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Submission #678988

# Submission time Handle Problem Language Result Execution time Memory
678988 2023-01-07T06:47:09 Z vjudge1 timeismoney (balkan11_timeismoney) C++17
100 / 100
 748 ms 1100 KB 
#include <bits/stdc++.h>
using namespace std;

typedef complex<long long> point;
const long long INF = (long long)1e18;

long long dot(point a, point b) {
    return (conj(a) * b).real();
}
long long cross(point a, point b) {
    return (conj(a) * b).imag();
}
long long area(point a, point b, point c) {
    return cross(b - a, c - a);
}

struct DSU {
    vector<int> f;
    DSU(int n) : f(n) { iota(f.begin(), f.end(), 0); }
    int leader(int x) {
        while (x != f[x]) {
            x = f[x] = f[f[x]];
        }
        return x;
    }
    bool unionize(int x, int y) {
        x = leader(x);
        y = leader(y);
        if (x == y) {
            return false;
        }
        f[y] = x;
        return true;
    }
};

int n, m;
vector<array<long long, 5>> edges0;

point f(point axis) { // find mst on axis
    vector<array<long long, 5>> edges = edges0;
    for (int i = 0; i < m; i++) {
        edges[i][4] = dot(axis, point(edges[i][2], edges[i][3]));
    }

    sort(edges.begin(), edges.end(), [&](auto x, auto y) {
        return x[4] < y[4];
    });

    point res(0, 0);
    DSU dsu(n);

    for (auto [u, v, a, b, w] : edges) {
        if (dsu.unionize(u, v)) {
            res += point(a, b);
        }
    }
    return res;
}

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

    cin >> n >> m;
    edges0.resize(m);
    for (int i = 0; i < m; i++) {
        int u, v, a, b;
        cin >> u >> v >> a >> b;
        edges0[i] = {u, v, a, b, 0};
    }

    vector<point> S;
    vector<point> T;

    function<void(point, point, point, point)> divide = [&](point lp, point rp, point l, point r) {
        point axis = point(lp.imag() - rp.imag(), rp.real() - lp.real());
        point mp = f(axis);
        if (area(lp, mp, rp) == 0) {
            S.push_back(lp);
            T.push_back(l);
            S.push_back(rp);
            T.push_back(r);
            return;
        }
        divide(lp, mp, l, axis);
        divide(mp, rp, axis, r);
    };
    point l0(1, 0);
    point r0(0, 1);
    divide(f(l0), f(r0), l0, r0);

    long long mn = INF;
    point key;
    point dir;
    for (int i = 0; i < S.size(); i++) {
        point p = S[i];
        point t = T[i];
        long long prod = p.real() * p.imag();
        if (prod < mn) {
            key = p;
            dir = t;
            mn = prod;
        }
    }

    cout << key.real() << " " << key.imag() << "\n";

    vector<array<long long, 5>> edges = edges0;
    for (int i = 0; i < m; i++) {
        edges[i][4] = dot(dir, point(edges[i][2], edges[i][3]));
    }

    sort(edges.begin(), edges.end(), [&](auto x, auto y) {
        return x[4] < y[4];
    });

    DSU dsu(n);

    for (auto [u, v, a, b, w] : edges) {
        if (dsu.unionize(u, v)) {
            cout << u << " " << v << "\n";
        }
    }
}

Compilation message

timeismoney.cpp: In function 'int main()':
timeismoney.cpp:96:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::complex<long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   96 |     for (int i = 0; i < S.size(); i++) {
      |                     ~~^~~~~~~~~~

Subtask #1
100.0 / 100.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 2 ms 468 KB Output is correct
8 Correct 10 ms 1100 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 5 ms 340 KB Output is correct
15 Correct 4 ms 340 KB Output is correct
16 Correct 97 ms 528 KB Output is correct
17 Correct 90 ms 508 KB Output is correct
18 Correct 83 ms 508 KB Output is correct
19 Correct 735 ms 1096 KB Output is correct
20 Correct 748 ms 1096 KB Output is correct