#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 mxprefc[N], mxsuffc[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]);
// }
int ldq, rdq, dq[N];
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))]);
// }
// }
For(i, 0, len){
mxprefc[i] = max(i == 0 ? -infll : mxprefc[i - 1], c[i]);
}
FordE(i, len - 1, 0){
mxsuffc[i] = max(i == len - 1 ? -infll : mxsuffc[i + 1], c[i]);
}
ldq = 0; rdq = 0;
int j = 0; ll hdist = 0;
For(i, 0, len){
if (j < i){
j = i;
hdist = 0;
ldq = 0; rdq = 0;
}
while ((hdist + b[node[j]]) * 2 <= dist){
hdist += b[node[j]];
j++; if (j == len) j = 0;
if (j >= i){
while (rdq > ldq and c[dq[rdq - 1]] <= c[j]){
rdq--;
}
rdq++; dq[rdq - 1] = j;
}
}
// cout << "i j " << i << ' ' << j << endl;
if (j >= i){
tans = max(tans, chain[node[i]] + dist + prefdist[i] + /*query(i + 1, j, mxc)*/ (i + 1 > j ? -infll : c[dq[ldq]]));
}
else{
tans = max(tans, chain[node[i]] + dist + prefdist[i] + /*query(i + 1, len - 1, mxc)*/ (i + 1 > len - 1 ? -infll : mxsuffc[i + 1]));
tans = max(tans, chain[node[i]] + prefdist[i] + /*query(0, j, mxc)*/ mxprefc[j]);
}
// cout << "tans " << tans << endl;
hdist -= b[node[i]];
if (ldq < rdq and dq[ldq] == i + 1){
ldq++;
}
}
ans += tans;
}
}
cout << ans << endl;
}
/*
==================================================+
INPUT: |
--------------------------------------------------|
--------------------------------------------------|
==================================================+
OUTPUT: |
--------------------------------------------------|
--------------------------------------------------|
==================================================+
*/
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
14 ms |
27732 KB |
Output is correct |
| 2 |
Correct |
13 ms |
27788 KB |
Output is correct |
| 3 |
Correct |
14 ms |
27800 KB |
Output is correct |
| 4 |
Correct |
14 ms |
27732 KB |
Output is correct |
| 5 |
Correct |
14 ms |
27800 KB |
Output is correct |
| 6 |
Correct |
14 ms |
27732 KB |
Output is correct |
| 7 |
Correct |
15 ms |
27740 KB |
Output is correct |
| 8 |
Correct |
17 ms |
27804 KB |
Output is correct |
| 9 |
Correct |
13 ms |
27732 KB |
Output is correct |
| 10 |
Correct |
14 ms |
27792 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 |
13 ms |
27860 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
15 ms |
27860 KB |
Output is correct |
| 2 |
Correct |
21 ms |
28224 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
25 ms |
28912 KB |
Output is correct |
| 2 |
Correct |
98 ms |
30996 KB |
Output is correct |
| 3 |
Correct |
32 ms |
29208 KB |
Output is correct |
| 4 |
Correct |
18 ms |
28448 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
148 ms |
32348 KB |
Output is correct |
| 2 |
Correct |
387 ms |
34936 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
541 ms |
40672 KB |
Output is correct |
| 2 |
Execution timed out |
2087 ms |
43840 KB |
Time limit exceeded |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1000 ms |
51324 KB |
Output is correct |
| 2 |
Execution timed out |
2087 ms |
70032 KB |
Time limit exceeded |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
279 ms |
75124 KB |
Output is correct |
| 2 |
Execution timed out |
2086 ms |
113852 KB |
Time limit exceeded |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
358 ms |
131072 KB |
Execution killed with signal 9 |
| 2 |
Halted |
0 ms |
0 KB |
- |
