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 inf = 1e10;
const int MAXN = 1e5 + 25;
vector <int> adj[MAXN];
pair <int, int> bad;
bool vis[MAXN];
void dfs (int pos, int par = -1) {
vis[pos] = 1;
for (auto j : adj[pos]) {
if (j == par) continue;
if (vis[j]) {
bad = {j, pos};
} else {
dfs(j, pos);
}
}
}
int dp[MAXN][2][2][2][2];
void dfs2 (int pos, int par) {
for (int j = 0; j < (int)adj[pos].size(); j++) {
if (adj[pos][j] == par) {
adj[pos].erase(adj[pos].begin() + j);
}
}
for (auto j : adj[pos]) dfs2(j, pos);
}
int ans (int pos, int w, int x, int y, int z) {
if (pos == bad.second && w != z) return inf;
if (pos == bad.first && w != y) return inf;
int &ret = dp[pos][w][x][y][z];
if (ret != -1) return ret;
int flag = x;
flag += (pos == bad.first && z);
flag += (pos == bad.second && y);
for (auto j : adj[pos]) flag += (j == bad.second && z);
if (flag > 1) return ret = inf;
if (flag) {
int sum = 0;
for (auto j : adj[pos]) {
if (j == bad.second) {
sum += ans(j, z, w, y, z);
} else {
sum += ans(j, 0, w, y, z);
}
}
return ret = w + sum;
}
int sum = 0;
for (auto j : adj[pos]) {
sum += ans(j, 0, w, y, z);
}
int mn = inf;
for (auto j : adj[pos]) {
mn = min(mn, ans(j, 1, w, y, z) - ans(j, 0, w, y, z));
}
return ret = w + sum + mn;
}
signed main () {
memset(dp, -1, sizeof(dp));
int n;
cin >> n;
for (int i = 1; i <= n; i++) {
int a, b;
cin >> a >> b;
adj[a].push_back(b);
adj[b].push_back(a);
}
dfs(1);
for (int i = 0; i < (int)adj[bad.first].size(); i++) {
if (adj[bad.first][i] == bad.second) {
adj[bad.first].erase(adj[bad.first].begin() + i);
break;
}
}
for (int i = 0; i < (int)adj[bad.second].size(); i++) {
if (adj[bad.second][i] == bad.first) {
adj[bad.second].erase(adj[bad.second].begin() + i);
break;
}
}
dfs2(bad.first, -1);
int x = min({
ans(bad.first, 0, 0, 0, 1),
ans(bad.first, 0, 0, 0, 0),
ans(bad.first, 1, 0, 1, 0),
ans(bad.first, 1, 0, 1, 1)
});
cout << (x >= inf ? -1 : x) << '\n';
}
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