Luzhiled's Library

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: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 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;
}
};  // namespace FastFourierTransform
#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 133 ms 31 MB
g++ almost_uni_01 :heavy_check_mark: AC 129 ms 32 MB
g++ example_00 :heavy_check_mark: AC 6 ms 4 MB
g++ line_00 :heavy_check_mark: AC 698 ms 51 MB
g++ line_star_00 :heavy_check_mark: AC 508 ms 46 MB
g++ line_star_01 :heavy_check_mark: AC 404 ms 46 MB
g++ line_star_02 :heavy_check_mark: AC 507 ms 47 MB
g++ max_random_00 :heavy_check_mark: AC 262 ms 32 MB
g++ max_random_01 :heavy_check_mark: AC 274 ms 32 MB
g++ random_00 :heavy_check_mark: AC 161 ms 22 MB
g++ random_01 :heavy_check_mark: AC 187 ms 25 MB
g++ random_02 :heavy_check_mark: AC 66 ms 11 MB
g++ random_03 :heavy_check_mark: AC 216 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 116 ms 30 MB
clang++ almost_uni_00 :heavy_check_mark: AC 141 ms 31 MB
clang++ almost_uni_01 :heavy_check_mark: AC 125 ms 32 MB
clang++ example_00 :heavy_check_mark: AC 6 ms 4 MB
clang++ line_00 :heavy_check_mark: AC 682 ms 53 MB
clang++ line_star_00 :heavy_check_mark: AC 521 ms 48 MB
clang++ line_star_01 :heavy_check_mark: AC 400 ms 47 MB
clang++ line_star_02 :heavy_check_mark: AC 540 ms 49 MB
clang++ max_random_00 :heavy_check_mark: AC 280 ms 32 MB
clang++ max_random_01 :heavy_check_mark: AC 285 ms 32 MB
clang++ random_00 :heavy_check_mark: AC 159 ms 22 MB
clang++ random_01 :heavy_check_mark: AC 203 ms 25 MB
clang++ random_02 :heavy_check_mark: AC 66 ms 11 MB
clang++ random_03 :heavy_check_mark: AC 241 ms 28 MB
clang++ random_04 :heavy_check_mark: AC 22 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 7 ms 4 MB
clang++ uni_00 :heavy_check_mark: AC 144 ms 30 MB
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