Submission #490163

#	Time	Username	Problem	Language	Result	Execution time	Memory
490163		8e7	Toll (APIO13_toll)	C++17	100 / 100	1758 ms	14324 KiB

toll

//Challenge: Accepted
#include <iostream>
#include <algorithm>
#include <vector>
#include <utility>
#include <bitset>
#include <set>
#include <queue>
#include <stack>
#include <assert.h>
#include <cmath>
#include <iomanip>
#include <random>
using namespace std;
void debug(){cout << endl;};
template<class T, class ...U> void debug(T a, U ... b){cout << a << " ", debug(b ...);};
template<class T> void pary(T l, T r) {
	while (l != r) cout << *l << " ", l++;
	cout << endl;
};
#define ll long long
#define maxn 100005
#define maxc 25
#define mod 1000000007
#define pii pair<int, int>
#define ff first
#define ss second
#define io ios_base::sync_with_stdio(0);cin.tie(0);
struct edge {
	int u, v, w;
	edge(){u = v = w = 0;}
	edge(int x, int y, int z){u = x, v = y, w = z;}
};
vector<edge> ed;
 
struct DSU{
	int par[maxn];
	void init(int n) {
		for (int i = 0;i <= n;i++) par[i] = i;
	}
	int find(int a) {
		return a == par[a] ? a : (par[a] = find(par[a]));
	}
	void Union(int a, int b) { // set par[a] = b
		par[find(a)] = find(b);
	}
} dsu, comp, built;
 
bool mark[maxn];
int vis[maxn];
int wei[maxc], pa[maxc], dep[maxc];
int minres[maxc][maxc]; // minres: minimum restricting edge weight
int c[maxn];
ll p[maxc], siz[maxc];
vector<pii> small[maxc];
void dfs(int n, int par, int d, ll &ans) { //builds small tree sizes
	siz[n] = p[n];
	pa[n] = par;
	dep[n] = d;
	for (auto v:small[n]) {
		if (v.ff != par) {
			dfs(v.ff, n, d+1, ans);
			siz[n] += siz[v.ff];
			if (v.ss) {
				//debug(v.ff, siz[v.ff], wei[v.ff]);
				ans += siz[v.ff] * wei[v.ff];
			}
		}
	}
}
void addedge(int a, int b, int val) { //updates added edges
	if (dep[a] < dep[b]) swap(a, b);
	while (dep[a] > dep[b]) {
		wei[a] = min(wei[a], val);
		a = pa[a];
	}	
	while (a != b) {
		wei[a] = min(wei[a], val), wei[b] = min(wei[b], val);
		a = pa[a], b = pa[b];
	}
}
int main() {
	io
	int n, m, k;
	cin >> n >> m >> k;
	for (int i = 0;i < m;i++) {
		int u, v, w;
		cin >> u >> v >> w;
		ed.push_back(edge(u, v, w));
	}
	sort(ed.begin(), ed.end(), [&](edge x, edge y){return x.w < y.w;});
	dsu.init(n);
	built.init(n);
	vector<edge> add, tree, rep;
	for (int i = 0;i < k;i++) {
		int u, v;
		cin >> u >> v;
		mark[u] = mark[v] = 1;
		built.Union(u, v);
		add.push_back(edge(u, v, 0));
	}
	for (int i = 1;i <= n;i++) cin >> c[i];
	for (auto e:ed) {
		if (dsu.find(e.u) != dsu.find(e.v)) {
			dsu.Union(e.u, e.v);
			tree.push_back(e);
		}	
	}
	dsu.init(n);
	int ind = 0;
	for (auto e:tree) {
		e.u = dsu.find(e.u), e.v = dsu.find(e.v);
		if (mark[e.u] && mark[e.v]) {
			if (built.find(e.u) == built.find(e.v)) rep.push_back(e); 
			else {
				dsu.Union(e.u, e.v);
			}
		} else if (mark[e.u] || mark[e.v]) {
			if (mark[e.u]) swap(e.u, e.v);
			dsu.Union(e.u, e.v);
		} else {
			dsu.Union(e.u, e.v);
		}
		built.Union(e.u, e.v);
	}
	for (int i = 1;i <= n;i++) {
		int f = dsu.find(i);
		if (!vis[f]) {
			vis[f] = ++ind;
		}
		p[vis[f]-1] += c[i];
		//debug("comp", i, vis[f] -1);
	}	
	for (auto &e:add) {
		e.u = vis[dsu.find(e.u)]-1, e.v = vis[dsu.find(e.v)]-1;
		//debug(e.u, e.v);
	}
	//debug();
	for (auto &e:rep) {
		e.u = vis[dsu.find(e.u)]-1, e.v = vis[dsu.find(e.v)]-1;
	}
	ll ans = 0;
	assert(rep.size() <= k);
	for (int i = 1;i < (1<<k);i++) {
		for (int j = 0;j < ind;j++) small[j].clear(), wei[j] = 1<<30;
		//debug(i);
		comp.init(ind);
		bool cy = 0;
		for (int j = 0;j < k;j++) {
			if (i & (1<<j)) {
				small[add[j].u].push_back({add[j].v, 1});
				small[add[j].v].push_back({add[j].u, 1});	
				//debug(add[j].u, add[j].v, comp.find(add[j].u), comp.find(add[j].v));
				if (comp.find(add[j].u) == comp.find(add[j].v)) {
					cy = 1;
					break;
				}
				comp.Union(add[j].u, add[j].v);
			}
		}
		if (cy) continue;
		vector<edge> lim;
		for (auto e:rep) {
			if (comp.find(e.u) == comp.find(e.v)) {
				lim.push_back(e);
			} else {
				comp.Union(e.u, e.v);
				small[e.u].push_back({e.v, 0});
				small[e.v].push_back({e.u, 0});
			}
		}	
		//pary(lim, lim + rs);
		ll tmp = 0;
		dfs(0, 0, 0, tmp);
		for (auto e:lim) addedge(e.u, e.v, e.w);
		tmp = 0;
		dfs(0, 0, 0, tmp);
		ans = max(ans, tmp);	
		//debug(i, tmp);	
	}	
	cout << ans << endl;
}
/*
5 5 1
3 5 2
1 2 3
2 3 5
2 4 4
4 3 6
1 3
10 20 30 40 50

8 8 2
1 2 1
1 3 5
2 7 7
4 7 2
4 6 8
1 6 6
3 8 3
5 8 4
2 4
3 5
1 1 1 1 1 1 1 1 

6 5 4
1 2 2
1 3 3
3 4 1
4 5 5
5 6 4
2 3
3 5
2 5
4 6
3 2 4 1 1 2
*/

Compilation message (stderr)

In file included from toll.cpp:10:
toll.cpp: In function 'int main()':
toll.cpp:143:20: warning: comparison of integer expressions of different signedness: 'std::vector<edge>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  143 |  assert(rep.size() <= k);
      |         ~~~~~~~~~~~^~~~

• Subtask 1: 16 / 16
• Subtask 2: 18 / 18
• Subtask 3: 22 / 22
• Subtask 4: 22 / 22
• Subtask 5: 22 / 22