Language: C++

#include <algorithm>
#include <array>
#include <bitset>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <valarray>
#include <vector>

#include <cassert>
#include <cctype>
#include <cstdio>
#include <cstdlib>
#include <cstring>

#include <chrono>
#include <random>
#include <thread>
#include <unordered_map>
#include <unordered_set>

using namespace std;

#define all(c) c.begin(), c.end()
#define repeat(i, n) for (int i = 0; i < static_cast<int>(n); i++)
#define debug(x) #x << "=" << (x)

#ifdef DEBUG
#define dump(x) std::cerr << debug(x) << " (L:" << __LINE__ << ")" << std::endl
#else
#define dump(x)
#endif

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v)
{
    os << "{";
    for (auto it = v.begin(); it != v.end(); ++it) {
        if (it != v.begin())
            os << ",";
        os << *it;
    }
    return os << "}";
}

template <typename A, typename B>
ostream& operator<<(ostream& os, const pair<A, B>& v)
{
    os << "{";
    os << v.first << ", " << v.second;
    return os << "}";
}

// ---------------------------------------------------------------------------

using point = complex<double>;
using ll = long long;

// 点の進行方向
int ccw(point a, point b, point c)
{
    b -= a;
    c -= a;
    if (cross(b, c) > 0)
        return +1; // counter clockwise
    if (cross(b, c) < 0)
        return -1; // clockwise
    if (dot(b, c) < 0)
        return +2; // c -- a -- b
    if (norm(b) < norm(c))
        return -2; // a -- b -- c
    return 0;
}

// 内積 (dot product) : a・b = |a||b|cosΘ
double dot(point a, point b)
{
    return real(conj(a) * b);
}

// 外積 (cross product) : |a×b| = |a||b|sinΘ
double cross(point a, point b)
{
    return imag(conj(a) * b);
}

int my_main(int argc, char** argv)
{
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin >> n;
    vector<double> x(n);
    vector<double> y(n);

    for (int i = 0; i < n; i++) {
        cin >> x[i] >> y[i];
    }

    if (n == 2) {
        cout << fixed << setprecision(10);
        cout << hypot(x[0] - x[1], y[0] - y[1]) / 2 << endl;
        return 0;
    }

    double rr = 10000000000000;
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            for (int k = j + 1; k < n; k++) {

                double a = x[i];
                double b = y[i];
                double c = x[j];
                double d = y[j];
                double e = x[k];
                double f = y[k];
                double aa = a * a;
                double bb = b * b;
                double cc = c * c;
                double dd = d * d;
                double ee = e * e;
                double ff = f * f;
                double py = ((e - a) * (aa + bb - cc - dd) - (c - a) * (aa + bb - ee - ff)) / (2 * (e - a) * (b - d) - 2 * (c - a) * (b - f));

                int cc = ccw({ a, b }, { c, d },
                    { e, f });

                if (cc == 2 || cc == -2)
                    continue;

                double px = 0;
                if (c == a) {
                    px = (2 * (b - f) * py - aa - bb + ee + ff) / (2 * (e - a));
                } else {
                    px = (2 * (b - d) * py - aa - bb + cc + dd) / (2 * (c - a));
                }
                double r = hypot(px - a, py - b);

                bool ok = true;
                for (int b = 0; b < n; b++) {
                    ok &= (hypot(px - x[b], py - y[b])) <= r + 1e-7;
                }
                if (ok)
                    rr = min(rr, r);
            }
        }
    }
    cout << fixed << setprecision(10);
    cout << rr << endl;
    return 0;
}

// ----------------------------------------------------------------------------
// Test driver

#ifdef DEBUG
#define MAY_RUN_TESTCASE
#endif

#ifdef MAY_RUN_TESTCASE
#include <fstream>

#if __has_include(<unistd.h>)
// Mac, Linux
#include <unistd.h>
#elif __has_include(<io.h>)
// Windows
#include <io.h>
#else
// Other?
#error "unistd.h or io.h not found"
#endif

bool test_file_exists(const std::string& str)
{
    std::ifstream fs(str);
    return fs.is_open();
}

