#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
vector<ll> adj[N];
vector<bool> cyc(N);
vector<ll> subsiz(N);
ll dp[N][2];
void dfs1(ll u, ll p){
subsiz[u] = 1;
trav(v,adj[u]){
if(v == p or cyc[v]) conts;
dfs1(v,u);
subsiz[u] += subsiz[v];
}
dp[u][0] = 0, dp[u][1] = 1;
ll mn = inf2;
trav(v,adj[u]){
if(v == p or cyc[v]) conts;
ll mnv = min(dp[v][0],dp[v][1]);
dp[u][0] += mnv, dp[u][1] += mnv;
ll pair_cost = dp[v][1]-1;
amin(mn,-mnv+pair_cost);
}
dp[u][0] += mn;
}
void solve(int test_case)
{
ll n; cin >> n;
map<string,ll> mp;
auto get_id = [&](string s){
if(mp.count(s)) return mp[s];
return mp[s] = sz(mp)+1;
};
vector<ll> indeg(n+5);
vector<ll> a(n+5);
rep1(i,n){
string s,t; cin >> s >> t;
ll u = get_id(s), v = get_id(t);
a[u] = v;
adj[v].pb(u);
indeg[v]++;
}
if(n&1){
cout << -1 << endl;
return;
}
queue<ll> q;
rep1(i,n) if(!indeg[i]) q.push(i);
rep1(i,n) cyc[i] = 1;
while(!q.empty()){
ll u = q.front();
q.pop();
cyc[u] = 0;
ll v = a[u];
indeg[v]--;
if(!indeg[v]){
q.push(v);
}
}
vector<bool> vis(n+5);
ll ans = 0;
rep1(i,n){
if(vis[i] or !cyc[i]) conts;
vector<int> nodes;
int j = i;
while(!vis[j]){
vis[j] = 1;
nodes.pb(j);
j = a[j];
}
trav(u,nodes){
dfs1(u,-1);
}
ll cost = 0;
if(sz(nodes) == 1){
ll u = nodes[0];
ll s = subsiz[u];
cost = min((dp[u][0]+s)/2,(dp[u][1]+s)/2);
ans += cost;
}
else if(sz(nodes) == 2){
ll u = nodes[0], v = nodes[1];
ll su = subsiz[u], sv = subsiz[v];
ll cost = inf2;
rep(j,2){
rep(k,2){
ll curr_cost = (dp[u][j]+su)/2+(dp[v][k]+sv)/2;
if(j == 1 and k == 1){
curr_cost -= 2;
}
amin(cost,curr_cost);
}
}
ans += cost;
}
else{
ll pairs = sz(nodes)/2;
ans += pairs;
ans += sz(nodes)&1;
conts;
ll best = inf2;
// dont pair ends
ll dp1[2], dp2[2];
memset(dp1,0x3f,sizeof dp1);
memset(dp2,0x3f,sizeof dp2);
dp1[0] = 0;
trav(u,nodes){
ll su = subsiz[u];
rep(j,2){
rep(k,2){
ll cost = dp1[j]+(dp[u][k]+su)/2;
amin(dp2[k],cost);
// pair up prev and u
if(j == 1 and k == 1){
amin(dp2[0],cost-1);
}
}
}
rep(j,2){
dp1[j] = dp2[j];
dp2[j] = inf2;
}
}
amin(best,dp1[0]);
amin(best,dp1[1]);
// pair ends
memset(dp1,0x3f,sizeof dp1);
memset(dp2,0x3f,sizeof dp2);
{
ll u = nodes[0], v = nodes.back();
ll su = subsiz[u], sv = subsiz[v];
dp1[1] = (dp[u][1]+su)/2+(dp[v][1]+sv)/2-1;
}
rep1(ind,sz(nodes)-2){
ll u = nodes[ind];
ll su = subsiz[u];
rep(j,2){
rep(k,2){
ll cost = dp1[j]+(dp[u][k]+su)/2;
amin(dp2[k],cost);
// pair up prev and u
if(j == 1 and k == 1){
amin(dp2[0],cost-1);
}
}
}
rep(j,2){
dp1[j] = dp2[j];
dp2[j] = inf2;
}
}
amin(best,dp1[0]);
amin(best,dp1[1]);
ans += best;
}
}
cout << ans << endl;
}
int main()
{
fastio;
int t = 1;
// cin >> t;
rep1(i, t) {
solve(i);
}
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
4952 KB |
Output is correct |
| 2 |
Correct |
2 ms |
4956 KB |
Output is correct |
| 3 |
Correct |
2 ms |
4956 KB |
Output is correct |
| 4 |
Incorrect |
2 ms |
4956 KB |
Output isn't correct |
| 5 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
4956 KB |
Output is correct |
| 2 |
Correct |
2 ms |
4956 KB |
Output is correct |
| 3 |
Correct |
1 ms |
4956 KB |
Output is correct |
| 4 |
Correct |
146 ms |
18132 KB |
Output is correct |
| 5 |
Correct |
157 ms |
19796 KB |
Output is correct |
| 6 |
Correct |
156 ms |
20208 KB |
Output is correct |
| 7 |
Correct |
127 ms |
19512 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
178 ms |
17084 KB |
Output is correct |
| 2 |
Correct |
173 ms |
18552 KB |
Output is correct |
| 3 |
Correct |
121 ms |
17548 KB |
Output is correct |
| 4 |
Correct |
158 ms |
16140 KB |
Output is correct |
| 5 |
Correct |
174 ms |
23404 KB |
Output is correct |
| 6 |
Correct |
155 ms |
16860 KB |
Output is correct |
| 7 |
Correct |
140 ms |
16724 KB |
Output is correct |
| 8 |
Correct |
141 ms |
16868 KB |
Output is correct |
| 9 |
Correct |
129 ms |
16460 KB |
Output is correct |
| 10 |
Correct |
88 ms |
16068 KB |
Output is correct |
| 11 |
Correct |
2 ms |
4956 KB |
Output is correct |
| 12 |
Correct |
2 ms |
4956 KB |
Output is correct |
| 13 |
Correct |
2 ms |
4952 KB |
Output is correct |
| 14 |
Correct |
1 ms |
4956 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
4952 KB |
Output is correct |
| 2 |
Correct |
2 ms |
4956 KB |
Output is correct |
| 3 |
Correct |
2 ms |
4956 KB |
Output is correct |
| 4 |
Incorrect |
2 ms |
4956 KB |
Output isn't correct |
| 5 |
Halted |
0 ms |
0 KB |
- |
