제출 #147020

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
147020		qkxwsm	통행료 (APIO13_toll)	C++14	0 / 100	41 ms	42788 KiB

toll

#include <bits/stdc++.h>

using namespace std;

template<class T, class U>
void ckmin(T &a, U b)
{
	if (a > b) a = b;
}
template<class T, class U>
void ckmax(T &a, U b)
{
	if (a < b) a = b;
}

#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define SZ(x) ((int) ((x).size()))
#define ALL(x) (x).begin(), (x).end()
#define MAXN 300013

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<pii> vpi;
typedef vector<pll> vpl;

int N, M, K,  T;
vector<pair<ll, pii> > edges;
vi edge[MAXN], edge1[MAXN];
int ancestor[20][MAXN];
ll arr[MAXN];
int st[MAXN];
vi nodes;
map<int, ll> cost[MAXN], weight[MAXN];
vpi cand;
int dsu[MAXN];
bitset<MAXN> flag, take, imp;
int parent[MAXN], depth[MAXN];
ll dp[MAXN], subtree[MAXN];
pii bound[MAXN];
ll ans;

bool cmp(int a, int b)
{
	return st[a] < st[b];
}
int get(int u)
{
	return (u == dsu[u] ? u : dsu[u] = get(dsu[u]));
}
bool merge(int u, int v)
{
	u = get(u); v = get(v);
	if (u == v) return false;
	dsu[u] = v;
	return true;
}
void dfs1(int u, int p)
{
	st[u] = T;
	T++;
	subtree[u] = arr[u];
	for (int v : edge[u])
	{
		if (v == p) continue;
		parent[v] = u;
		depth[v] = depth[u] + 1;
		dfs1(v, u);
		subtree[u] += subtree[v];
	}
}
void dfs(int u, int p)
{
	subtree[u] = weight[u][u];
	for (int v : edge1[u])
	{
		if (v == p) continue;
		parent[v] = u;
		dfs(v, u);
		subtree[u] += subtree[v];
		subtree[u] += weight[u][v];
	}
	return;
}
void mark(int u)
{
	//lower, upper
	if (flag[u]) bound[u].se = u;
	for (int v : edge[u])
	{
		if (v == parent[u]) continue;
		bound[v].se = bound[u].se;
		mark(v);
		bound[u].fi = bound[v].fi;
	}
	if (flag[u]) bound[u].fi = u;
}
int lca(int u, int v)
{
	if (depth[u] > depth[v]) swap(u, v);
	FORD(i, 20, 0)
	{
		if ((depth[v] - depth[u]) & (1 << i)) v = ancestor[i][v];
	}
	if (u == v) return u;
	FORD(i, 20, 0)
	{
		if (ancestor[i][v] != ancestor[i][u])
		{
			u = ancestor[i][u];
			v = ancestor[i][v];
		}
	}
	return parent[u];
}

