Submission #676768

#	Time	Username	Problem	Language	Result	Execution time	Memory
676768		victor_gao	Capital City (JOI20_capital_city)	C++17	100 / 100	2180 ms	469440 KiB

capital_city

//#pragma GCC optimize("Ofast,unroll-loops,O3")
//#pragma GCC optimize("avx,avx2,sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,fma,tune=native")
#include<bits/stdc++.h>
//#include<bits/extc++.h>
//#pragma pack(1)
#define fast ios::sync_with_stdio(0); cin.tie(0);
#define pii pair<int,int>
#define x first
#define y second
#define N 200015
#define C 25
using namespace std;
//using namespace __gnu_pbds;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//typedef tree<int, null_type,less_equal<int>, rb_tree_tag,tree_order_statistics_node_update> order_multiset;
//typedef tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update> order_set;
int n,k;
struct SCC{
    vector<int>g[C*N];
    vector<pii>edge;
    int dfn[C*N],low[C*N],dft=0,boss[C*N],val[C*N];
    long long dp[C*N],nscc=0;
    bool ins[C*N],vis[C*N];
    stack<int>st;
    void init(){
        edge.clear();
        while (!st.empty()) st.pop();
        for (int i=0;i<C*N;i++){
            dfn[i]=low[i]=boss[i]=val[i]=dp[i]=0;
            g[i].clear();
            ins[i]=vis[i]=0;
        }
    }
    void add_edge(int i,int j){
        // i -> j
        g[i].push_back(j);
        edge.push_back({i,j});
    }
    void tarjan(int p){
        dfn[p]=low[p]=++dft;
        st.push(p); ins[p]=1;
        for (auto i:g[p]){
            if (!dfn[i]){
                tarjan(i);
                low[p]=min(low[p],low[i]);
            }
            else if (ins[i]&&dfn[i]<dfn[p])
                low[p]=min(low[p],dfn[i]);
        }
        if (low[p]==dfn[p]){
            nscc++;
        //    cout<<"find cycle "<<nscc<<" : ";
            for (int x=0;x!=p;st.pop()){
                x=st.top(); ins[x]=0;
                boss[x]=nscc;
                if (x<=k) val[nscc]++;
    //            cout<<x<<" ";
            }
     //       cout<<"val "<<val[nscc]<<'\n';
        }
    }
    void build(){
        for (int i=0;i<C*n;i++)
            g[i].clear();
        for (auto i:edge){
            if (boss[i.x]!=boss[i.y]){
    //            cout<<"edge "<<boss[i.x]<<' '<<boss[i.y]<<'\n';
                g[boss[i.x]].push_back(boss[i.y]);
            }
        }
    }
    int dfs(int p){
        if (vis[p]) return dp[p];
        vis[p]=1; dp[p]=val[p];
        for (auto i:g[p]){
            dp[p]+=dfs(i);
            dp[p]=min(dp[p],1000000LL);
        }
        return dp[p];
    }
}scc;
int cap[N],vis[N],son[N],all_col[N],sub_col[N],fa[N],have[N];
vector<int>g[N],path,sub_path;
int get_centroid(int p,int lp,int sz){
    for (auto i:g[p]){
        if (!vis[i]&&i!=lp&&son[i]>sz/2)
            return get_centroid(i,p,sz);
    }
    return p;
}
int dfs1(int p,int lp){
    son[p]=1;
    path.push_back(p);
    for (auto i:g[p]){
        if (!vis[i]&&i!=lp)
            son[p]+=dfs1(i,p);
    }
    return son[p];
}
void dfs2(int p,int lp){
    fa[p]=lp;
    sub_path.push_back(p);
    for (auto i:g[p]){
        if (!vis[i]&&i!=lp)
            dfs2(i,p);
    }
}
void build(int root,int dep){
    for (auto i:sub_path){
        sub_col[cap[i]]++;
        scc.add_edge(dep*n+i,cap[i]);
  //      cout<<"add_1 "<<dep*n+i<<' '<<cap[i]<<'\n';
    }
    /*
    cout<<"sub_col ";
    for (int i=1;i<=k;i++)
        cout<<sub_col[i]<<' ';
    cout<<'\n';
    */
    for (auto i:sub_path){
        if (all_col[cap[i]]==sub_col[cap[i]])
            continue;
        int p=i;
      //  cout<<"try "<<i<<" "<<cap[i]<<'\n';
        scc.add_edge(cap[i],dep*n+fa[p]);
        while (!have[p]){
            scc.add_edge(cap[i],dep*n+fa[p]);
          //  cout<<"add_2 "<<cap[i]<<" "<<dep*n+fa[p]<<'\n';
            have[p]=1; p=fa[p];
        }
    }
    for (auto i:sub_path)
        sub_col[cap[i]]--;
}
void Cut(int p,int lp,int dep){
    path.clear();
  //  cout<<p<<" "<<lp<<" "<<dep<<'\n';
    int sz=dfs1(p,lp);
    int mid=get_centroid(p,lp,sz);
  //  cout<<mid<<" : \n";
    vis[mid]=1; have[mid]=1;
    scc.add_edge(dep*n+mid,cap[mid]);
 //   cout<<"add1 "<<dep*n+mid<<" "<<cap[mid]<<'\n';
    for (auto i:path)
        all_col[cap[i]]++;
 //   cout<<"all_col ";
  //  for (int i=1;i<=k;i++)
  //      cout<<all_col[i]<<" ";
  //  cout<<'\n';
    for (auto i:g[mid]){
        if (vis[i]) continue;
        dfs2(i,mid);
        build(i,dep);
        sub_path.clear();
    }
    for (auto i:path){
        have[i]=0;
        all_col[cap[i]]--;
    }
    for (auto i:g[mid]){
        if (!vis[i])
            Cut(i,mid,dep+1);
    }
}
signed main(){
    fast
    cin>>n>>k;
    scc.init();
    for (int i=1;i<n;i++){
        int a,b; cin>>a>>b;
        g[a].push_back(b);
        g[b].push_back(a);
    }
    for (int i=1;i<=n;i++)
        cin>>cap[i];
    Cut(1,0,1);

    for (int i=1;i<=k;i++){
        if (!scc.dfn[i])
            scc.tarjan(i);
    }
    scc.build();
    int ans=1e9;
    for (int i=1;i<=k;i++){
  //      cout<<scc.boss[i]<<" "<<scc.dfs(scc.boss[i])<<'\n';
        ans=min(scc.dfs(scc.boss[i]),ans);
    }
    assert(ans<=k);
    cout<<ans-1<<'\n';
}

• Subtask 1: 1 / 1
• Subtask 2: 10 / 10
• Subtask 3: 30 / 30
• Subtask 4: 59 / 59