Submission #667250

#	Time	Username	Problem	Language	Result	Execution time	Memory
667250		kirakaminski968	Toll (APIO13_toll)	C++11	100 / 100	1714 ms	14480 KiB

toll

#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;
#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;
    int v; 
    int 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) { 
		par[find(a)] = find(b);
	}
} dsu, comp, built;
bool mark[maxn];
int vis[maxn];
int wei[maxc], pa[maxc], dep[maxc]; 
int c[maxn]; 
ll p[maxc], siz[maxc]; 
vector<pii> small[maxc]; 
void dfs(int n, int par, int d, ll &ans) { 
	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) ans += siz[v.ff] * wei[v.ff];
		}
	}
}
void addedge(int a, int b, int val) { 
	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];
	}	
	for (auto &e:add) e.u = vis[dsu.find(e.u)]-1, e.v = vis[dsu.find(e.v)]-1;
	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;
		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});	
				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});
			}
		}	
		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);
	}	
	cout << ans << endl;
}

Compilation message (stderr)

In file included from toll.cpp:9:
toll.cpp: In function 'int main()':
toll.cpp:126:20: warning: comparison of integer expressions of different signedness: 'std::vector<edge>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  126 |  assert(rep.size() <= k);
      |         ~~~~~~~~~~~^~~~

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