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Submission #223885

# Submission time Handle Problem Language Result Execution time Memory
223885 2020-04-16T19:54:06 Z medk Capital City (JOI20_capital_city) C++14
11 / 100
 3000 ms 47076 KB 
#include <bits/stdc++.h>

#define ll long long
#define pb push_back
#define x first
#define y second
#define all(u) u.begin(),u.end()
#define sz(u) (int)(u.size())
#define INF (int)(1e9)

using namespace std;

const int MAXN=2e5+5;

int n,k,ans=INF;
vector<vector<int>> tr(MAXN),grp(MAXN),cd(MAXN);
int col[MAXN],subsz[MAXN],parcd[MAXN],par[MAXN],dpth[MAXN],in[MAXN],dpthcd[MAXN];
bool blocked[MAXN];
int lca[MAXN][20];
int root=-1;
vector<int> eul;

void calc_sz(int u, int pr)
{
    subsz[u]=1;
    for(int v:tr[u])
    {
        if(v==pr || blocked[v]) continue;
        calc_sz(v,u);
        subsz[u]+=subsz[v];
    }
}

int find_centroid(int u, int pr, int tar)
{
    for(int v:tr[u])
    {
        if(v==pr || blocked[v]) continue;
        if(subsz[v]>tar) return find_centroid(v,u,tar);
    }
    return u;
}

void decomp(int u, int pr, int d=0)
{
    memset(subsz,0,sizeof(subsz));
    calc_sz(u,pr);
    int centroid=find_centroid(u,pr,subsz[u]/2);
    blocked[centroid]=1;
    parcd[centroid]=pr;
    dpthcd[centroid]=d;
    if(pr==-1) root=centroid;
    else
    {
        cd[centroid].pb(pr);
        cd[pr].pb(centroid);
    }
    for(int v:tr[centroid])
    {
        if(blocked[v]) continue;
        decomp(v,centroid,d+1);
    }
}

void makeul(int u, int pr, int d)
{
    in[u]=sz(eul);
    eul.pb(u);
    dpth[u]=d;
    par[u]=pr;
    d++;
    for(int v:tr[u])
    {
        if(pr==v) continue;
        makeul(v,u,d);
        eul.pb(u);
    }
}

int getlca(int u, int v)
{
    int l=in[u], r=in[v];
    if(l>r) swap(l,r);
    int lg=log2(r-l+1);
    if(dpth[lca[l][lg]]<=dpth[lca[r-(1<<lg)+1][lg]]) return lca[l][lg];
    return lca[r-(1<<lg)+1][lg];
}

int lcacd(int u, int v)
{
    if(dpthcd[u]==dpthcd[v])
    {
        if(u==v) return u;
        else return lcacd(parcd[u],parcd[v]);
    }
    if(dpthcd[v]<dpthcd[u]) swap(u,v);
    return lcacd(u,parcd[v]);
}

void solve(int rt, int pr)
{
    vector<bool> viscol(k,0);
    vector<int> visver(n,0);
    int lc=rt, used=0;
    queue<int> q;
    q.push(rt);
    visver[rt]=1;
    bool bug=0;
    while(!q.empty())
    {
        int u=q.front(); q.pop();
        visver[u]=2;
        if(u!=lc)
        {
            int mypar=par[u];
            if(visver[mypar]==0 && !viscol[col[mypar]] && col[mypar]!=col[u])
            {
                if(lcacd(mypar,rt)!=rt)
                {
                    bug=1;
                    break;
                }
                q.push(mypar);
                visver[mypar]=1;
            }
        }
        if(viscol[col[u]]) continue;
        viscol[col[u]]=1;
        used++;
        for(int v:grp[col[u]])
        {
            if(v==u) continue;
            int newlc=getlca(lc,v);
            if(newlc!=lc)
            {
                if(visver[lc]==2)
                {
                    if(lcacd(par[lc],rt)!=rt)
                    {
                        bug=1;
                        break;
                    }
                    q.push(par[lc]);
                    visver[par[lc]]=1;
                }
                lc=newlc;
            }
            if(lcacd(v,rt)!=rt)
            {
                bug=1;
                break;
            }
            visver[v]=1;
            q.push(v);
        }
        if(bug) break;
    }
    if(!bug) ans=min(ans,used);
    for(int v:cd[rt])
    {
        if(v==pr) continue;
        solve(v,rt);
    }
}

int main()
{
    //freopen("test.in","r",stdin);
    ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    cin>>n>>k;
    for(int i=0;i<n-1;i++)
    {
        int u,v; cin>>u>>v;
        u--,v--;
        tr[u].pb(v);
        tr[v].pb(u);
    }
    for(int i=0;i<n;i++)
    {
        cin>>col[i];
        col[i]--;
        grp[col[i]].pb(i);
    }
    decomp(0,-1);
    makeul(0,-1,0);
    for(int i=0;i<sz(eul);i++) lca[i][0]=eul[i];
    for(int j=1;j<20;j++)
        for(int i=0;i+(1<<j)<=sz(eul);i++)
            lca[i][j]=(dpth[lca[i][j-1]]<=dpth[lca[i+(1<<(j-1))][j-1]]?lca[i][j-1]:lca[i+(1<<(j-1))][j-1]);
    solve(root,-1);
    cout<<ans-1<<'\n';
}

