Luzhiled's Library

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View the Project on GitHub ei1333/library

:heavy_check_mark: test/verify/yosupo-frequency-table-of-tree-distance.test.cpp

Depends on

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/frequency_table_of_tree_distance

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

#include "../../graph/tree/centroid-decomposition.hpp"

#include "../../math/fft/fast-fourier-transform.hpp"

int main() {
  int N;
  cin >> N;
  CentroidDecomposition< int > g(N);
  g.read(N - 1, 0);
  int root = g.build();
  vector< int > used(N);
  vector< int64 > dist(N);
  MFP([&](auto rec, int centroid) -> void {
    used[centroid] = true;
    vector< int > cnt{1};
    for(auto &ch : g.g[centroid]) {
      if(used[ch]) continue;
      vector< int > num;
      queue< tuple< int, int, int > > que;
      que.emplace(ch, centroid, 1);
      while(!que.empty()) {
        int idx, par, dep;
        tie(idx, par, dep) = que.front();
        que.pop();
        if(cnt.size() <= dep) cnt.resize(dep + 1, 0);
        if(num.size() <= dep) num.resize(dep + 1, 0);
        cnt[dep]++;
        num[dep]++;
        for(auto &to : g.g[idx]) {
          if(to == par || used[to]) continue;
          que.emplace(to.to, idx, dep + 1);
        }
      }
      auto ret = FastFourierTransform::multiply(num, num);
      for(int i = 0; i < ret.size(); i++) dist[i] -= ret[i];
    }
    auto ret = FastFourierTransform::multiply(cnt, cnt);
    for(int i = 0; i < ret.size(); i++) dist[i] += ret[i];
    for(auto &to : g.tree.g[centroid]) rec(to);
  })(root);
  dist.erase(begin(dist));
  for(auto &p : dist) p /= 2;
  cout << dist << "\n";
}


#line 1 "test/verify/yosupo-frequency-table-of-tree-distance.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/frequency_table_of_tree_distance

#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/yosupo-frequency-table-of-tree-distance.test.cpp"

#line 2 "graph/tree/centroid-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/centroid-decomposition.hpp"

/**
 * @brief Centroid-Decomosition(重心分解)
 */
template< typename T >
struct CentroidDecomposition : Graph< T > {
public:
  using Graph< T >::Graph;
  using Graph< T >::g;
  Graph< int > tree;

  int build(int t = 0) {
    sub.assign(g.size(), 0);
    v.assign(g.size(), 0);
    tree = Graph< int >(g.size());
    return build_dfs(0);
  }

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

private:
  vector< int > sub;
  vector< int > v;

  inline int build_dfs(int idx, int par) {
    sub[idx] = 1;
    for(auto &to : g[idx]) {
      if(to == par || v[to]) continue;
      sub[idx] += build_dfs(to, idx);
    }
    return sub[idx];
  }

  inline int search_centroid(int idx, int par, const int mid) {
    for(auto &to : g[idx]) {
      if(to == par || v[to]) continue;
      if(sub[to] > mid) return search_centroid(to, idx, mid);
    }
    return idx;
  }

  inline int build_dfs(int idx) {
    int centroid = search_centroid(idx, -1, build_dfs(idx, -1) / 2);
    v[centroid] = true;
    for(auto &to : g[centroid]) {
      if(!v[to]) tree.add_directed_edge(centroid, build_dfs(to));
    }
    v[centroid] = false;
    return centroid;
  }
};
#line 6 "test/verify/yosupo-frequency-table-of-tree-distance.test.cpp"

#line 1 "math/fft/fast-fourier-transform.hpp"
namespace FastFourierTransform {
  using real = double;

  struct C {
    real x, y;

    C() : x(0), y(0) {}

    C(real x, real y) : x(x), y(y) {}

    inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }

    inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }

    inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }

    inline C conj() const { return C(x, -y); }
  };

  const real PI = acosl(-1);
  int base = 1;
  vector< C > rts = { {0, 0},
                     {1, 0} };
  vector< int > rev = {0, 1};


  void ensure_base(int nbase) {
    if(nbase <= base) return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for(int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    while(base < nbase) {
      real angle = PI * 2.0 / (1 << (base + 1));
      for(int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        real angle_i = angle * (2 * i + 1 - (1 << base));
        rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
      }
      ++base;
    }
  }

  void fft(vector< C > &a, int n) {
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for(int i = 0; i < n; i++) {
      if(i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for(int k = 1; k < n; k <<= 1) {
      for(int i = 0; i < n; i += 2 * k) {
        for(int j = 0; j < k; j++) {
          C z = a[i + j + k] * rts[j + k];
          a[i + j + k] = a[i + j] - z;
          a[i + j] = a[i + j] + z;
        }
      }
    }
  }

  vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
    int need = (int) a.size() + (int) b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < sz; i++) {
      int x = (i < (int) a.size() ? a[i] : 0);
      int y = (i < (int) b.size() ? b[i] : 0);
      fa[i] = C(x, y);
    }
    fft(fa, sz);
    C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
      fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
      fa[i] = z;
    }
    for(int i = 0; i < (sz >> 1); i++) {
      C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
      C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
      fa[i] = A0 + A1 * s;
    }
    fft(fa, sz >> 1);
    vector< int64_t > ret(need);
    for(int i = 0; i < need; i++) {
      ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
    }
    return ret;
  }
};
#line 8 "test/verify/yosupo-frequency-table-of-tree-distance.test.cpp"

