/////////////////////include/////////////////////
//#include <bits/stdc++.h>
#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <string>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <cassert>
#include <set>
#include <map>
#include <unordered_map>
#include <vector>
#include <stack>
#include <queue>
#include <iomanip>
#include <bitset>
#include <stdio.h>
#include <climits>
#include <numeric>
using namespace std;
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
//template <typename T>
//using ordered_set = tree <T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
/////////////////////define/////////////////////
#define ci(x) if(x) cout << "YES" << '\n'; else cout << "NO" << '\n';
#define cii(x) if(check(x))
#define MOD 1000000007
#define MOD2 998244353
#define oo 1e9
#define ool 1e18L
#define pii pair<int, int>
#define pll pair<long long, long long>
#define mii map<int, int>
#define vi vector<int>
#define vpi vector<pair<int, int>>
#define vll vector <ll>
#define ff first
#define ss second
#define mp make_pair
#define ll long long
#define ld long double
#define pb push_back
#define eb emplace_back
#define pob pop_back
#define lb lower_bound
#define ub upper_bound
#define bs binary_search
#define sz(x) (int((x).size()))
#define all(x) (x).begin(), (x).end()
#define alll(x) (x), (x) + n
#define clr(x) (x).clear();
#define fri(x) for(int i = 0; i < x; ++i)
#define frj(x) for(int j = 0; j < x; ++j)
#define frp(x) for(int p = 0; p < x; ++p)
#define frr(a, b) for(int i = a; i < b; ++i)
#define frrj(a, b) for(int j = a; j < b; ++j)
#define fra(x) for(int i = 0; i < x; ++i) cin >> a[i];
#define frb(x) for(int i = 0; i < x; ++i) cin >> b[i];
#define frs(x) for(auto it = x.begin(); it != x.end(); ++it)
#define fr(x) for(auto it : x) //el
#define fastio ios_base::sync_with_stdio(false); cin.tie(0);
#define dbg(x) cerr << #x << ": " << x << endl;
#define ce(x) cout << x << endl;
#define uniq(x) x.resize(unique(all(x)) - x.begin()); //make all one after sorting
#define blt __builtin_popcount
/////////////////////print array, vector, deque, set, multiset, pair, map /////////////////////
void print(long long t) {cerr << t;}
void print(int t) {cerr << t;}
void print(string t) {cerr << t;}
void print(char t) {cerr << t;}
void print(double t) {cerr << t;}
void print(long double t) {cerr << t;}
void print(unsigned long long t) {cerr << t;}
template <class T, class V> void print(pair <T, V> p) {cerr << "{"; print(p.first); cerr << ","; print(p.second); cerr << "}";}
template <class T, class V> void print(T v[],V n) {cerr << "["; for(int i = 0; i < n; i++) {print(v[i]); cerr << " "; } cerr << "]"; cout << endl;}
template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]"; cout << endl;}
template <class T> void print(set <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]"; cout << endl;}
template <class T> void print(multiset <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]"; cout << endl;}
template <class T> void print(stack <T> v) {cerr << "[ "; stack<T> s = v; while(s.size()) {T i = s.top(); print(i); s.pop(); cerr << " ";} cerr << "]"; cout << endl;}
template <class T> void print(queue <T> v) {cerr << "[ "; queue<T> s = v; while(s.size()) {T i = s.front(); print(i); s.pop(); cerr << " ";} cerr << "]"; cout << endl;}
template <class T> void print(deque <T> v) {cerr << "[ "; deque<T> s = v; while(s.size()) {T i = s.front(); print(i); s.pop_front(); cerr << " ";} cerr << "]"; cout << endl;}
template <class T, class V> void print(map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]"; cout << endl;}
template <class T, class V> void print(unordered_map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]"; cout << endl;}
/////////////////////code/////////////////////
vi t[100005];
int dp[100005][2][2][2][2], root, special; //ira guyn, parenti guyn, rooti, speciali
bool dfs(int v, int p) {
int cnt = 0;
bool f = 0;
for(int u : t[v]) {
if(u == p) continue;
f |= dfs(u, v);
cnt++;
}
fri(2) {
frj(2) {
for(int rc = 0; rc < 2; rc++) {
for(int sc = 0; sc < 2; sc++) {
if((v==root && i != rc) ||
(v==special && i != sc) ||
(p==root && j != rc) ||
