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 int long long
const int N=2e5+10;
map<int, int> mp[N];
int n, a[N], h[N], c[N], sz[N];
vector<int> g[N];
int vis[N];
void dfs_sz(int u){
vis[u]=1;
sz[u]=1;
for (int &v:g[u]){
dfs_sz(v);
sz[u]+=sz[v];
if (sz[v]>sz[g[u][0]]) swap(v, g[u][0]);
}
}
void dfs_merge(int u){
if (g[u].empty()){
mp[u][1]=c[u];
mp[u][h[u]+1]=-c[u];
return;
}
for (int &v:g[u]){
dfs_merge(v);
if (v==g[u][0]) mp[u].swap(mp[v]);
else{
for (auto &i:mp[v]){
mp[u][i.first]+=i.second;
}
}
}
mp[u][h[u]+1]-=c[u];
auto it=mp[u].find(h[u]+1);
int cur=c[u];
while (it!=mp[u].begin()){
--it;
if (it->second<0 && cur>=-it->second){
cur-=-it->second;
it=mp[u].erase(it);
}else{
it->second+=cur;
cur=0;
break;
}
}
}
int32_t main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n;
vector<int> vals{-1};
for (int i=1; i<=n; ++i){
cin >> a[i] >> h[i] >> c[i];
vals.push_back(h[i]);
if (a[i]!=i) g[a[i]].push_back(i);
}
sort(vals.begin(), vals.end());
vals.resize(unique(vals.begin(), vals.end())-vals.begin());
for (int i=1; i<=n; ++i) h[i]=lower_bound(vals.begin(), vals.end(), h[i])-vals.begin();
int ans=0;
for (int i=1; i<=n; ++i) if (!vis[i]){
int u=i;
vector<int> tmp;
while (!vis[u]){
tmp.push_back(u);
vis[u]=1;
u=a[u];
}
vector<int> cycle(find(tmp.begin(), tmp.end(), u), tmp.end());
for (int j:cycle) vis[j]=2;
vector<int> child;
for (int j:cycle) for (int k:g[j]) if (vis[k]!=2) child.push_back(k);
for (int &v:child){
dfs_sz(v);
if (sz[v]>sz[child[0]]) swap(v, child[0]);
}
map<int, int> mpp;
for (int &v:child){
dfs_merge(v);
if (v==child[0]){
mpp.swap(mp[v]);
}else{
for (auto &j:mp[v]) mpp[j.first]+=j.second;
}
}
int cur=mpp.empty()?0:mpp.begin()->second;
map<int, int> cc;
for (int v:cycle) cc[h[v]]+=c[v];
vector<pair<int, int>> vv;
vv.emplace_back(0, 0);
for (auto &j:mpp) vv.emplace_back(j.first, vv.back().second+j.second);
for (auto &j:cc){
auto it=lower_bound(vv.begin(), vv.end(), make_pair(j.first+1, (int)-1e18))-1;
cur=max(cur, it->second+j.second);
}
ans+=cur;
}
cout << accumulate(c+1, c+n+1, 0ll)-ans << '\n';
return 0;
}
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