#endif

int main(int argc, char** argv)
{
#ifndef MAY_RUN_TESTCASE
    return my_main(argc, argv);
#else
    if (argc == 1) {
        return my_main(argc, argv);
    } else if (argc == 2) {

        char* stdin_file = argv[1];
        freopen(stdin_file, "r", stdin);
        return my_main(argc, argv);

    } else if (argc == 5) {

        std::string stdin_file = argv[1];
        std::string expected_file = argv[2];
        std::string stdout_file = argv[3];
        std::string stderr_file = argv[4];

        if (!test_file_exists(stdin_file)) {
            std::cerr << stdin_file << " not found" << std::endl;
            return 3;
        }

        if (!test_file_exists(expected_file)) {
            std::cerr << expected_file << " not found" << std::endl;
            return 3;
        }

        int original_stdin = dup(fileno(stdin));
        int original_stdout = dup(fileno(stdout));
        int original_stderr = dup(fileno(stderr));

        freopen(stdin_file.c_str(), "r", stdin);
        freopen(stdout_file.c_str(), "w", stdout);
        freopen(stderr_file.c_str(), "w", stderr);

        int ret = my_main(argc, argv);

        fflush(stdout);
        fflush(stderr);

        dup2(original_stderr, fileno(stderr));
        dup2(original_stdout, fileno(stdout));
        dup2(original_stdin, fileno(stdin));

        if (ret != 0) {
            std::cerr << "main returns " << ret << std::endl;
            return ret;
        }

        std::ifstream inp(stdin_file);
        std::ifstream out(stdout_file);
        std::ifstream err(stderr_file);
        std::ifstream exp(expected_file);

        // Clear is needed if the file is empty.
        std::cout << "----- input -----" << std::endl;
        std::cout << inp.rdbuf() << std::endl;
        std::cout.clear();
        std::cout << "-----------------" << std::endl
                  << std::endl;

        std::cout << "----- output ----" << std::endl;
        std::cout << out.rdbuf() << std::endl;
        std::cout.clear();
        std::cout << "-----------------" << std::endl
                  << std::endl;

        std::cout << "---- expected ---" << std::endl;
        std::cout << exp.rdbuf() << std::endl;
        std::cout.clear();
        std::cout << "-----------------" << std::endl
                  << std::endl;

        std::cout << "----- stderr ----" << std::endl;
        std::cout << err.rdbuf() << std::endl;
        std::cout.clear();
        std::cout << "-----------------" << std::endl;

        inp.seekg(0);
        out.seekg(0);
        exp.seekg(0);
        err.seekg(0);

        std::string output_str, expected_str;
        {
            std::stringstream output_ss;
            output_ss << out.rdbuf();
            output_str = output_ss.str();

            std::stringstream expected_ss;
            expected_ss << exp.rdbuf();
            expected_str = expected_ss.str();
        }

        // Remove trailing spaces
        output_str.erase(output_str.find_last_not_of(" \n\r\t") + 1);
        expected_str.erase(expected_str.find_last_not_of(" \n\r\t") + 1);

        if (output_str == expected_str)
            return 0;
        else
            return 1;
    }
    return 1;
#endif
}


Compiler output:
a.cc: In function 'int ccw(point, point, point)':
a.cc:74:9: error: 'cross' was not declared in this scope
   74 |     if (cross(b, c) > 0)
      |         ^~~~~
a.cc:76:9: error: 'cross' was not declared in this scope
   76 |     if (cross(b, c) < 0)
      |         ^~~~~
a.cc:78:9: error: 'dot' was not declared in this scope
   78 |     if (dot(b, c) < 0)
      |         ^~~
a.cc: In function 'int my_main(int, char**)':
a.cc:136:21: error: conflicting declaration 'int cc'
  136 |                 int cc = ccw({ a, b }, { c, d },
      |                     ^~
a.cc:130:24: note: previous declaration as 'double cc'
  130 |                 double cc = c * c;
      |                        ^~