 0};
    db x = -(d * e - b * f) / det;
    db y = -(a * f - c * e) / det;
    return {x, y};
}

int main(void) {}