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;
#define TRACE(x) cerr << #x << " :: " << x << endl
#define _ << " " <<
#define SZ(x) (int)(x).size()
#define ALL(x) (x).begin(),(x).end()
#define FOR(i,a,b) for(int i=(a);i<=(b);++i)
#define RFOR(i,a,b) for(int i=(a);i>=(b);--i)
typedef long long ll;
const int mxN = 2e5+5;
int N, A[mxN], H[mxN], C[mxN], V;
vector<int> al[mxN], vals, cyc;
int vis[mxN], pa[mxN], onstk[mxN], incyc[mxN];
map<int,ll> dp[mxN];
void dfs(int u) {
dp[u].insert(make_pair(0,0));
for (int v : al[u]) {
dfs(v);
if (dp[v].count(H[v]+1)) dp[v][H[v]+1] += C[v];
else dp[v].insert(make_pair(H[v]+1, C[v]));
if (0 < H[v]) {
if (dp[v].count(0)) dp[v][0] += C[v];
else dp[v].insert(make_pair(0,C[v]));
auto it = --dp[v].lower_bound(H[v]+1);
while (it != dp[v].begin() && it->second <= C[v]) {
auto x = prev(it);
x->second += it->second;
dp[v].erase(it);
it = x;
}
it->second -= C[v];
}
if (SZ(dp[v]) > SZ(dp[u])) swap(dp[v],dp[u]);
for (auto& x : dp[v]) {
if (dp[u].count(x.first)) dp[u][x.first] += x.second;
else dp[u].insert(x);
}
}
}
void dfs2(int u) {
vis[u] = 1;
onstk[u] = 1;
for (int& v : al[u]) {
if (!vis[v]) {
pa[v] = u;
dfs2(v);
} else if (onstk[v]) {
cyc.push_back(v);
for (int x = u; x != v; x = pa[x]) cyc.push_back(x);
}
}
onstk[u] = 0;
}
int main() {
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
cin >> N;
FOR(i,1,N){
cin >> A[i] >> H[i] >> C[i];
al[A[i]].push_back(i);
vals.push_back(H[i]);
}
vals.push_back(1);
sort(ALL(vals));
vals.resize(unique(ALL(vals))-vals.begin());
FOR(i,1,N){
H[i] = lower_bound(ALL(vals),H[i])-vals.begin();
}
V = SZ(vals);
ll tot = 0;
memset(vis,0,sizeof vis);
FOR(i,1,N) if (!vis[i]) {
cyc.clear();
dfs2(i);
if (cyc.empty()) continue;
sort(ALL(cyc), [](int u, int v){ return H[u] < H[v]; });
for (int& u : cyc) incyc[u] = 1;
auto& adj = al[cyc[0]];
RFOR(j,SZ(adj)-1,0) if (incyc[adj[j]]) {
adj.erase(adj.begin()+j);
}
FOR(j,1,SZ(cyc)-1){
for (int& v : al[cyc[j]]) if (!incyc[v]) {
adj.push_back(v);
}
al[cyc[j]].clear();
al[cyc[j]].push_back(cyc[j-1]);
}
int root = cyc.back();
dfs(root);
ll ans = dp[root][0] + C[root], cur = 0;
for (auto& x : dp[root]) {
if (x.first > H[root]) break;
cur += x.second;
}
ans = min(ans, cur);
//TRACE(ans);
tot += ans;
}
cout << tot << '\n';
}
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