C++ 等分三点圆n点 源代码

以下是一个简单的 C++ 源代码，用于计算等分 $n$ 点圆的坐标：

#include <iostream>
#include <cmath>
#include <vector>
using namespace std;

const double EPS = 1e-6;  // 浮点误差

int n;  // 点的个数
vector<pair<double, double>> points;  // 存储点的坐标

// 计算两个点之间的距离
double dist(double x1, double y1, double x2, double y2) {
    return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}

// 计算圆心坐标
pair<double, double> getCenter(double x1, double y1, double x2, double y2, double x3, double y3) {
    double a = x2 - x1;
    double b = y2 - y1;
    double c = x3 - x1;
    double d = y3 - y1;
    double e = a * (x1 + x2) + b * (y1 + y2);
    double f = c * (x1 + x3) + d * (y1 + y3);
    double g = 2.0 * (a * (y3 - y2) - b * (x3 - x2));

    if (fabs(g) < EPS) {
        // 三点共线
        return make_pair(-1, -1);
    }

    double centerX = (d * e - b * f) / g;
    double centerY = (a * f - c * e) / g;
    return make_pair(centerX, centerY);
}

// 判断是否所有点都在圆内
bool isAllInCircle(double centerX, double centerY, double radius) {
    for (int i = 0; i < n; i++) {
        double d = dist(centerX, centerY, points[i].first, points[i].second);
        if (d > radius + EPS) {
            return false;
        }
    }
    return true;
}

// 计算等分n点圆的圆心坐标和半径
pair<double, double> getCenterAndRadius() {
    pair<double, double> center = make_pair(-1, -1);  // 圆心坐标初始化为 (-1, -1)
    double radius = -1;  // 半径初始化为 -1

    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            for (int k = j + 1; k < n; k++) {
                pair<double, double> c = getCenter(points[i].first, points[i].second, points[j].first, points[j].second, points[k].first, points[k].second);
                if (c.first == -1 && c.second == -1) {
                    // 三点共线，无法构成等分三点圆
                    continue;
                }
                double r = dist(c.first, c.second, points[i].first, points[i].second);
                if (r < radius || radius < 0) {
                    // 如果计算出来的圆半径比之前的小，则更新圆心坐标和半径
                    if (isAllInCircle(c.first, c.second, r)) {
                        center = c;
                        radius = r;
                    }
                }
            }
        }
    }

    return make_pair(center.first, radius);
}

int main() {
    cout << "请输入点的个数：" << endl;
    cin >> n;

    cout << "请输入每个点的坐标：" << endl;
    for (int i = 0; i < n; i++) {
        double x, y;
        cin >> x >> y;
        points.push_back(make_pair(x, y));
    }

    pair<double, double> center = getCenterAndRadius();
    if (center.first == -1 && center.second == -1) {
        cout << "无法构成等分 " << n << " 点圆！" << endl;
    } else {
        cout << "等分 " << n << " 点圆的圆心坐标为(" << center.first << ", " << center.second << ")" << endl;
        cout << "等分 " << n << " 点圆的半径为" << center.second << endl;
    }

    return 0;
}

这段代码使用输入的 $n$ 个点的坐标计算等分 $n$ 点圆的圆心坐标和半径，并输出结果。