(p==special && j != sc) ||
(v==special && rc && j) ||
(!cnt && !j && !(v == special && rc)) ||
(v==root && j) ||
(p == root && i && sc) ||
(p == special && i && rc)
)
{
dp[v][i][j][rc][sc] = -1;
}
else {
// if(v==1) { dbg(i) dbg(j) dbg(rc) dbg(sc) }
if(j || (v==root && sc) || (v==special && rc)) { //ira erexeqi guyn 0
dp[v][i][j][rc][sc] = i;
for(int u : t[v]) {
if(u == p) continue;
if(dp[u][0][i][rc][sc] == -1) {
dp[v][i][j][rc][sc] = -1;
break;
}
else dp[v][i][j][rc][sc] += dp[u][0][i][rc][sc];
}
} else { //erexeqic uxix 1y pti 1lini
vi anhnarner;
dp[v][i][j][rc][sc] = i;
for(int u : t[v]) {
if(u == p) continue;
if(dp[u][0][i][rc][sc] == -1)
anhnarner.pb(u);
else dp[v][i][j][rc][sc] += dp[u][0][i][rc][sc];
}
if(anhnarner.size() >= 2) dp[v][i][j][rc][sc] = -1;
else if(anhnarner.size() == 1) {
if(dp[anhnarner[0]][1][i][rc][sc] != -1)
dp[v][i][j][rc][sc] += dp[anhnarner[0]][1][i][rc][sc];
else dp[v][i][j][rc][sc] = -1;
} else {
int cur = dp[v][i][j][rc][sc];
dp[v][i][j][rc][sc] = 1e9;
for(int u : t[v]) {
if(u == p || dp[u][1][i][rc][sc] == -1) continue;
dp[v][i][j][rc][sc] = min(dp[v][i][j][rc][sc],
cur - dp[u][0][i][rc][sc] + dp[u][1][i][rc][sc]);
}
if(dp[v][i][j][rc][sc] == 1e9) dp[v][i][j][rc][sc] = -1;
}
}
}
}
}
}
}
// dbg(v) dbg(cnt)
if(!cnt)
return 1;
return 0;
}
vi g[100005];
vi cycle;
int vis[100005], f;
int p[100005];
void find_cycle(int v, int par) {
vis[v] = 1;
p[v] = par;
for(int u : g[v]) {
if(u == par) continue;
if(vis[u] == 1) {
int cur = v;
while(cur != u) {
cycle.pb(cur);
if(cur == p[cur]) assert(0);
cur = p[cur];
}
cycle.pb(cur);
f = 1;
return;
}
else if(!vis[u])
find_cycle(u, v);
if(f) return;
}
vis[v] = 2;
}
int x[100005], y[100005];
int main() {
fastio;
int n; cin >> n;
fri(n) {
cin >> x[i] >> y[i];
g[x[i]].pb(y[i]);
g[y[i]].pb(x[i]);
}
find_cycle(1, 1);
assert(cycle.size() > 2);
root = cycle[0], special = cycle[1];
fri(n) {
if(root==x[i]&&special==y[i]) continue;
if(special==x[i]&&root==y[i]) continue;
t[x[i]].pb(y[i]);
t[y[i]].pb(x[i]);
}
// frr(1, 1 + n) print(t[i]);
// dbg(root) dbg(special)
dfs(root, root);
// for(int v = 1; v <= n; v++) {
// dbg(v)
// fri(2) {
// frj(2) {
// for(int rc = 0; rc < 2; rc++) {
// for(int sc = 0; sc < 2; sc++) {
// if(dp[v][i][j][rc][sc] == -1) continue;
// dbg(i) dbg(j) dbg(rc) dbg(sc) dbg(dp[v][i][j][rc][sc])
// }
// }
// }
// }
// }
int ans = 1e9;
fri(2) {
frj(2) {
for(int rc = 0; rc < 2; rc++) {
for(int sc = 0; sc < 2; sc++) {
if(dp[root][i][j][rc][sc] != -1)
ans = min(ans, dp[root][i][j][rc][sc]);
}
}
}
}
if(ans == 1e9) ans = -1;
cout << ans;
return 0;
}
// ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥
// ♥ ♥ ♥ ♥ ♥ ♥ ♥
// ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥
// ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥
// ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥
//
// God loves Fil, Fil accepts God's will
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
4948 KB |
Output is correct |
| 2 |
Correct |
3 ms |
4948 KB |
Output is correct |
| 3 |
Correct |
3 ms |
5032 KB |
Output is correct |
| 4 |
Correct |
3 ms |
4948 KB |
Output is correct |
| 5 |
Correct |
173 ms |
45636 KB |
Output is correct |
| 6 |
Correct |
139 ms |
45756 KB |
Output is correct |
| 7 |
Correct |
138 ms |
45588 KB |
Output is correct |
| 8 |
Correct |
182 ms |
45652 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
4948 KB |
Output is correct |
| 2 |
Incorrect |
3 ms |
4948 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
4948 KB |
Output is correct |
| 2 |
Incorrect |
3 ms |
4948 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
4948 KB |
Output is correct |
| 2 |
Correct |
3 ms |
4948 KB |
Output is correct |
| 3 |
Correct |
3 ms |
5032 KB |
Output is correct |
| 4 |
Correct |
3 ms |
4948 KB |
Output is correct |
| 5 |
Correct |
173 ms |
45636 KB |
Output is correct |
| 6 |
Correct |
139 ms |
45756 KB |
Output is correct |
| 7 |
Correct |
138 ms |
45588 KB |
Output is correct |
| 8 |
Correct |
182 ms |
45652 KB |
Output is correct |
| 9 |
Correct |
3 ms |
4948 KB |
Output is correct |
| 10 |
Incorrect |
3 ms |
4948 KB |
Output isn't correct |
| 11 |
Halted |
0 ms |
0 KB |
- |
