#include <bits/stdc++.h>
#define int long long
#pragma GCC optimize("O3")
#pragma GCC target("avx2")
typedef long long ll;
using namespace std;
struct Edge{
int s, e, x;
Edge(){}
Edge(int _s, int _e, int _x): s(_s), e(_e), x(_x) {}
bool operator<(const Edge &E) const{
return x < E.x;
}
}a[500500], b[44], aa[44][44];
struct DSU{
int path[500500];
vector<int> st;
void init(int n){for (int i=1;i<=n;i++) path[i] = i;}
void clear(){for (auto &x:st) path[x] = x; st.clear();}
int find(int s){
if (s==path[s]) return s;
return path[s] = find(path[s]);
}
bool merge(int s, int v){
s = find(s), v = find(v);
if (s==v) return 0;
path[s] = v;
st.push_back(s);
return 1;
}
}dsu1, dsu2;
int n, m, k, w[500500];
bool valid_bit(int z){
dsu1.clear();
for (int i=0;i<k;i++) if (z&(1<<i)){
if (!dsu1.merge(b[i].s, b[i].e)) return 0;
}
return 1;
}
ll sw[44], P[44];
int idx[500500], mn[44], ns, aaa[500500];
vector<pair<int, int>> adj[44];
ll dfs0(int s, int pa = -1){
ll ret = sw[s];
for (auto &[v, i]:adj[s]) if (v!=pa){
ll tmp = dfs0(v, s);
ret += tmp;
P[i] = tmp;
}
return ret;
}
int ST[44], stc;
bool dfs(int s, int e, int pa = -1){
if (s==e) return 1;
for (auto &[v, i]:adj[s]) if (v!=pa){
ST[stc++] = i;
if (dfs(v, e, s)) return 1;
stc--;
}
return 0;
}
ll solve(int z, bool flag = 0){
if (!z) return 0;
if (!valid_bit(z)){
if (!flag) return 0;
}
///init
dsu2.clear();
for (int i=0;i<=k+10;i++){
adj[i].clear();
sw[i] = 0;
P[i] = 0;
mn[i] = 1e9;
}
for (int i=0;i<=n;i++) aaa[i] = -1;
///
for (int i=1;i<=m;i++) if (dsu1.merge(a[i].s, a[i].e)){
dsu2.merge(a[i].s, a[i].e);
}
int aac = 1;
for (int i=1;i<=n;i++) if (aaa[dsu2.find(i)]==-1) aaa[dsu2.find(i)] = aac++;
for (int i=1;i<=n;i++){
idx[i] = aaa[dsu2.find(i)];
sw[idx[i]] += w[i];
//printf(" YES %d %d\n", i, w[i]);
}
for (int i=0;i<k;i++) if (z&(1<<i)){
adj[idx[b[i].s]].emplace_back(idx[b[i].e], i);
adj[idx[b[i].e]].emplace_back(idx[b[i].s], i);
}
///new graph
if (flag){
int nc = aac-1;
ns = idx[1];
for (int i=1;i<=m;i++) if (idx[a[i].s]!=idx[a[i].e]){
int x = idx[a[i].s], y = idx[a[i].e];
if (x>y){
swap(a[i].s, a[i].e);
swap(x, y);
}
if (aa[x][y].x) aa[x][y] = min(aa[x][y], Edge(idx[a[i].s], idx[a[i].e], a[i].x));
else aa[x][y] = Edge(idx[a[i].s], idx[a[i].e], a[i].x);
}
int ncnt = 1;
for (int i=1;i<=nc;i++){
for (int j=1;j<=nc;j++) if (aa[i][j].x) a[ncnt++] = aa[i][j];
}
for (int i=0;i<k;i++){
b[i].s = idx[b[i].s];
b[i].e = idx[b[i].e];
}
m = ncnt-1;
n = nc;
for (int i=1;i<=n;i++) w[i] = sw[i];
sort(a+1, a+m+1);
vector<Edge> tmptmp;
dsu1.clear();
for (int i=1;i<=m;i++) if (dsu1.merge(a[i].s, a[i].e)) tmptmp.push_back(a[i]);
for (int i=0;i<(int)tmptmp.size();i++) a[i+1] = tmptmp[i];
m = tmptmp.size();
return 0;
}
///subtask 3
dfs0(idx[ns]);
for (int i=1;i<=m;i++) if (idx[a[i].s]!=idx[a[i].e]){
stc = 0;
assert(dfs(idx[a[i].s], idx[a[i].e]));
for (int j=0;j<stc;j++) mn[ST[j]] = min(mn[ST[j]], a[i].x);
}
ll ret = 0;
