#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define endl '\n'
#define fi first
#define se second
#define For(i, l, r) for (auto i = (l); i < (r); i++)
#define ForE(i, l, r) for (auto i = (l); i <= (r); i++)
#define FordE(i, l, r) for (auto i = (l); i >= (r); i--)
#define Fora(v, a) for (auto v: (a))
#define bend(a) (a).begin(), (a).end()
#define isz(a) ((signed)(a).size())
using ll = long long;
using ld = long double;
using pii = pair <int, int>;
using vi = vector <int>;
using vpii = vector <pii>;
using vvi = vector <vi>;
const int N = 1e6 + 5, LN = 20;
const ll infll = (ll)1e18 + 7;
int n;
int a[N], b[N];
vpii adj[N];
ll ans;
int vis[N], incycle[N];
void dfs_incycle(int u){
vis[u] = 2;
if (vis[a[u]] == 1){
}
else if (vis[a[u]] == 2){
int v = u;
do{
incycle[v] = 1;
v = a[v];
} while (v != u);
}
else{
dfs_incycle(a[u]);
}
vis[u] = 1;
}
ll chain[N];
pair <ll, int> dfs_farthest(int r, int u, int p){
pair <ll, int> ans = make_pair(0ll, u);
for (auto &[v, w]: adj[u]){
if ((incycle[v] and v != r) or v == p){
continue;
}
auto tans = dfs_farthest(r, v, u); tans.fi += w;
ans = max(ans, tans);
}
return ans;
}
ll dfs_dist(int u, int p){
ll ans = 0;
for (auto &[v, w]: adj[u]){
if (incycle[v] or v == p){
continue;
}
ans = max(ans, dfs_dist(v, u) + w);
}
return ans;
}
int node[N]; ll prefdist[N];
ll c[N];
ll mxc[LN][N];
ll query(int l, int r, ll mxa[][N]){
if (l > r){
return -infll;
}
int z = __lg(r - l + 1);
return max(mxa[z][l], mxa[z][r - (1 << z) + 1]);
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
// freopen("KEK.inp", "r", stdin);
// freopen("KEK.out", "w", stdout);
cin >> n;
ForE(u, 1, n){
int v, w; cin >> v >> w;
a[u] = v; b[u] = w;
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
}
memset(vis, 0, sizeof(vis));
ForE(u, 1, n){
if (vis[u] == 0){
dfs_incycle(u);
}
}
memset(vis, 0, sizeof(vis));
ForE(u, 1, n){
if (vis[u] == 0 and incycle[u] == 1){
chain[u] = dfs_dist(u, u);
}
}
memset(vis, 0, sizeof(vis));
ForE(u, 1, n){
if (vis[u] == 0 and incycle[u] == 1){
ll tans = 0;
int len = 0; ll dist = 0;
{
int v = u, i = 0; ll d = 0;
do{
{
int d1 = dfs_farthest(v, v, v).se;
tans = max(tans, dfs_farthest(v, d1, d1).fi);
}
vis[v] = 1;
node[i] = v;
prefdist[i] = d;
c[i] = chain[v] - prefdist[i];
d += b[v];
v = a[v];
i++;
} while (v != u);
len = i; dist = d;
}
// cout << "cycle " << u << endl;
// For(i, 0, len){
// cout << node[i] << ' ' << prefdist[i] << ' ' << c[i] << endl;
// }
For(i, 0, len){
mxc[0][i] = c[i];
}
For(j, 1, LN){
For(i, 0, len - (1 << j) + 1){
mxc[j][i] = max(mxc[j - 1][i], mxc[j - 1][i + (1 << (j - 1))]);
}
}
int j = 0; ll hdist = 0;
For(i, 0, len){
while ((hdist + b[node[j]]) * 2 <= dist){
hdist += b[node[j]];
j++; if (j == len) j = 0;
}
// cout << "i j " << i << ' ' << j << endl;
if (j >= i){
tans = max(tans, chain[node[i]] + dist + prefdist[i] + query(i + 1, j, mxc));
}
else{
tans = max(tans, chain[node[i]] + dist + prefdist[i] + query(i + 1, len - 1, mxc));
tans = max(tans, chain[node[i]] + prefdist[i] + query(0, j, mxc));
}
// cout << "tans " << tans << endl;
hdist -= b[node[i]];
}
ans += tans;
}
}
cout << ans << endl;
}
/*
==================================================+
INPUT: |
--------------------------------------------------|
--------------------------------------------------|
==================================================+
OUTPUT: |
--------------------------------------------------|
--------------------------------------------------|
==================================================+
*/
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
14 ms |
27732 KB |
Output is correct |
| 2 |
Correct |
16 ms |
27800 KB |
Output is correct |
| 3 |
Correct |
14 ms |
27896 KB |
Output is correct |
| 4 |
Correct |
14 ms |
27732 KB |
Output is correct |
| 5 |
Correct |
14 ms |
27732 KB |
Output is correct |
| 6 |
Correct |
14 ms |
27784 KB |
Output is correct |
| 7 |
Correct |
14 ms |
27700 KB |
Output is correct |
| 8 |
Correct |
14 ms |
27732 KB |
Output is correct |
| 9 |
Correct |
14 ms |
27712 KB |
Output is correct |
| 10 |
Correct |
14 ms |
27732 KB |
Output is correct |
| 11 |
Correct |
14 ms |
27732 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
14 ms |
27860 KB |
Output is correct |
| 2 |
Correct |
15 ms |
27908 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
15 ms |
27860 KB |
Output is correct |
| 2 |
Correct |
19 ms |
28224 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
21 ms |
28976 KB |
Output is correct |
| 2 |
Correct |
31 ms |
32092 KB |
Output is correct |
| 3 |
Correct |
24 ms |
29048 KB |
Output is correct |
| 4 |
Correct |
22 ms |
28428 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
38 ms |
33772 KB |
Output is correct |
| 2 |
Correct |
46 ms |
36168 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
87 ms |
42216 KB |
Output is correct |
| 2 |
Correct |
89 ms |
51556 KB |
Output is correct |
| 3 |
Correct |
113 ms |
68820 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
134 ms |
52192 KB |
Output is correct |
| 2 |
Correct |
187 ms |
92868 KB |
Output is correct |
| 3 |
Correct |
213 ms |
105448 KB |
Output is correct |
| 4 |
Runtime error |
266 ms |
131072 KB |
Execution killed with signal 9 |
| 5 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
291 ms |
74764 KB |
Output is correct |
| 2 |
Runtime error |
607 ms |
131072 KB |
Execution killed with signal 9 |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
346 ms |
131072 KB |
Execution killed with signal 9 |
| 2 |
Halted |
0 ms |
0 KB |
- |
