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 lg long long
const lg N = 2e5+5;
vector<lg> adj[N], adj2[N];
lg dp[N][4][2][2], par[N], vis[N], tmp, node1, node2;
lg get(lg src)
{
if(par[src] == src) return src;
return par[src] = get(par[src]);
}
lg dfs(lg src, lg b, lg x, lg y, lg par = -1)
{
b &= 3;
auto&ret = dp[src][b][x][y];
if(src == node1 && (b&1) != x) return ret = 1e18;
if(src == node2 && (b&1) != y) return ret = 1e18;
if(~ret) return ret;
ret = 1e18;
lg sum = 0;
if(adj[src].empty()) ret = 0;
lg check = 0;
for(auto it : adj[src])
{
if(it == par) continue;
if((it == node1 && x) || (it == node2 && y)) check++;
sum += dfs(it, (b << 1), x, y, src);
}
if(check == 2)
{
return ret;
}
if(b&2)
{
if(check)
{
ret = 1e18;
return ret;
}
ret = sum;
return ret;
}
for(auto it : adj[src])
{
if(it == par) continue;
if(it == node1 && !x) continue;
if(it == node2 && !y) continue;
if(check && it != node1 && it != node2) continue;
ret = min(ret, dfs(it, (b << 1)|1, x, y, src)-dfs(it, (b << 1), x, y, src)+sum+1);
}
return ret;
}
vector<lg> path;
lg odd_cycle(lg src, lg par = -1)
{
vis[src] = ++tmp;
for(auto it : adj2[src])
{
if(it == par) continue;
if(vis[it])
{
path.push_back(it);
return (vis[src]-vis[it]-1)%2;
}
if(odd_cycle(it, src))
{
path.push_back(src);
return true;
}
}
return 0;
}
int main()
{
lg n;
cin >> n;
for(int i = 1; i <= n; i++) par[i] = i;
for(int i = 0; i < n; i++)
{
lg u, v;
cin >> u >> v;
int a = get(u), b = get(v);
adj2[u].push_back(v);
adj2[v].push_back(u);
if(a == b)
{
node1 = a;
node2 = b;
continue;
}
par[a] = b;
adj[u].push_back(v);
adj[v].push_back(u);
}
memset(dp, -1, sizeof(dp));
lg ans = 1e18;
for(int i = 0; i < 4; i++)
{
ans = min({ans, dfs(1, 0, i, i/2), dfs(1, 1, i, i/2)+1});
}
// for(int i = 1; i <= n; i++)
// {
// for(int j = 0; j < 4; j++)
// {
// for(int k = 0; k < 2; k++)
// {
// for(int z = 0; z < 2; z++)
// {
// cout << (dp[i][j][k][z] >= 1e17 ? -2 : dp[i][j][k][z]) << ' ';
// }
// }
// }
// cout << '\n';
// }
if(ans >= 1e17) ans = -1;
cout << ans << '\n';
}
/*
1 2
2 3
3 1
1 4
1
*/
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