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;
int main() {
int n, m, ans = 0, t = 0;
cin >> n >> m;
vector<int> tin(n + 1), tout(n + 1), p(n + 1), nr(n + 1), d(n + 1);
vector<array<int, 10>> dpu(n + 1);
vector<vector<int>> G(n + 1), dp(n + 1);
vector<vector<tuple<int, int, int>>> q(n + 1);
vector<tuple<int, int, int>> E;
tout[0] = n + 1;
while (m--) {
int x, y, z;
cin >> x >> y >> z;
if (z == 0)
G[x].emplace_back(y), G[y].emplace_back(x);
ans += z;
E.emplace_back(x, y, z);
}
function<void(int, int)> dfs = [&](int node, int last) {
tin[node] = ++t;
d[node] = d[last] + 1;
p[node] = dpu[node][0] = last;
int cnt = 0;
for (auto x : G[node])
if (x != last) {
nr[x] = 1 << cnt++;
dfs(x, node);
}
dp[node].resize(1 << cnt);
tout[node] = t;
};
dfs(1, 0);
for (int i = 1; i < 10; ++i)
for (int j = 1; j <= n; ++j)
dpu[j][i] = dpu[dpu[j][i - 1]][i - 1];
auto ok = [&](int x, int y) {return tin[x] <= tin[y] && tout[x] >= tout[y]; };
auto lca = [&](int a, int b) {
if (d[a] > d[b])
swap(a, b);
if (ok(a, b))
return a;
for (int i = 9; ~i; --i)
if (!ok(dpu[b][i], a))
b = dpu[b][i];
return dpu[b][0];
};
for (auto [x, y, z] : E) {
int w = lca(x, y);
if (z == 0 || !((d[x] + d[y] - 2 * d[w]) & 1))
q[w].emplace_back(x, y, z);
}
function<void(int, int)> dfs2 = [&](int node, int last) {
for (auto x : G[node])
if (x != last)
dfs2(x, node);
for (auto [x, y, z] : q[node]) {
int xx = 0, yy = 0, cost = z, mask = dp[node].size() - 1;
for (; x != node; xx = nr[x], x = p[x])
cost += dp[x][xx];
for (; y != node; yy = nr[y], y = p[y])
cost += dp[y][yy];
mask ^= xx, mask ^= yy;
for (int i = mask; i >= 0; i = (i - 1) & mask) {
dp[node][i] = max(dp[node][i], dp[node][i | xx | yy] + cost);
if (!i)
break;
}
}
};
dfs2(1, 0);
cout << ans - dp[1][0];
}
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