test/yosupo/closest_pair.test.cpp

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Last update: 2025-01-11 16:44:40+09:00
Problem: https://judge.yosupo.jp/problem/closest_pair

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/closest_pair"

#include "../../geometry/closest_pair.hpp"

#include <bits/stdc++.h>

#include "../../geometry/geometry.hpp"
using namespace std;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int T;
    cin >> T;
    while (T--) {
        int N;
        cin >> N;
        vector<Vec> pts(N);
        for (auto& p : pts) cin >> p;
        auto [d, i, j] = closest_pair(pts);
        cout << i << " " << j << "\n";
    }
}

#line 1 "test/yosupo/closest_pair.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/closest_pair"

#line 2 "geometry/closest_pair.hpp"
#include <numeric>
#include <ranges>
#include <vector>

#line 2 "geometry/geometry.hpp"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <complex>
#include <iostream>
#include <numbers>
#line 10 "geometry/geometry.hpp"

// note that if T is of an integer type, std::abs does not work
using T = double;
using Vec = std::complex<T>;

std::istream& operator>>(std::istream& is, Vec& p) {
    T x, y;
    is >> x >> y;
    p = {x, y};
    return is;
}

T dot(const Vec& a, const Vec& b) { return (std::conj(a) * b).real(); }

T cross(const Vec& a, const Vec& b) { return (std::conj(a) * b).imag(); }

constexpr T PI = std::numbers::pi_v<T>;
constexpr T eps = 1e-10;
inline bool eq(T a, T b) { return std::abs(a - b) <= eps; }
inline bool eq(Vec a, Vec b) { return std::abs(a - b) <= eps; }
inline bool lt(T a, T b) { return a < b - eps; }
inline bool leq(T a, T b) { return a <= b + eps; }

struct Line {
    Vec p1, p2;
    Line() = default;
    Line(const Vec& p1, const Vec& p2) : p1(p1), p2(p2) {}
    Vec dir() const { return p2 - p1; }
};

struct Segment : Line {
    using Line::Line;
};

struct Circle {
    Vec c;
    T r;
    Circle() = default;
    Circle(const Vec& c, T r) : c(c), r(r) {}
};

using Polygon = std::vector<Vec>;

Vec rot(const Vec& a, T ang) { return a * Vec(std::cos(ang), std::sin(ang)); }

Vec perp(const Vec& a) { return Vec(-a.imag(), a.real()); }

Vec projection(const Line& l, const Vec& p) {
    return l.p1 + dot(p - l.p1, l.dir()) * l.dir() / std::norm(l.dir());
}

Vec reflection(const Line& l, const Vec& p) {
    return T(2) * projection(l, p) - p;
}

// 0: collinear
// 1: counter-clockwise
// -1: clockwise
int ccw(const Vec& a, const Vec& b, const Vec& c) {
    if (eq(cross(b - a, c - a), 0)) return 0;
    if (lt(cross(b - a, c - a), 0)) return -1;
    return 1;
}

void sort_by_arg(std::vector<Vec>& pts) {
    std::ranges::sort(pts, [&](auto& p, auto& q) {
        if ((p.imag() < 0) != (q.imag() < 0)) return (p.imag() < 0);
        if (cross(p, q) == 0) {
            if (p == Vec(0, 0))
                return !(q.imag() < 0 || (q.imag() == 0 && q.real() > 0));
            if (q == Vec(0, 0))
                return (p.imag() < 0 || (p.imag() == 0 && p.real() > 0));
            return (p.real() > q.real());
        }
        return (cross(p, q) > 0);
    });
}
#line 7 "geometry/closest_pair.hpp"

/**
 * @brief Closest Pair
 */
std::tuple<T, int, int> closest_pair(const std::vector<Vec>& pts_) {
    std::vector<std::pair<Vec, int>> pts;
    for (int i = 0; i < (int)pts_.size(); ++i) pts.emplace_back(pts_[i], i);
    std::ranges::sort(pts, {}, [](const auto& v) { return v.first.real(); });

    auto rec = [&](const auto& rec, int l, int r) -> std::tuple<T, int, int> {
        if (r - l <= 1) return {std::numeric_limits<T>::max(), -1, -1};
        int m = std::midpoint(l, r);
        T x = pts[m].first.real();
        auto closest = std::min(rec(rec, l, m), rec(rec, m, r));
        std::ranges::inplace_merge(
            pts.begin() + l, pts.begin() + m, pts.begin() + r, {},
            [](const auto& v) { return v.first.imag(); });
        std::vector<std::pair<Vec, int>> b;
        for (int i = l; i < r; ++i) {
            if (leq(std::get<0>(closest), std::abs(pts[i].first.real() - x)))
                continue;
            for (auto& p : b | std::views::reverse) {
                if (leq(std::get<0>(closest),
                        std::abs(pts[i].first.imag() - p.first.imag())))
                    break;
                closest = std::min(closest, {std::abs(pts[i].first - p.first),
                                             pts[i].second, p.second});
            }
            b.push_back(pts[i]);
        }
        return closest;
    };

    return rec(rec, 0, pts.size());
}
#line 4 "test/yosupo/closest_pair.test.cpp"

#include <bits/stdc++.h>

#line 8 "test/yosupo/closest_pair.test.cpp"
using namespace std;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int T;
    cin >> T;
    while (T--) {
        int N;
        cin >> N;
        vector<Vec> pts(N);
        for (auto& p : pts) cin >> p;
        auto [d, i, j] = closest_pair(pts);
        cout << i << " " << j << "\n";
    }
}