This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e3, maxchildren = 10;
vector<int> g[maxn], through[maxn];
int par[maxn], parIdx[maxn], h[maxn], tin[maxn], tout[maxn], tt;
vector<pair<int, int>> edges;
vector<int> w;
void dfsRoot(int v) {
tin[v] = tt++;
for (int i = 0; i < (int)g[v].size(); ++i) {
int u = g[v][i];
if (u != par[v]) {
par[u] = v;
parIdx[u] = i;
h[u] = h[v] + 1;
dfsRoot(u);
} else {
swap(g[v][i], g[v].back());
g[v].pop_back();
--i;
}
}
tout[v] = tt++;
}
bool isAncestor(int v, int u) {
return tin[v] <= tin[u] && tout[v] >= tout[u];
}
int dp[maxn][1 << maxchildren];
void dfsAns(int v) {
for (const int& u : g[v]) {
dfsAns(u);
}
int c = g[v].size();
for (int mask = 0; mask < (1 << c); ++mask) {
dp[v][mask] = 0;
for (int i = 0; i < c; ++i) {
if (mask & (1 << i)) {
dp[v][mask] += dp[g[v][i]][(1 << g[g[v][i]].size()) - 1];
}
}
}
int m = through[v].size();
for (int i = 0; i < m; ++i) {
int cost = w[through[v][i]], u, sub = 0;
u = edges[through[v][i]].first;
if (u != v) {
cost += dp[u][(1 << g[u].size()) - 1];
while (par[u] != v) {
int p = par[u];
cost += dp[p][((1 << g[p].size()) - 1) ^ (1 << parIdx[u])];
u = p;
}
sub |= (1 << parIdx[u]);
}
u = edges[through[v][i]].second;
if (u != v) {
cost += dp[u][(1 << g[u].size()) - 1];
while (par[u] != v) {
int p = par[u];
cost += dp[p][((1 << g[p].size()) - 1) ^ (1 << parIdx[u])];
u = p;
}
sub |= (1 << parIdx[u]);
}
for (int mask = (1 << c) - 1; mask >= 0; --mask) {
if ((mask & sub) == sub) {
dp[v][mask] = max(dp[v][mask], cost + dp[v][mask ^ sub]);
}
}
}
}
void solve() {
int n, m;
cin >> n >> m;
int sumAll = 0;
for (int i = 0; i < m; ++i) {
int v, u, weight;
cin >> v >> u >> weight;
--v, --u;
if (weight == 0) {
g[v].emplace_back(u);
g[u].emplace_back(v);
} else {
sumAll += weight;
edges.emplace_back(v, u);
w.emplace_back(weight);
}
}
par[0] = parIdx[0] = -1;
h[0] = 0;
tt = 0;
dfsRoot(0);
for (int i = 0; i < (int)edges.size(); ++i) {
int v = edges[i].first, u = edges[i].second;
if (h[v] % 2 != h[u] % 2) {
swap(edges[i], edges.back());
swap(w[i], w.back());
edges.pop_back();
w.pop_back();
--i;
continue;
}
if (tin[v] > tin[u]) {
swap(edges[i].first, edges[i].second);
swap(v, u);
}
int lca = v;
while (!isAncestor(lca, u)) {
lca = par[lca];
}
through[lca].emplace_back(i);
}
dfsAns(0);
cout << sumAll - dp[0][(1 << g[0].size()) - 1] << '\n';
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#ifdef LOCAL
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
int T = 1;
cin >> T;
while (T--) {
solve();
cerr << "-----------\n";
cout << "-----------\n";
}
#else
int T = 1;
// cin >> T;
while (T--) {
solve();
}
#endif
return 0;
}
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