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>
//#pragma GCC target ("avx2")
using namespace std;
int viz[100002], dp[100002][2][2], n, nod1, nod2;
vector<int>G[100002];
int c1, c2;
void dfs (int x, int par) {
viz[x] = 1;
for (auto it : G[x]) {
if (it != par) {
if (viz[it]) {
nod1 = x, nod2 = it;
}
else
dfs(it, x);
}
}
}
void dfs (int x) {
viz[x] = 1;
vector<int>sons;
for (auto it : G[x])
if (!viz[it]){
dfs(it);
sons.push_back(it);
}
for (int par = 0; par < 2; par++)
for (int c= 0; c < 2; c++) {
if (x == nod1 && (c != c1 || par != 0))
dp[x][c][par]= -1;
else if (x == nod2 && (c != c2 || par + c1 == 2))
dp[x][c][par] = -1;
else {
int sum = 0, prost = 0;
for (auto it : sons) {
if (dp[it][0][c] == -1) prost++;
sum += dp[it][0][c];
}
if (par || (x == nod1 && c2) || (x == nod2 && c1))
dp[x][c][par] = (!prost ? sum+c : -1);
else {
int mn = 1e9;
if (prost > 1) {
dp[x][c][par] = -1;
continue;
}
for (auto it : sons) {
if (dp[it][0][c] == -1 && dp[it][1][c] != -1) {
mn = dp[it][1][c] - dp[it][0][c];
break;
}
if (dp[it][1][c] != -1)
mn = min(dp[it][1][c] - dp[it][0][c], mn);
}
if (mn != 1e9)
dp[x][c][par] = mn+sum+c;
else
dp[x][c][par] = -1;
}
}
}
}
int main ()
{
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cin >> n;
for (int i = 1; i <= n; i++) {
int x, y;
cin >> x >> y;
G[x].push_back(y);
G[y].push_back(x);
}
dfs(1, 0);
int ans = 1e9;
for (c1 = 0; c1 < 2; c1++)
for (c2 = 0; c2 < 2; c2++) {
memset(dp, 0, sizeof(dp));
memset(viz, 0, sizeof(viz));
dfs(nod1);
if (dp[nod1][0][0] != -1) ans = min(ans, dp[nod1][0][0]);
if (dp[nod1][1][0] != -1) ans = min(ans, dp[nod1][1][0]);
}
cout << ((ans == 1e9 || ans < 0) ? -1 : ans);
return 0;
}
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