#include <bits/stdc++.h>
using namespace std;
int n, m, k;
int a[300000], b[300000], c[300000], ord[300000], cnt[300000];
int x[20], y[20], cost[20];
int id[100000];
int pa[40], up[40], depth[40];
int64_t p[100000], pp[100000], sz[100000];
int par[100000];
vector<pair<int, int>> adj[40];
inline int root(int u) { return par[u] < 0 ? u : par[u] = root(par[u]); }
inline bool is_connected(int u, int v) { return root(u) == root(v); }
inline bool unite(int u, int v) {
u = root(u), v = root(v);
if (u == v) return 0;
if (par[u] > par[v]) swap(u, v);
p[u] += p[v];
par[u] += par[v];
par[v] = u;
return 1;
}
int64_t ans;
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m >> k;
for (int i = 0; i < m; i++) cin >> a[i] >> b[i] >> c[i], a[i]--, b[i]--;
for (int i = 0; i < k; i++) cin >> x[i] >> y[i], x[i]--, y[i]--;
for (int i = 0; i < n; i++) cin >> pp[i];
memset(par, -1, n * sizeof *par);
iota(ord, ord + m, 0);
sort(ord, ord + m, [&](int a, int b) {
return c[a] < c[b];
});
for (int j = 0; j < m; j++) {
cnt[ord[j]] += unite(a[ord[j]], b[ord[j]]);
} // spanning tree with 0 new edge
memset(par, -1, n * sizeof *par);
for (int i = 0; i < k; i++) {
unite(x[i], y[i]);
}
for (int j = 0; j < m; j++) {
cnt[ord[j]] += unite(a[ord[j]], b[ord[j]]);
} // spanning tree with k new edges
vector<int> almost_mst;
memset(par, -1, n * sizeof *par);
for (int i = 0; i < n; i++) p[i] = pp[i];
for (int i = 0; i < m; i++) {
if (cnt[ord[i]] == 1) almost_mst.emplace_back(ord[i]);
if (cnt[ord[i]] == 2) unite(a[ord[i]], b[ord[i]]);
}
int N = 0;
for (int i = 0; i < n; i++) {
if (root(i) == i) id[i] = N, pp[N++] = p[i];
}
for (int j = 0; j < k; j++) x[j] = id[root(x[j])];
for (int j = 0; j < k; j++) y[j] = id[root(y[j])];
for (int j : almost_mst) a[j] = id[root(a[j])];
for (int j : almost_mst) b[j] = id[root(b[j])];
const int ROOT = id[root(0)];
int64_t res = 0;
for (int i = 1; i < 1 << k; i++) {
memset(par, -1, N * sizeof *par);
bool ok = 1;
for (int j = 0; j < k; j++) {
if (i >> j & 1) {
cost[j] = 1e9;
if (!unite(x[j], y[j])) ok = 0;
}
}
if (!ok) continue;
vector<int> not_mst, mst;
for (int j : almost_mst) {
if (!unite(a[j], b[j])) {
not_mst.emplace_back(j);
} else {
mst.emplace_back(j);
adj[a[j]].emplace_back(b[j], -1);
adj[b[j]].emplace_back(a[j], -1);
}
}
for (int j = 0; j < k; j++) {
if (i >> j & 1) {
adj[y[j]].emplace_back(x[j], j);
adj[x[j]].emplace_back(y[j], j);
}
}
int64_t ans = 0;
function<void(int, int)> dfs = [&](int u, int pr) {
pa[u] = pr;
sz[u] = p[u];
for (pair<int, int>& e : adj[u]) {
if (e.first == pr) continue;
up[e.first] = e.second;
depth[e.first] = depth[u] + 1;
dfs(e.first, u);
sz[u] += sz[e.first];
if (e.second != -1) ans += 1ll * cost[e.second] * sz[e.first];
}
};
depth[root(ROOT)] = 0;
dfs(root(ROOT), -1);
for (int j : not_mst) {
int u = a[j], v = b[j];
if (depth[u] < depth[v]) swap(u, v);
while (depth[u] > depth[v]) {
int id = up[u];
if (id != -1) cost[id] = min(cost[id], c[j]);
u = pa[u];
}
while (u != v) {
int id;
id = up[u];
if (id != -1) cost[id] = min(cost[id], c[j]);
u = pa[u];
id = up[v];
if (id != -1) cost[id] = min(cost[id], c[j]);
v = pa[v];
}
}
memset(par, -1, N * sizeof *par);
for (int j = 0; j < N; j++) p[j] = pp[j];
for (int j : mst) unite(a[j], b[j]);
ans = 0;
dfs(root(ROOT), -1);
for (int j = 0; j < N; j++) vector<pair<int, int>>().swap(adj[j]);
res = max(res, ans);
}
cout << res;
}
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
0 ms |
340 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
0 ms |
340 KB |
Output is correct |
| 3 |
Incorrect |
2 ms |
340 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
0 ms |
340 KB |
Output is correct |
| 3 |
Incorrect |
2 ms |
340 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
0 ms |
340 KB |
Output is correct |
| 3 |
Incorrect |
2 ms |
340 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
0 ms |
340 KB |
Output is correct |
| 3 |
Incorrect |
2 ms |
340 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
