test/verify/aoj-2667.test.cpp

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• Last update: 2022-09-11 00:53:50+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2667

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)
• Heavy-Light-Decomposition(HL分解) (graph/tree/heavy-light-decomposition.hpp)
• template/template.hpp

Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2667"

#include "../../template/template.hpp"

#include "../../graph/tree/heavy-light-decomposition.hpp"

int main() {
  int N, Q;
  cin >> N >> Q;
  HeavyLightDecomposition<> hld(N);
  hld.read(N - 1, 0);
  hld.build();

  struct Query {
    int t, a, b;

    void input() {
      cin >> t >> a >> b;
    }
  };

  vector< int > remark;
  vector< Query > qs;
  vector< int64 > sum(N);

  vector< int > index(N);
  for(int i = 0; i < Q; i++) {
    Query q;
    q.input();
    qs.emplace_back(q);
    if(q.t == 0) {
      remark.emplace_back(q.a);
      remark.emplace_back(q.b);
    } else {
      remark.emplace_back(q.a);
    }
    if(remark.size() >= 2000 || i + 1 == Q) {
      auto es = hld.compress(remark);
      for(int j = 0; j < remark.size(); j++) index[remark[j]] = j;
      vector< int > dist(remark.size()), par(remark.size());
      Graph<> h(remark.size());
      for(auto &p : es) {
        p.first = index[p.first];
        p.second = index[p.second];
        par[p.second] = p.first;
        dist[p.second] = hld.dist(remark[p.first], remark[p.second]);
        h.add_directed_edge(p.first, p.second);
      }
      vector< int64 > lazy_add(N), backet_add(N);
      for(auto &q : qs) {
        if(q.t == 0) {
          int64 ret = 0;
          ret += sum[q.a] + sum[q.b] - 2 * sum[hld.lca(q.a, q.b)];
          ret += backet_add[q.a] + backet_add[q.b] - 2 * backet_add[hld.lca(q.a, q.b)];
          cout << ret << "\n";
        } else {
          lazy_add[q.a] += q.b;
          q.a = index[q.a];
          MFP([&](auto dfs, int idx, int p, int64 sz) -> void {
            for(auto &to : h.g[idx]) {
              if(to != p) {
                backet_add[remark[to]] += (sz + dist[to]) * q.b;
                dfs(to, idx, sz + dist[to]);
              }
            }
          })(q.a, par[q.a], 0);
        }
      }
      MFP([&](auto dfs, int idx, int par, int64 add, int64 all) -> void {
        all += add;
        add += lazy_add[idx];
        sum[idx] += all;
        for(auto &to : hld.g[idx]) {
          if(to != par) dfs(to, idx, add, all);
        }
      })(0, -1, 0, 0);
      qs.clear();
      remark.clear();
    }
  }
}

#line 1 "test/verify/aoj-2667.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2667"

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};
 
template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}
#line 4 "test/verify/aoj-2667.test.cpp"

#line 2 "graph/tree/heavy-light-decomposition.hpp"

#line 2 "graph/graph-template.hpp"

/**
 * @brief Graph Template(グラフテンプレート)
 */
template< typename T = int >
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template< typename T = int >
struct Graph {
  vector< vector< Edge< T > > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  size_t size() const {
    return g.size();
  }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false, bool directed = false) {
    for(int i = 0; i < M; i++) {
      int a, b;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if(weighted) cin >> c;
      if(directed) add_directed_edge(a, b, c);
      else add_edge(a, b, c);
    }
  }

  inline vector< Edge< T > > &operator[](const int &k) {
    return g[k];
  }

  inline const vector< Edge< T > > &operator[](const int &k) const {
    return g[k];
  }
};

template< typename T = int >
using Edges = vector< Edge< T > >;
#line 4 "graph/tree/heavy-light-decomposition.hpp"

/**
 * @brief Heavy-Light-Decomposition(HL分解)
 * @see https://smijake3.hatenablog.com/entry/2019/09/15/200200
 */
template< typename T = int >
struct HeavyLightDecomposition : Graph< T > {
public:
  using Graph< T >::Graph;
  using Graph< T >::g;
  vector< int > sz, in, out, head, rev, par, dep;

  void build() {
    sz.assign(g.size(), 0);
    in.assign(g.size(), 0);
    out.assign(g.size(), 0);
    head.assign(g.size(), 0);
    rev.assign(g.size(), 0);
    par.assign(g.size(), 0);
    dep.assign(g.size(), 0);
    dfs_sz(0, -1, 0);
    int t = 0;
    dfs_hld(0, -1, t);
  }