for (int i=0;i<k;i++) if (z&(1<<i)){
ret += P[i] * mn[i];
//printf("%lld %d\n", P[i], mn[i]);
}
return ret;
}
signed main(){
cin.tie(NULL);
ios_base::sync_with_stdio(false);
cin >> n >> m >> k;
for (int i=1;i<=m;i++) cin >> a[i].s >> a[i].e >> a[i].x;
for (int i=0;i<k;i++) cin >> b[i].s >> b[i].e;
sort(a+1, a+m+1);
for (int i=1;i<=n;i++) cin >> w[i];
dsu1.init(n); dsu2.init(n);
solve((1<<k)-1, 1);
assert(m<=30);
//printf(" %d %d %d %d\n", n, m, k, ns);
//for (int i=1;i<=m;i++) printf(" %d %d %d\n", a[i].s, a[i].e, a[i].x);
//for (int i=1;i<=n;i++) printf(" %d ", w[i]);
//printf("\n");
ll ans = 0;
for (int z=1;z<(1<<k);z++) ans = max(ans, solve(z));
printf("%lld\n", ans);
return 0;
}
Compilation message
toll.cpp: In function 'll dfs0(long long int, long long int)':
toll.cpp:53:16: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
53 | for (auto &[v, i]:adj[s]) if (v!=pa){
| ^
toll.cpp: In function 'bool dfs(long long int, long long int, long long int)':
toll.cpp:64:16: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
64 | for (auto &[v, i]:adj[s]) if (v!=pa){
| ^
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
340 KB |
Output is correct |
| 2 |
Correct |
1 ms |
340 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
340 KB |
Output is correct |
| 2 |
Correct |
1 ms |
340 KB |
Output is correct |
| 3 |
Correct |
2 ms |
340 KB |
Output is correct |
| 4 |
Correct |
2 ms |
340 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
340 KB |
Output is correct |
| 2 |
Correct |
1 ms |
340 KB |
Output is correct |
| 3 |
Correct |
2 ms |
340 KB |
Output is correct |
| 4 |
Correct |
2 ms |
340 KB |
Output is correct |
| 5 |
Correct |
3 ms |
468 KB |
Output is correct |
| 6 |
Correct |
3 ms |
468 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
340 KB |
Output is correct |
| 2 |
Correct |
1 ms |
340 KB |
Output is correct |
| 3 |
Correct |
2 ms |
340 KB |
Output is correct |
| 4 |
Correct |
2 ms |
340 KB |
Output is correct |
| 5 |
Correct |
3 ms |
468 KB |
Output is correct |
| 6 |
Correct |
3 ms |
468 KB |
Output is correct |
| 7 |
Correct |
194 ms |
13012 KB |
Output is correct |
| 8 |
Correct |
197 ms |
13116 KB |
Output is correct |
| 9 |
Correct |
192 ms |
13128 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
340 KB |
Output is correct |
| 2 |
Correct |
1 ms |
340 KB |
Output is correct |
| 3 |
Correct |
2 ms |
340 KB |
Output is correct |
| 4 |
Correct |
2 ms |
340 KB |
Output is correct |
| 5 |
Correct |
3 ms |
468 KB |
Output is correct |
| 6 |
Correct |
3 ms |
468 KB |
Output is correct |
| 7 |
Correct |
194 ms |
13012 KB |
Output is correct |
| 8 |
Correct |
197 ms |
13116 KB |
Output is correct |
| 9 |
Correct |
192 ms |
13128 KB |
Output is correct |
| 10 |
Correct |
1825 ms |
13116 KB |
Output is correct |
| 11 |
Correct |
2214 ms |
13084 KB |
Output is correct |
| 12 |
Correct |
2288 ms |
19640 KB |
Output is correct |
