Submission #956480

#	Time	Username	Problem	Language	Result	Execution time	Memory
956480		GrindMachine	Love Polygon (BOI18_polygon)	C++17	54 / 100	178 ms	23404 KiB

polygon

#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;
}

• Subtask 1: 0 / 21
• Subtask 2: 25 / 25
• Subtask 3: 29 / 29
• Subtask 4: 0 / 25