제출 #305683

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
305683		ntfx	시간이 돈 (balkan11_timeismoney)	C++17	100 / 100	855 ms	632 KiB

timeismoney

/*
    Problem: https://oj.uz/problem/view/balkan11_timeismoney

    Solution: http://www.boi2011.ro/resurse/tasks/timeismoney-sol.pdf
*/
#include <bits/stdc++.h>
using namespace std;

#ifdef LOCAL
    #define D(a) cerr << #a << " = " << a << endl
#else 
    #define D(a) 8 
#endif
#define fastio ios_base::sync_with_stdio(0); cin.tie(0)
#define dforsn(i,s,n) for(int i=int(n-1);i>=int(s);i--)
#define forsn(i,s,n) for(int i=int(s);i<int(n);i++)
#define all(a) (a).begin(),(a).end()
#define dforn(i,n) dforsn(i,0,n)
#define forn(i,n) forsn(i,0,n)
#define si(a) int((a).size())
#define pb emplace_back
#define mp make_pair
#define snd second
#define fst first
#define endl '\n'
using pii = pair<int,int>;
using vi = vector<int>;
using ll = long long;

struct DSU {
    vi par;
    DSU(int n): par(n) { iota(all(par), 0); }
    int find(int u) { return par[u] == u ? u : par[u] = find(par[u]); }
    bool join(int u, int v) {
        if ((u = find(u)) == (v = find(v))) return false;
        return par[v] = u, true;
    }
};

const int N = 200, M = 1e4;
int n, m, A, B, sumT, sumC;
int t[M], c[M], mst[N];
int src[M], dst[M];
ll mn = 1e18;
pii ids[M];

struct Point {
    int x, y;
    bool collinear(const Point &p1, const Point &p2) {
        return ll(p2.y - p1.y) * (x - p1.x) == ll(y - p1.y) * (p2.x - p1.x);
    }
};

// Minimize a * sumT + b * sumC = v
Point optimize(int a, int b) { 
    forn(i, m) ids[i] = {a*t[i] + b*c[i], i};
    sort(ids, ids + m);
    sumT = 0, sumC = 0;
    int pos = 0;
    DSU dsu(n);
    forn(i, m) {
        int id = ids[i].snd;
        if (dsu.join(src[id], dst[id]))
            sumT += t[id], sumC += c[id], mst[pos++] = id;
    }
    ll v = ll(sumT) * sumC;
    if (v < mn) mn = v, A = a, B = b;
    return {sumC, sumT};
}

void computeConvexHull(const Point &p1, const Point &p2) {
    Point p = optimize(p2.x - p1.x, p1.y - p2.y);
    if (p.collinear(p1, p2)) return;
    computeConvexHull(p1, p), computeConvexHull(p, p2);
}

int main() {
    fastio;

    cin >> n >> m;
    forn(i, m) cin >> src[i] >> dst[i] >> t[i] >> c[i];

    computeConvexHull(optimize(0, 1), optimize(1, 0));

    optimize(A, B); 
    cout << sumT << ' ' << sumC << endl;
    forn(i, n-1) cout << src[mst[i]] << ' ' << dst[mst[i]] << endl;
    return 0;
}

• Subtask 1: 100 / 100