  /* k: 0-indexed */
  int la(int v, int k) {
    while(1) {
      int u = head[v];
      if(in[v] - k >= in[u]) return rev[in[v] - k];
      k -= in[v] - in[u] + 1;
      v = par[u];
    }
  }

  int lca(int u, int v) const {
    for(;; v = par[head[v]]) {
      if(in[u] > in[v]) swap(u, v);
      if(head[u] == head[v]) return u;
    }
  }

  int dist(int u, int v) const {
    return dep[u] + dep[v] - 2 * dep[lca(u, v)];
  }

  template< typename E, typename Q, typename F, typename S >
  E query(int u, int v, const E &ti, const Q &q, const F &f, const S &s, bool edge = false) {
    E l = ti, r = ti;
    for(;; v = par[head[v]]) {
      if(in[u] > in[v]) swap(u, v), swap(l, r);
      if(head[u] == head[v]) break;
      l = f(q(in[head[v]], in[v] + 1), l);
    }
    return s(f(q(in[u] + edge, in[v] + 1), l), r);
  }

  template< typename E, typename Q, typename F >
  E query(int u, int v, const E &ti, const Q &q, const F &f, bool edge = false) {
    return query(u, v, ti, q, f, f, edge);
  }

  template< typename Q >
  void add(int u, int v, const Q &q, bool edge = false) {
    for(;; v = par[head[v]]) {
      if(in[u] > in[v]) swap(u, v);
      if(head[u] == head[v]) break;
      q(in[head[v]], in[v] + 1);
    }
    q(in[u] + edge, in[v] + 1);
  }

  /* {parent, child} */
  vector< pair< int, int > > compress(vector< int > &remark) {
    auto cmp = [&](int a, int b) { return in[a] < in[b]; };
    sort(begin(remark), end(remark), cmp);
    remark.erase(unique(begin(remark), end(remark)), end(remark));
    int K = (int) remark.size();
    for(int k = 1; k < K; k++) remark.emplace_back(lca(remark[k - 1], remark[k]));
    sort(begin(remark), end(remark), cmp);
    remark.erase(unique(begin(remark), end(remark)), end(remark));
    vector< pair< int, int > > es;
    stack< int > st;
    for(auto &k : remark) {
      while(!st.empty() && out[st.top()] <= in[k]) st.pop();
      if(!st.empty()) es.emplace_back(st.top(), k);
      st.emplace(k);
    }
    return es;
  }

  explicit HeavyLightDecomposition(const Graph< T > &g) : Graph< T >(g) {}

private:
  void dfs_sz(int idx, int p, int d) {
    dep[idx] = d;
    par[idx] = p;
    sz[idx] = 1;
    if(g[idx].size() && g[idx][0] == p) swap(g[idx][0], g[idx].back());
    for(auto &to : g[idx]) {
      if(to == p) continue;
      dfs_sz(to, idx, d + 1);
      sz[idx] += sz[to];
      if(sz[g[idx][0]] < sz[to]) swap(g[idx][0], to);
    }
  }

  void dfs_hld(int idx, int p, int &times) {
    in[idx] = times++;
    rev[in[idx]] = idx;
    for(auto &to : g[idx]) {
      if(to == p) continue;
      head[to] = (g[idx][0] == to ? head[idx] : to);
      dfs_hld(to, idx, times);
    }
    out[idx] = times;
  }
};
#line 6 "test/verify/aoj-2667.test.cpp"

int main() {
  int N, Q;
  cin >> N >> Q;
  HeavyLightDecomposition<> hld(N);
  hld.read(N - 1, 0);
  hld.build();

  struct Query {
    int t, a, b;

    void input() {
      cin >> t >> a >> b;
    }
  };

  vector< int > remark;
  vector< Query > qs;
  vector< int64 > sum(N);

  vector< int > index(N);
  for(int i = 0; i < Q; i++) {
    Query q;
    q.input();
    qs.emplace_back(q);
    if(q.t == 0) {
      remark.emplace_back(q.a);
      remark.emplace_back(q.b);
    } else {
      remark.emplace_back(q.a);
    }
    if(remark.size() >= 2000 || i + 1 == Q) {
      auto es = hld.compress(remark);
      for(int j = 0; j < remark.size(); j++) index[remark[j]] = j;
      vector< int > dist(remark.size()), par(remark.size());
      Graph<> h(remark.size());
      for(auto &p : es) {
        p.first = index[p.first];
        p.second = index[p.second];
        par[p.second] = p.first;
        dist[p.second] = hld.dist(remark[p.first], remark[p.second]);
        h.add_directed_edge(p.first, p.second);
      }
      vector< int64 > lazy_add(N), backet_add(N);
      for(auto &q : qs) {
        if(q.t == 0) {
          int64 ret = 0;
          ret += sum[q.a] + sum[q.b] - 2 * sum[hld.lca(q.a, q.b)];
          ret += backet_add[q.a] + backet_add[q.b] - 2 * backet_add[hld.lca(q.a, q.b)];
          cout << ret << "\n";
        } else {
          lazy_add[q.a] += q.b;
          q.a = index[q.a];
          MFP([&](auto dfs, int idx, int p, int64 sz) -> void {
            for(auto &to : h.g[idx]) {
              if(to != p) {
                backet_add[remark[to]] += (sz + dist[to]) * q.b;
                dfs(to, idx, sz + dist[to]);
              }
            }
          })(q.a, par[q.a], 0);
        }
      }
      MFP([&](auto dfs, int idx, int par, int64 add, int64 all) -> void {
        all += add;
        add += lazy_add[idx];
        sum[idx] += all;
        for(auto &to : hld.g[idx]) {
          if(to != par) dfs(to, idx, add, all);
        }
      })(0, -1, 0, 0);
      qs.clear();
      remark.clear();
    }
  }
}

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