int32_t main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	cin >> N >> M >> K;
	flag[0] = true;
	FOR(i, 0, M)
	{
		int u, v; ll d;
		cin >> u >> v >> d; u--; v--; if (u > v) swap(u, v);
		edges.PB({d, {u, v}});
	}
	FOR(i, 0, K)
	{
		int u, v; cin >> u >> v; u--; v--;
		cand.PB({u, v});
		flag[u] = true;
		flag[v] = true;
	}
	flag[0] = true;
	FOR(i, 0, N)
	{
		cin >> arr[i];
		dsu[i] = i;
	}
	sort(ALL(edges));
	for (auto e : edges)
	{
		// cerr << "HI\n";
		int u = e.se.fi, v = e.se.se; ll d = e.fi;
		if (merge(u, v))
		{
			cost[u][v] = d;
			cost[v][u] = d;
			edge[u].PB(v);
			edge[v].PB(u);
			// cerr << u << ' ' << v << ' ' << cost[u][v] << endl;
		}
	}
	parent[0] = N;
	dfs1(0, N);
	FOR(i, 0, 20) ancestor[i][N] = N;
	FOR(i, 0, N) ancestor[0][i] = parent[i];
	FOR(i, 0, 19)
	{
		FOR(j, 0, N)
		{
			ancestor[i + 1][j] = ancestor[i][ancestor[i][j]];
		}
	}
	FOR(i, 0, N) if (flag[i]) nodes.PB(i);
	sort(ALL(nodes), cmp);
	vi tmp; tmp.PB(0);
	FOR(i, 1, SZ(nodes))
	{
		int u = nodes[i - 1], v = nodes[i], w = lca(u, v);
		if (w != u && w != v) tmp.PB(w);
		tmp.PB(v);
	}
	nodes = tmp;
	for (int u : nodes) flag[u] = true;
	FOR(i, 0, SZ(nodes) - 1)
	{
		int u = nodes[i], v = nodes[i + 1]; if (depth[v] < depth[u]) swap(u, v);
		ll len = 0, wei = 0;
		while(v != u)
		{
			assert(v != N);
			wei += arr[v];
			ckmax(len, cost[v][parent[v]]);
			v = parent[v];
		}
		edges.PB({len, {u, v}});
	}
	sort(ALL(edges));
	FOR(i, 0, N) bound[i] = {-1, -1};
	mark(0);
	FOR(i, 0, N) if (bound[i].fi == -1) bound[i].fi = bound[i].se;
	FOR(i, 0, N)
	{
		weight[bound[i].fi][bound[i].se] += arr[i];
		if (bound[i].fi != bound[i].se) weight[bound[i].se][bound[i].fi] += arr[i];
	}
	parent[0] = N;
	sort(ALL(nodes));
	nodes.erase(unique(ALL(nodes)), nodes.end());
	FOR(i, 0, (1 << K))
	{
		// cerr << "SOLVE " << i << endl;
		for (int x : nodes)
		{
			dsu[x] = x;
			edge1[x].clear();
			dp[x] = 0;
			imp[x] = false;
		}
		FOR(j, 0, K)
		{
			if (!(i & (1 << j))) continue;
			int u = cand[j].fi, v = cand[j].se;
			merge(u, v);
		}
		FOR(j, 0, SZ(edges))
		{
			int u = edges[j].se.fi, v = edges[j].se.se;
			take[j] = merge(u, v);
		}
		FOR(j, 0, K)
		{
			if (!(i & (1 << j))) continue;
			int u = cand[j].fi, v = cand[j].se;
			edge1[u].PB(v);
			edge1[v].PB(u);
			// cerr << u << " -> " << v << endl;
		}
		FOR(j, 0, SZ(edges))
		{
			if (!take[j]) continue;
			int u = edges[j].se.fi, v = edges[j].se.se;
			edge1[u].PB(v);
			edge1[v].PB(u);
			// cerr << u << " -> " << v << endl;
		}
		dfs(0, N);
		FOR(j, 0, K)
		{
			if (!(i & (1 << j))) continue;
			int u = cand[j].fi, v = cand[j].se;
			if (v == parent[u]) swap(u, v);
			imp[v] = true;
		}
		FORD(j, SZ(edges), 0)
		{
			if (take[j]) continue;
			int u = edges[j].se.fi, v = edges[j].se.se; ll d = edges[j].fi;
			//everything on the path u...v gets capped to
			vi pu, pv;
			while(u != 0)
			{
				pu.PB(u);
				u = parent[u];
			}
			while(v != 0)
			{
				pv.PB(v);
				v = parent[v];
			}
			while(!pu.empty() && !pv.empty() && pu.back() == pv.back())
			{
				pu.pop_back(); pv.pop_back();
			}
			for (int x : pu) dp[x] = d;
			for (int x : pv) dp[x] = d;
		}
		ll res = 0;
		for (int x : nodes)
		{
			if (!imp[x]) continue;
			// cerr << "ADD " << x << endl;
			res += subtree[x] * dp[x];
		}
		ckmax(ans, res);
		// cerr << "RES " << res << endl;
	}
	cout << ans << '\n';
	return 0;
}

• Subtask 1: 0 / 16
• Subtask 2: 0 / 18
• Subtask 3: 0 / 22
• Subtask 4: 0 / 22
• Subtask 5: 0 / 22