int main() {
  int N;
  cin >> N;
  CentroidDecomposition< int > g(N);
  g.read(N - 1, 0);
  int root = g.build();
  vector< int > used(N);
  vector< int64 > dist(N);
  MFP([&](auto rec, int centroid) -> void {
    used[centroid] = true;
    vector< int > cnt{1};
    for(auto &ch : g.g[centroid]) {
      if(used[ch]) continue;
      vector< int > num;
      queue< tuple< int, int, int > > que;
      que.emplace(ch, centroid, 1);
      while(!que.empty()) {
        int idx, par, dep;
        tie(idx, par, dep) = que.front();
        que.pop();
        if(cnt.size() <= dep) cnt.resize(dep + 1, 0);
        if(num.size() <= dep) num.resize(dep + 1, 0);
        cnt[dep]++;
        num[dep]++;
        for(auto &to : g.g[idx]) {
          if(to == par || used[to]) continue;
          que.emplace(to.to, idx, dep + 1);
        }
      }
      auto ret = FastFourierTransform::multiply(num, num);
      for(int i = 0; i < ret.size(); i++) dist[i] -= ret[i];
    }
    auto ret = FastFourierTransform::multiply(cnt, cnt);
    for(int i = 0; i < ret.size(); i++) dist[i] += ret[i];
    for(auto &to : g.tree.g[centroid]) rec(to);
  })(root);
  dist.erase(begin(dist));
  for(auto &p : dist) p /= 2;
  cout << dist << "\n";
}

Test cases

Env Name Status Elapsed Memory
g++ almost_uni_00 :heavy_check_mark: AC 120 ms 32 MB
g++ almost_uni_01 :heavy_check_mark: AC 120 ms 31 MB
g++ example_00 :heavy_check_mark: AC 6 ms 4 MB
g++ line_00 :heavy_check_mark: AC 666 ms 51 MB
g++ line_star_00 :heavy_check_mark: AC 467 ms 47 MB
g++ line_star_01 :heavy_check_mark: AC 375 ms 46 MB
g++ line_star_02 :heavy_check_mark: AC 467 ms 47 MB
g++ max_random_00 :heavy_check_mark: AC 241 ms 32 MB
g++ max_random_01 :heavy_check_mark: AC 244 ms 32 MB
g++ random_00 :heavy_check_mark: AC 150 ms 22 MB
g++ random_01 :heavy_check_mark: AC 176 ms 25 MB
g++ random_02 :heavy_check_mark: AC 63 ms 11 MB
g++ random_03 :heavy_check_mark: AC 200 ms 28 MB
g++ random_04 :heavy_check_mark: AC 21 ms 6 MB
g++ small_random_00 :heavy_check_mark: AC 7 ms 4 MB
g++ small_random_01 :heavy_check_mark: AC 6 ms 4 MB
g++ small_random_02 :heavy_check_mark: AC 6 ms 4 MB
g++ small_random_03 :heavy_check_mark: AC 6 ms 4 MB
g++ small_random_04 :heavy_check_mark: AC 6 ms 4 MB
g++ uni_00 :heavy_check_mark: AC 115 ms 31 MB
clang++ almost_uni_00 :heavy_check_mark: AC 124 ms 31 MB
clang++ almost_uni_01 :heavy_check_mark: AC 122 ms 32 MB
clang++ example_00 :heavy_check_mark: AC 6 ms 4 MB
clang++ line_00 :heavy_check_mark: AC 640 ms 53 MB
clang++ line_star_00 :heavy_check_mark: AC 450 ms 48 MB
clang++ line_star_01 :heavy_check_mark: AC 379 ms 47 MB
clang++ line_star_02 :heavy_check_mark: AC 475 ms 49 MB
clang++ max_random_00 :heavy_check_mark: AC 244 ms 32 MB
clang++ max_random_01 :heavy_check_mark: AC 234 ms 32 MB
clang++ random_00 :heavy_check_mark: AC 143 ms 22 MB
clang++ random_01 :heavy_check_mark: AC 177 ms 25 MB
clang++ random_02 :heavy_check_mark: AC 64 ms 11 MB
clang++ random_03 :heavy_check_mark: AC 199 ms 28 MB
clang++ random_04 :heavy_check_mark: AC 21 ms 6 MB
clang++ small_random_00 :heavy_check_mark: AC 6 ms 4 MB
clang++ small_random_01 :heavy_check_mark: AC 6 ms 4 MB
clang++ small_random_02 :heavy_check_mark: AC 6 ms 4 MB
clang++ small_random_03 :heavy_check_mark: AC 6 ms 4 MB
clang++ small_random_04 :heavy_check_mark: AC 6 ms 4 MB
clang++ uni_00 :heavy_check_mark: AC 117 ms 30 MB
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