Tree.cpp

// 重心列挙 O(n) verified AGC018-D
// see http://www.learning-algorithms.com/entry/2018/01/03/215559
// TODO 再帰除去
vector<int> centroid(int n, vector<int> *vec) {
  vector<int> centroid;
  vector<int> sz(n);
  function<void(int,int)> dfs = [&](int v, int prev){
    sz[v] = 1;
    bool is_centroid = true;
    for(auto to : g[v]) if(to != prev){
      dfs(to, v);
      sz[v] += sz[to];
      if(sz[to] > n/2) is_centroid = false;
    }
    if(n - sz[v] > n/2) is_centroid = false;
    if(is_centroid) centroid.push_back(v);
  };
  dfs(0, -1);
  return centroid;
}


// 木の直径パス (unweighted)
// verify for weighted: AOJ GRL 5A
vector<int> diameter(int n, vector<int> *vec){
  if(n==1) return {0};
  vector<int> dist(n);
  vector<int> pre(n);
  auto bfs = [&](int ini){
    queue<pair<int,int>> q;
    q.push({ini,-1});
    dist[ini] = 0;
    int farthest = ini;
    while(q.size()){
      auto p = q.front(); q.pop();
      int v = p.first;
      int from = p.second;
      if(dist[farthest] < dist[v]){
        farthest = v;
      }
      for(auto to : vec[v]) if(to!=from){
        q.push({to, v});
        dist[to] = dist[v] + 1;
        pre[to] = v;
      }
    }
    return farthest;
  };
  int p = bfs(0);
  int q = bfs(p);
  int cur = q;
  vector<int> res;
  res.push_back(cur);
  while(cur != p){
    cur = pre[cur];
    res.push_back(cur);
  }
  assert(res[0]==q && res.back()==p);
  return res;
}



// 木・森に対する同型判定．
// 根つき木のときはcenterのかわりに根を設定する．

map<vector<int>,int> conv;
int pre[300005];
int val[300005];
bool checked[300005];

// vec上でvを含む木の中心
// TODO use diameter
vector<int> center(int v, vector<int> *vec){
  auto bfs = [&](int d){
    queue<pair<int,int>> q;
    q.push(mp(d,-1));
    val[d] = 0;
    int last = d;
    while(q.size()){
      auto p = q.front(); q.pop();
      int node = p.first;
      int from = p.second;
      checked[node]=true;
      for(auto to : vec[node]) if(to!=from){
        q.push(mp(to,node));
        val[to] = val[node]+1;
        pre[to] = node;
      }
      last = node;
    }
    return last;
  };
  int p = bfs(v);
  int q = bfs(p);

  int d = q;
  rep(i,val[q]/2) d = pre[d];

  if(val[q]%2==1) return {d, pre[d]};
  else return {d};
}

// vec上でiを含む木の同型判定用ナンバリング
pair<int,int> tree2idx(int i, vector<int> *vec){
  auto c = center(i, vec);

  function<int(int,int)> dfs = [&](int d, int from){
    vector<int> ord;
    queue<pair<int,int>> q;
    q.push(mp(d,from));
    while(q.size()){
      auto p = q.front(); q.pop();
      int node = p.first;
      int prev = p.second;
      ord.pb(node);
      pre[node] = prev;
      for(auto to : vec[node]) if(to != prev){
        q.push(mp(to, node));
      }
    }
    reverse(all(ord));
    for(auto node : ord){
      vector<int> v;
      for(auto to : vec[node]) if(to!=pre[node]) v.pb(val[to]);
      sort(all(v));
      if(conv.count(v)==0) conv[v] = conv.size();
      val[node] = conv[v];
    }
    return val[d];
  };

  if(c.size()==1){
    return mp(-1, dfs(c[0],-1));
  }
  else if(c.size()==2){
    int a = dfs(c[0], c[1]);
    int b = dfs(c[1], c[0]);
    return mp(min(a,b), max(a,b));
  }
  else assert(false);
}

vector<pair<int,int>> forest2vec(int sz, vector<int> *vec){
  vector<pair<int,int>> ret;
  fill(checked, checked+sz, false);
  rep(i,sz) if(!checked[i]) ret.pb(tree2idx(i, vec));
  sort(all(ret));
  return ret;
}