oj.uz

Submission #969853

# Submission time Handle Problem Language Result Execution time Memory
969853 2024-04-25T17:04:18 Z happy_node timeismoney (balkan11_timeismoney) C++17
100 / 100
 335 ms 1452 KB 
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const int MX=205;
int N,M;
vector<array<int,3>> adj[MX];

ll w[10005];
array<ll,4> e[10005];

struct DSU {
	int par[MX];

	int find(int v) {
		return par[v]==v?v:par[v]=find(par[v]);
	}

	bool merge(int u, int v) {
		u=find(u), v=find(v);
		if(u==v) return false;
		par[u]=v;
		return true;
	}

	void prep() {
		for(int i=0;i<MX;i++) par[i]=i;
	}
} ds;

#define pt pair<ll,ll>
#define px first
#define py second

ll optV=0, optT=0, optC=0;
vector<pair<ll,ll>> optE, cur;

ll area(pt a, pt b, pt c) {
	return (b.px-a.px)*(c.py-b.py)-(c.px-b.px)*(b.py-a.py);
}

vector<int> ord;

pt kruskal() {
	cur.clear();
	sort(ord.begin(),ord.end(),[&](int i, int j){
		return w[i]<w[j];
	});

	ll st=0, sc=0;
	ds.prep();
	
	for(auto x:ord) {
		auto [u,v,t,c]=e[x];
		if(ds.merge(u,v)) {
			cur.push_back({u,v});
			st+=t;
			sc+=c;
		}
	}

	return {st,sc};
}

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

	cin>>N>>M;

	for(int i=0;i<M;i++) {
		int x,y,t,c;
		cin>>x>>y>>t>>c;
		adj[x].push_back({y,t,c});
		adj[y].push_back({x,t,c});
		e[i]={x,y,t,c};
	}

	for(int i=0;i<M;i++) ord.push_back(i);

	// time on x axis cost on y axis

	// get point A -> minimize x axis 
	for(int i=0;i<M;i++) 
		w[i]=e[i][2];

	pt A=kruskal();

	optV=A.px*A.py;
	optT=A.px;
	optC=A.py;
	optE=cur;

	// get point B -> minimize y axis
	for(int i=0;i<M;i++)
		w[i]=e[i][3];

	pt B=kruskal();

	if(B.px*B.py<optV) {
		optV=B.px*B.py;
		optT=B.px;
		optC=B.py;
		optE=cur;
	}

	vector<pair<pt,pt>> stk;
	stk.push_back({A,B});

	while(!stk.empty()) {
		auto [A,B]=stk.back(); stk.pop_back();

		// assing new weight based on Py(Bx - Ax) + Px(Ay - By)
		// y axis is cost, x axis is time

		for(int i=0;i<M;i++) 
			w[i]=e[i][3]*(B.px-A.px) + e[i][2]*(A.py-B.py);
		
		pt P=kruskal();

		// isn't on the lower convex hull
		if(area(A,B,P)>=0) continue;

		if(P.px*P.py<optV) {
			optV=P.px*P.py;
			optT=P.px;
			optC=P.py;
			optE=cur;
		}

		stk.push_back({A,P});
		stk.push_back({P,B});
	}

	cout<<optT<<" "<<optC<<'\n';
	for(auto [u,v]:optE) {
		cout<<u<<" "<<v<<'\n';
	}
}

Subtask #1
100.0 / 100.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 600 KB Output is correct
3 Correct 0 ms 600 KB Output is correct
4 Correct 0 ms 344 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 4 ms 1248 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 3 ms 348 KB Output is correct
15 Correct 3 ms 344 KB Output is correct
16 Correct 41 ms 604 KB Output is correct
17 Correct 44 ms 668 KB Output is correct
18 Correct 39 ms 604 KB Output is correct
19 Correct 307 ms 1372 KB Output is correct
20 Correct 335 ms 1452 KB Output is correct