Codeforces-solutions/2024 (ICPC) Jiangxi Provincial Contest -- Official Contest/I. Neuvillette Circling.cpp

/* Problem URL: https://codeforces.com/gym/105231/problem/I */

#include <bits/stdc++.h>

#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")
#pragma GCC target("bmi,bmi2,popcnt,lzcnt")

using namespace std;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}
using pd = pair<double, double>;

pd operator+(pd a, pd b) {
    pd fds = {a.first + b.first, a.second + b.second};
    return fds;
}

pd operator-(pd a, pd b) {
    pd fds = {a.first - b.first, a.second - b.second};
    return fds;
}

pd operator/(pd a, double f) {
    return make_pair(a.first / f, a.second / f);
}

pd operator*(pd a, double f) {
    return make_pair(a.first * f, a.second * f);
}

pd rotate90(pd a) {
    return pd(-a.second, a.first);
}

double operator^(pd a, pd b) {
    return a.first * b.second - a.second * b.first;
}

struct line {
    pd p, q;
};

double get_t(pd v, line r) {
    return (r.p^r.q) / ((r.p - r.q)^v);
}

double EPS = 1e-6;
double inf = 1e18;
pd inter(line r, line s)
{
    if (abs((r.p - r.q) ^ (s.p - s.q)) < EPS) {
        return pd(inf, inf);
    }

    r.q = r.q - r.p, s.p = s.p - r.p, s.q = s.q - r.p;
    return (r.q * get_t(r.q, s)) + r.p;
}

pd getcenter(pd a, pd b, pd c) {
    b = (a + b)  / 2;
    c = (a + c) / 2;
    return inter(line(b, b + rotate90(a - b)), line(c, c + rotate90(a - c)));
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n;
    cin >> n;

    V<pair<double, double>> points(n);

    repv(i, points) {
        cin >> i.first >> i.second;
    }

    V<double> disses(n, 1e16);

    auto dis = [&](pair<double, double> &a, pair<double, double> &b) {
        double x = a.first - b.first;
        double y = a.second - b.second;
        return sqrt(x * x + y * y);
    };

    V<double> lol(n);

    auto calc = [&](pair<double, double> center) {
        rep(i, n) {
            lol[i] = dis(center, points[i]);
        }
    };

    auto search = [&](pair<double, double> point) {
        sortv(lol);

        nrep(i, 1, n) {
            rmin(disses[i], lol[i]);
        }
    };

    rep(i, n - 1) {
        nrep(j, i + 1, n) {
            pair<double, double> center = {(points[i].first + points[j].first) / 2, (points[i].second + points[j].second) / 2};
            calc(center);
            search(center);
        }
    }

    rep(i, n - 2) {
        nrep(j, i + 1, n - 1) {
            nrep(k, j + 1, n) {
                auto center = getcenter(points[i], points[j], points[k]);
                calc(center);
                search(center);
            }
        }
    }

    int act = 1;
    nrep(i, 1, n) {
        rep(j, act) {
            cout << fixed << setprecision(8) << disses[i] << '\n';
        }
        act++;
    }
}