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Submission #956491

# Submission time Handle Problem Language Result Execution time Memory
956491 2024-04-02T05:32:35 Z GrindMachine Love Polygon (BOI18_polygon) C++17
100 / 100
 185 ms 25424 KB 
#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 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[0] = (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
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4956 KB Output is correct
2 Correct 1 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 2 ms 4956 KB Output is correct
6 Correct 2 ms 4956 KB Output is correct
7 Correct 2 ms 4956 KB Output is correct
8 Correct 2 ms 4956 KB Output is correct
9 Correct 2 ms 4952 KB Output is correct
10 Correct 2 ms 4956 KB Output is correct
11 Correct 2 ms 4956 KB Output is correct
12 Correct 2 ms 4952 KB Output is correct
13 Correct 2 ms 5208 KB Output is correct
14 Correct 2 ms 4956 KB Output is correct
15 Correct 2 ms 4956 KB Output is correct

Subtask #2
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 5208 KB Output is correct
2 Correct 2 ms 4996 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 185 ms 19464 KB Output is correct
5 Correct 157 ms 18772 KB Output is correct
6 Correct 150 ms 19364 KB Output is correct
7 Correct 169 ms 18648 KB Output is correct

Subtask #3
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 158 ms 18256 KB Output is correct
2 Correct 174 ms 19940 KB Output is correct
3 Correct 114 ms 18856 KB Output is correct
4 Correct 145 ms 17312 KB Output is correct
5 Correct 159 ms 24512 KB Output is correct
6 Correct 136 ms 17996 KB Output is correct
7 Correct 155 ms 18284 KB Output is correct
8 Correct 133 ms 18000 KB Output is correct
9 Correct 125 ms 17744 KB Output is correct
10 Correct 90 ms 17348 KB Output is correct
11 Correct 2 ms 4952 KB Output is correct
12 Correct 2 ms 4956 KB Output is correct
13 Correct 2 ms 5020 KB Output is correct
14 Correct 2 ms 4956 KB Output is correct

Subtask #4
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4956 KB Output is correct
2 Correct 1 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 2 ms 4956 KB Output is correct
6 Correct 2 ms 4956 KB Output is correct
7 Correct 2 ms 4956 KB Output is correct
8 Correct 2 ms 4956 KB Output is correct
9 Correct 2 ms 4952 KB Output is correct
10 Correct 2 ms 4956 KB Output is correct
11 Correct 2 ms 4956 KB Output is correct
12 Correct 2 ms 4952 KB Output is correct
13 Correct 2 ms 5208 KB Output is correct
14 Correct 2 ms 4956 KB Output is correct
15 Correct 2 ms 4956 KB Output is correct
16 Correct 2 ms 5208 KB Output is correct
17 Correct 2 ms 4996 KB Output is correct
18 Correct 2 ms 4956 KB Output is correct
19 Correct 185 ms 19464 KB Output is correct
20 Correct 157 ms 18772 KB Output is correct
21 Correct 150 ms 19364 KB Output is correct
22 Correct 169 ms 18648 KB Output is correct
23 Correct 158 ms 18256 KB Output is correct
24 Correct 174 ms 19940 KB Output is correct
25 Correct 114 ms 18856 KB Output is correct
26 Correct 145 ms 17312 KB Output is correct
27 Correct 159 ms 24512 KB Output is correct
28 Correct 136 ms 17996 KB Output is correct
29 Correct 155 ms 18284 KB Output is correct
30 Correct 133 ms 18000 KB Output is correct
31 Correct 125 ms 17744 KB Output is correct
32 Correct 90 ms 17348 KB Output is correct
33 Correct 2 ms 4952 KB Output is correct
34 Correct 2 ms 4956 KB Output is correct
35 Correct 2 ms 5020 KB Output is correct
36 Correct 2 ms 4956 KB Output is correct
37 Correct 155 ms 19536 KB Output is correct
38 Correct 159 ms 18944 KB Output is correct
39 Correct 146 ms 19020 KB Output is correct
40 Correct 161 ms 18868 KB Output is correct
41 Correct 133 ms 18768 KB Output is correct
42 Correct 162 ms 19084 KB Output is correct
43 Correct 154 ms 19144 KB Output is correct
44 Correct 144 ms 19024 KB Output is correct
45 Correct 164 ms 19300 KB Output is correct
46 Correct 142 ms 19132 KB Output is correct
47 Correct 134 ms 18824 KB Output is correct
48 Correct 150 ms 19340 KB Output is correct
49 Correct 157 ms 20896 KB Output is correct
50 Correct 114 ms 19796 KB Output is correct
51 Correct 130 ms 18380 KB Output is correct
52 Correct 163 ms 25424 KB Output is correct
53 Correct 130 ms 18768 KB Output is correct
54 Correct 143 ms 18812 KB Output is correct
55 Correct 132 ms 19028 KB Output is correct
56 Correct 141 ms 18768 KB Output is correct
57 Correct 91 ms 18120 KB Output is correct
58 Correct 2 ms 4956 KB Output is correct
59 Correct 2 ms 5020 KB Output is correct
60 Correct 2 ms 4956 KB Output is correct
61 Correct 2 ms 4956 KB Output is correct
62 Correct 2 ms 4956 KB Output is correct
63 Correct 2 ms 4956 KB Output is correct
64 Correct 3 ms 4952 KB Output is correct
65 Correct 139 ms 20336 KB Output is correct
66 Correct 178 ms 19692 KB Output is correct
67 Correct 144 ms 20192 KB Output is correct
68 Correct 146 ms 19868 KB Output is correct
69 Correct 2 ms 4956 KB Output is correct
70 Correct 2 ms 4956 KB Output is correct
71 Correct 2 ms 4956 KB Output is correct
72 Correct 2 ms 4952 KB Output is correct
73 Correct 2 ms 4952 KB Output is correct
74 Correct 1 ms 4956 KB Output is correct
75 Correct 2 ms 4956 KB Output is correct
76 Correct 2 ms 4956 KB Output is correct
77 Correct 2 ms 4956 KB Output is correct
78 Correct 2 ms 4956 KB Output is correct
79 Correct 2 ms 4956 KB Output is correct
80 Correct 1 ms 4956 KB Output is correct
81 Correct 2 ms 4956 KB Output is correct
82 Correct 2 ms 4956 KB Output is correct
83 Correct 2 ms 4956 KB Output is correct