#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
const int MOD = 1000000007;
const ll INF = 1e18;
const int MX = 500001;
int n, dist[MX], pre[MX], besDist[MX];
vi adj[MX];
pl bes = {-1,0};
void tri(pl x) {
if (x.f > bes.f) bes = {x.f,0};
if (x.f == bes.f) bes.s += x.s;
}
void dfs(int cur) {
for (int i: adj[cur]) if (i != pre[cur]) {
pre[i] = cur;
dist[i] = dist[cur]+1;
dfs(i);
}
}
void genDist(int cur) {
memset(dist,0,sizeof dist);
pre[cur] = -1;
dfs(cur);
}
int treeDiameter() {
genDist(1);
int bes = 0; FOR(i,1,n+1) if (dist[i] > dist[bes]) bes = i;
genDist(bes); FOR(i,1,n+1) if (dist[i] > dist[bes]) bes = i;
return dist[bes];
}
int t;
vi x;
vi genCenter() {
t = treeDiameter();
int bes = 0; FOR(i,1,n+1) if (dist[i] > dist[bes]) bes = i;
F0R(i,t/2) bes = pre[bes];
if (t&1) return {bes,pre[bes]};
return {bes};
}
pi dfs(int a, int b, int c) {
vpi v;
pi z = {0,0};
for (int i: adj[a]) if (i != b) {
pi t = dfs(i,a,c+1); t.f ++;
v.pb(t);
if (t.f > z.f) z.s = z.f, z.f = t.f;
else if (t.f > z.s) z.s = t.f;
}
int co = 0;
for (int i: adj[a]) if (i != b) {
if (v[co].f == z.f) besDist[i] = z.s;
else besDist[i] = z.f;
co ++;
}
if (sz(v) == 0) v.pb({0,1});
if (sz(v) == 1) return v[0];
sort(v.rbegin(),v.rend());
int ind = 0, sum = v[0].s;
while (ind+1 < sz(v) && v[ind+1].f == v[ind].f)
sum += v[++ind].s;
if (ind > 0) {
ll t = (ll)sum*(sum-1)/2;
F0R(i,ind+1) t -= (ll)v[i].s*(v[i].s-1)/2;
tri({(ll)v[0].f*2*c,t});
} else {
ll sum2 = 0;
int ind = 1;
while (ind < sz(v) && v[ind].f == v[1].f) sum2 += v[ind++].s;
tri({(ll)(v[0].f+v[1].f)*c,(ll)sum2*sum});
}
return {v[0].f,sum};
}
vpi tmp;
void solveNoCenter() {
if (sz(x) == 2) {
tmp.pb(dfs(x[1],x[0],t/2+1));
tmp.pb(dfs(x[0],x[1],t/2+1));
} else {
for (int i: adj[x[0]]) tmp.pb(dfs(i,x[0],t/2+1));
}
}
vpi z[2];
void dfs2(int cur, int pre, int cdist, int cmx, int ind) {
bool isLeaf = 1;
for (int i: adj[cur]) if (i != pre) {
dfs2(i,cur,cdist+1,max(cmx,besDist[i]),ind);
isLeaf = 0;
}
if (isLeaf) z[ind].pb({cmx,cdist});
}
int stor[2][500001];
void solveCenter() {
vi maj;
ll sum = 0, bad = 0;
int mx = 0;
if (sz(x) == 2) maj = x;
else {
F0R(i,sz(tmp)) if (tmp[i].f == t/2-1) {
maj.pb(adj[x[0]][i]);
sum += tmp[i].s;
bad += (ll)tmp[i].s*(tmp[i].s-1)/2;
} else {
mx = max(mx,tmp[i].f+1);
}
}
if (sz(maj) > 2) {
tri({(ll)t*t/2,(ll)sum*(sum-1)/2-bad});
return;
}
// cout << "OH " << sz(x) << " " << maj[0] << " " << maj[1] << "\n";
//cout << sz(maj) << " " << x[0] << "\n";
//exit(0);
//cout << maj[0] << " " << maj[1] << " " << x[0] << " " << mx << "\n";
if (sz(x) == 2) {
dfs2(x[0],x[1],0,0,0);
dfs2(x[1],x[0],1,0,0);
} else {
dfs2(maj[0],x[0],1,mx,0);
dfs2(maj[1],x[0],1,mx,1);
}
sort(all(z[0])), sort(all(z[1]));
F0R(k,2) for (auto a: z[k]) stor[k][a.s] ++;
array<int,2> t = {500000,500000};
while (sz(z[0]) && sz(z[1])) {
F0R(k,2) while (!stor[k][t[k]]) t[k] --;
if (z[0].back().f < z[1].back().f) {
tri({(ll)(t[0]+z[1].back().s)*z[1].back().f,stor[0][t[0]]});
stor[1][z[1].back().s] --; z[1].pop_back();
} else {
tri({(ll)(t[1]+z[0].back().s)*z[0].back().f,stor[1][t[1]]});
stor[0][z[0].back().s] --; z[0].pop_back();
}
}
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
cin >> n;
F0R(i,n-1) {
int a, b; cin >> a >> b;
adj[a].pb(b), adj[b].pb(a);
}
x = genCenter();
solveNoCenter();
// cout << bes.f << " " << bes.s << "\n";
solveCenter();
cout << bes.f << " " << bes.s;
}
/* Look for:
* the exact constraints (multiple sets are too slow for n=10^6 :( )
* special cases (n=1?)
* overflow (ll vs int?)
* array bounds
*/
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
15 ms |
14196 KB |
Output is correct |
| 2 |
Correct |
16 ms |
14196 KB |
Output is correct |
| 3 |
Correct |
16 ms |
14196 KB |
Output is correct |
| 4 |
Correct |
17 ms |
14196 KB |
Output is correct |
| 5 |
Correct |
17 ms |
14196 KB |
Output is correct |
| 6 |
Incorrect |
17 ms |
14236 KB |
Output isn't correct |
| 7 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
15 ms |
14196 KB |
Output is correct |
| 2 |
Correct |
16 ms |
14196 KB |
Output is correct |
| 3 |
Correct |
16 ms |
14196 KB |
Output is correct |
| 4 |
Correct |
17 ms |
14196 KB |
Output is correct |
| 5 |
Correct |
17 ms |
14196 KB |
Output is correct |
| 6 |
Incorrect |
17 ms |
14236 KB |
Output isn't correct |
| 7 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
15 ms |
14196 KB |
Output is correct |
| 2 |
Correct |
16 ms |
14196 KB |
Output is correct |
| 3 |
Correct |
16 ms |
14196 KB |
Output is correct |
| 4 |
Correct |
17 ms |
14196 KB |
Output is correct |
| 5 |
Correct |
17 ms |
14196 KB |
Output is correct |
| 6 |
Incorrect |
17 ms |
14236 KB |
Output isn't correct |
| 7 |
Halted |
0 ms |
0 KB |
- |
