Codeforces-solutions/Educational Codeforces Round 1/C. Nearest vectors.cpp

/* Problem URL: https://codeforces.com/contest/598/problem/C */

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#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;
}

#define sq(x) ((x)*(ll)(x))

struct pt { // ponto
	ll x, y;
	pt(int x_ = 0, int y_ = 0) : x(x_), y(y_) {}
	bool operator < (const pt p) const {
		if (x != p.x) return x < p.x;
		return y < p.y;
	}
	bool operator == (const pt p) const {
		return x == p.x and y == p.y;
	}
	pt operator + (const pt p) const { return pt(x+p.x, y+p.y); }
	pt operator - (const pt p) const { return pt(x-p.x, y-p.y); }
	pt operator * (const int c) const { return pt(x*c, y*c); }
	ll operator * (const pt p) const { return x*(ll)p.x + y*(ll)p.y; }
	ll operator ^ (const pt p) const { return x*(ll)p.y - y*(ll)p.x; }
	friend istream& operator >> (istream& in, pt& p) {
		return in >> p.x >> p.y;
	}
};

struct line { // reta
	pt p, q;
	line() {}
	line(pt p_, pt q_) : p(p_), q(q_) {}
	friend istream& operator >> (istream& in, line& r) {
		return in >> r.p >> r.q;
	}
};

// PONTO & VETOR

ll dist2(pt p, pt q) { // quadrado da distancia
	return sq(p.x - q.x) + sq(p.y - q.y);
}

ll sarea2(pt p, pt q, pt r) { // 2 * area com sinal
	return (q-p)^(r-q);
}

bool col(pt p, pt q, pt r) { // se p, q e r sao colin.
	return sarea2(p, q, r) == 0;
}

bool ccw(pt p, pt q, pt r) { // se p, q, r sao ccw
	return sarea2(p, q, r) > 0;
}

int quad(pt p) { // quadrante de um ponto
	return (p.x<0)^3*(p.y<0);
}

bool compare_angle(pt p, pt q) { // retorna se ang(p) < ang(q)
	if (quad(p) != quad(q)) return quad(p) < quad(q);
	return ccw(q, pt(0, 0), p);
}

pt rotate90(pt p) { // rotaciona 90 graus
	return pt(-p.y, p.x);
}

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

    int n;
    cin >> n;

    V<pair<pt, int>> fds(n);
    rep(i, n) {
        cin >> fds[i].first;
        fds[i].second = i + 1;
    }

    sort(all(fds), [&](pair<pt, int> &a, pair<pt, int> &b) {
            return compare_angle(a.first, b.first);
         });

    auto better = [&](pt &a, pt &b, pt &c, pt &d) {
        pt p1(a * b, abs(a ^ b));
        pt p2(c * d, abs(c ^ d));
        return (p1 ^ p2) > 0;
    };

    int ans1 = 0;
    int ans2 = 1;
    nrep(i, 1, n - 1) {
        pt &one = fds[i].first;
        pt &two = fds[i + 1].first;
        if (better(one, two, fds[ans1].first, fds[ans2].first)) {
            ans1 = i;
            ans2 = i + 1;
        }
    }

    pt &one = fds.back().first;
    pt &two = fds[0].first;
    if (better(one, two, fds[ans1].first, fds[ans2].first)) {
        ans1 = n - 1;
        ans2 = 0;
    }

    cout << fds[ans1].second << ' ' << fds[ans2].second << '\n';
}