Subtask #1
1.0 / 1.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 15232 KB Output is correct
2 Correct 13 ms 15360 KB Output is correct
3 Correct 16 ms 15360 KB Output is correct
4 Correct 13 ms 15232 KB Output is correct
5 Correct 13 ms 15232 KB Output is correct
6 Correct 13 ms 15232 KB Output is correct
7 Correct 13 ms 15360 KB Output is correct
8 Correct 13 ms 15232 KB Output is correct
9 Correct 13 ms 15360 KB Output is correct
10 Correct 13 ms 15232 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 15232 KB Output is correct
2 Correct 13 ms 15360 KB Output is correct
3 Correct 16 ms 15360 KB Output is correct
4 Correct 13 ms 15232 KB Output is correct
5 Correct 13 ms 15232 KB Output is correct
6 Correct 13 ms 15232 KB Output is correct
7 Correct 13 ms 15360 KB Output is correct
8 Correct 13 ms 15232 KB Output is correct
9 Correct 13 ms 15360 KB Output is correct
10 Correct 13 ms 15232 KB Output is correct
11 Correct 70 ms 15864 KB Output is correct
12 Correct 65 ms 15864 KB Output is correct
13 Correct 66 ms 15864 KB Output is correct
14 Correct 64 ms 15864 KB Output is correct
15 Correct 64 ms 15992 KB Output is correct
16 Correct 64 ms 15992 KB Output is correct
17 Correct 64 ms 15992 KB Output is correct
18 Correct 64 ms 15992 KB Output is correct
19 Correct 63 ms 15992 KB Output is correct
20 Correct 64 ms 15992 KB Output is correct
21 Correct 63 ms 15992 KB Output is correct
22 Correct 63 ms 16080 KB Output is correct
23 Correct 66 ms 15952 KB Output is correct
24 Correct 74 ms 15992 KB Output is correct
25 Correct 65 ms 15992 KB Output is correct
26 Correct 64 ms 15992 KB Output is correct
27 Correct 65 ms 15992 KB Output is correct
28 Correct 64 ms 15992 KB Output is correct
29 Correct 64 ms 15908 KB Output is correct
30 Correct 65 ms 15992 KB Output is correct

Subtask #3
0 / 30.0

# Verdict Execution time Memory Grader output
1 Execution timed out 3076 ms 47076 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #4
0 / 59.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 15232 KB Output is correct
2 Correct 13 ms 15360 KB Output is correct
3 Correct 16 ms 15360 KB Output is correct
4 Correct 13 ms 15232 KB Output is correct
5 Correct 13 ms 15232 KB Output is correct
6 Correct 13 ms 15232 KB Output is correct
7 Correct 13 ms 15360 KB Output is correct
8 Correct 13 ms 15232 KB Output is correct
9 Correct 13 ms 15360 KB Output is correct
10 Correct 13 ms 15232 KB Output is correct
11 Correct 70 ms 15864 KB Output is correct
12 Correct 65 ms 15864 KB Output is correct
13 Correct 66 ms 15864 KB Output is correct
14 Correct 64 ms 15864 KB Output is correct
15 Correct 64 ms 15992 KB Output is correct
16 Correct 64 ms 15992 KB Output is correct
17 Correct 64 ms 15992 KB Output is correct
18 Correct 64 ms 15992 KB Output is correct
19 Correct 63 ms 15992 KB Output is correct
20 Correct 64 ms 15992 KB Output is correct
21 Correct 63 ms 15992 KB Output is correct
22 Correct 63 ms 16080 KB Output is correct
23 Correct 66 ms 15952 KB Output is correct
24 Correct 74 ms 15992 KB Output is correct
25 Correct 65 ms 15992 KB Output is correct
26 Correct 64 ms 15992 KB Output is correct
27 Correct 65 ms 15992 KB Output is correct
28 Correct 64 ms 15992 KB Output is correct
29 Correct 64 ms 15908 KB Output is correct
30 Correct 65 ms 15992 KB Output is correct
31 Execution timed out 3076 ms 47076 KB Time limit exceeded
32 Halted 0 ms 0 KB -