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#define PROBLEM \ "https://judge.yosupo.jp/problem/frequency_table_of_tree_distance" #include "../../convolution/convolution_mod_2_64.hpp" #include "../../graph/base.hpp" #include "../../template/template.hpp" #include "../../tree/centroid_decomposition.hpp" namespace ebi { void main_() { int n; std::cin >> n; Graph<int> g(n); g.read_tree(0); std::vector<i64> ans(n, 0); auto f = [&](const std::vector<int> &par, const std::vector<int> &vs, const std::vector<int> &index_ptr) -> void { int sz = par.size(); std::vector<int> dist(sz, 0); rep(v, 1, sz) { dist[v] = dist[par[v]] + 1; } auto calc = [&](int l, int r, int sgn) -> void { int max = *std::max_element(dist.begin() + l, dist.begin() + r); std::vector<u64> table(max + 1, 0); rep(v, l, r) { table[dist[v]]++; } auto a = convolution_mod_2_64(table, table); rep(i, 1, a.size()) { ans[i] += sgn * i64(a[i]); } }; calc(0, sz, 1); rep(c, 1, index_ptr.size() - 1) { int l = index_ptr[c]; int r = index_ptr[c + 1]; calc(l, r, -1); } }; centroid_decomposition<0>(g, f); ans.erase(ans.begin()); for (auto &x : ans) { x /= 2; } std::cout << ans << '\n'; } } // namespace ebi int main() { ebi::fast_io(); int t = 1; // std::cin >> t; while (t--) { ebi::main_(); } return 0; }
#line 1 "test/tree/Frequency_Table_of_Tree_Distance_MODE_0.test.cpp" #define PROBLEM \ "https://judge.yosupo.jp/problem/frequency_table_of_tree_distance" #line 2 "convolution/convolution_mod_2_64.hpp" #include <cstdint> #include <vector> #line 2 "convolution/ntt.hpp" #include <algorithm> #include <array> #include <bit> #include <cassert> #line 8 "convolution/ntt.hpp" #line 2 "math/internal_math.hpp" #line 4 "math/internal_math.hpp" namespace ebi { namespace internal { constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; if (m == 880803841) return 26; if (m == 924844033) return 5; return -1; } template <int m> constexpr int primitive_root = primitive_root_constexpr(m); } // namespace internal } // namespace ebi #line 2 "modint/base.hpp" #include <concepts> #include <iostream> #include <utility> namespace ebi { template <class T> concept Modint = requires(T a, T b) { a + b; a - b; a * b; a / b; a.inv(); a.val(); a.pow(std::declval<long long>()); T::mod(); }; template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) { long long x; os >> x; a = x; return os; } template <Modint mint> std::ostream &operator<<(std::ostream &os, const mint &a) { return os << a.val(); } } // namespace ebi #line 11 "convolution/ntt.hpp" namespace ebi { namespace internal { template <Modint mint, int g = internal::primitive_root<mint::mod()>> struct ntt_info { static constexpr int rank2 = std::countr_zero((unsigned int)(mint::mod() - 1)); std::array<mint, rank2 + 1> root, inv_root; ntt_info() { root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2); inv_root[rank2] = root[rank2].inv(); for (int i = rank2 - 1; i >= 0; i--) { root[i] = root[i + 1] * root[i + 1]; inv_root[i] = inv_root[i + 1] * inv_root[i + 1]; } } }; template <Modint mint> void butterfly(std::vector<mint>& a) { static const ntt_info<mint> info; int n = int(a.size()); int bit_size = std::countr_zero(a.size()); assert(n == (int)std::bit_ceil(a.size())); // bit reverse for (int i = 0, j = 1; j < n - 1; j++) { for (int k = n >> 1; k > (i ^= k); k >>= 1) ; if (j < i) { std::swap(a[i], a[j]); } } for (int bit = 0; bit < bit_size; bit++) { for (int i = 0; i < n / (1 << (bit + 1)); i++) { mint zeta1 = 1; mint zeta2 = info.root[1]; for (int j = 0; j < (1 << bit); j++) { int idx = i * (1 << (bit + 1)) + j; int jdx = idx + (1 << bit); mint p1 = a[idx]; mint p2 = a[jdx]; a[idx] = p1 + zeta1 * p2; a[jdx] = p1 + zeta2 * p2; zeta1 *= info.root[bit + 1]; zeta2 *= info.root[bit + 1]; } } } } template <Modint mint> void butterfly_inv(std::vector<mint>& a) { static const ntt_info<mint> info; int n = int(a.size()); int bit_size = std::countr_zero(a.size()); assert(n == (int)std::bit_ceil(a.size())); // bit reverse for (int i = 0, j = 1; j < n - 1; j++) { for (int k = n >> 1; k > (i ^= k); k >>= 1) ; if (j < i) { std::swap(a[i], a[j]); } } for (int bit = 0; bit < bit_size; bit++) { for (int i = 0; i < n / (1 << (bit + 1)); i++) { mint zeta1 = 1; mint zeta2 = info.inv_root[1]; for (int j = 0; j < (1 << bit); j++) { int idx = i * (1 << (bit + 1)) + j; int jdx = idx + (1 << bit); mint p1 = a[idx]; mint p2 = a[jdx]; a[idx] = p1 + zeta1 * p2; a[jdx] = p1 + zeta2 * p2; zeta1 *= info.inv_root[bit + 1]; zeta2 *= info.inv_root[bit + 1]; } } } mint inv_n = mint(n).inv(); for (int i = 0; i < n; i++) { a[i] *= inv_n; } } } // namespace internal template <Modint mint> std::vector<mint> convolution_naive(const std::vector<mint>& f, const std::vector<mint>& g) { if (f.empty() || g.empty()) return {}; int n = int(f.size()), m = int(g.size()); std::vector<mint> c(n + m - 1); if (n < m) { for (int j = 0; j < m; j++) { for (int i = 0; i < n; i++) { c[i + j] += f[i] * g[j]; } } } else { for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { c[i + j] += f[i] * g[j]; } } } return c; } template <Modint mint> std::vector<mint> convolution(const std::vector<mint>& f, const std::vector<mint>& g) { if (f.empty() || g.empty()) return {}; if (std::min(f.size(), g.size()) < 60) return convolution_naive(f, g); int n = std::bit_ceil(f.size() + g.size() - 1); std::vector<mint> a(n), b(n); std::copy(f.begin(), f.end(), a.begin()); std::copy(g.begin(), g.end(), b.begin()); internal::butterfly(a); internal::butterfly(b); for (int i = 0; i < n; i++) { a[i] *= b[i]; } internal::butterfly_inv(a); a.resize(f.size() + g.size() - 1); return a; } } // namespace ebi #line 2 "modint/modint.hpp" #line 5 "modint/modint.hpp" #line 7 "modint/modint.hpp" namespace ebi { template <int m> struct static_modint { private: using modint = static_modint; public: static constexpr int mod() { return m; } static constexpr modint raw(int v) { modint x; x._v = v; return x; } constexpr static_modint() : _v(0) {} constexpr static_modint(long long v) { v %= (long long)umod(); if (v < 0) v += (long long)umod(); _v = (unsigned int)v; } constexpr unsigned int val() const { return _v; } constexpr unsigned int value() const { return val(); } constexpr modint &operator++() { _v++; if (_v == umod()) _v = 0; return *this; } constexpr modint &operator--() { if (_v == 0) _v = umod(); _v--; return *this; } constexpr modint operator++(int) { modint res = *this; ++*this; return res; } constexpr modint operator--(int) { modint res = *this; --*this; return res; } constexpr modint &operator+=(const modint &rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } constexpr modint &operator-=(const modint &rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } constexpr modint &operator*=(const modint &rhs) { unsigned long long x = _v; x *= rhs._v; _v = (unsigned int)(x % (unsigned long long)umod()); return *this; } constexpr modint &operator/=(const modint &rhs) { return *this = *this * rhs.inv(); } constexpr modint operator+() const { return *this; } constexpr modint operator-() const { return modint() - *this; } constexpr modint pow(long long n) const { assert(0 <= n); modint x = *this, res = 1; while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } constexpr modint inv() const { assert(_v); return pow(umod() - 2); } friend modint operator+(const modint &lhs, const modint &rhs) { return modint(lhs) += rhs; } friend modint operator-(const modint &lhs, const modint &rhs) { return modint(lhs) -= rhs; } friend modint operator*(const modint &lhs, const modint &rhs) { return modint(lhs) *= rhs; } friend modint operator/(const modint &lhs, const modint &rhs) { return modint(lhs) /= rhs; } friend bool operator==(const modint &lhs, const modint &rhs) { return lhs.val() == rhs.val(); } friend bool operator!=(const modint &lhs, const modint &rhs) { return !(lhs == rhs); } private: unsigned int _v = 0; static constexpr unsigned int umod() { return m; } }; using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; } // namespace ebi #line 9 "convolution/convolution_mod_2_64.hpp" namespace ebi { namespace internal { template <Modint mint> std::vector<mint> multiply_uint64_t(const std::vector<std::uint64_t>& f, const std::vector<std::uint64_t>& g) { std::vector<mint> a, b; a.reserve(f.size()); b.reserve(g.size()); for (auto x : f) a.emplace_back(x % mint::mod()); for (auto x : g) b.emplace_back(x % mint::mod()); return convolution<mint>(a, b); } } // namespace internal std::vector<std::uint64_t> convolution_mod_2_64( const std::vector<std::uint64_t>& f, const std::vector<std::uint64_t>& g) { if (f.empty() || g.empty()) return {}; using i32 = std::int32_t; using i64 = std::int64_t; using u64 = std::uint64_t; static constexpr i32 m0 = 998244353; static constexpr i32 m1 = 754974721; static constexpr i32 m2 = 167772161; static constexpr i32 m3 = 469762049; static constexpr i32 m4 = 880803841; using mint0 = static_modint<m0>; using mint1 = static_modint<m1>; using mint2 = static_modint<m2>; using mint3 = static_modint<m3>; using mint4 = static_modint<m4>; auto d0 = internal::multiply_uint64_t<mint0>(f, g); auto d1 = internal::multiply_uint64_t<mint1>(f, g); auto d2 = internal::multiply_uint64_t<mint2>(f, g); auto d3 = internal::multiply_uint64_t<mint3>(f, g); auto d4 = internal::multiply_uint64_t<mint4>(f, g); static const mint1 inv10 = mint1(m0).inv(); static const mint2 inv21 = mint2(m1).inv(), inv20 = inv21 / mint2(m0); static const mint3 inv32 = mint3(m2).inv(), inv31 = inv32 / mint3(m1), inv30 = inv31 / mint3(m0); static const mint4 inv43 = mint4(m3).inv(), inv42 = inv43 / mint4(m2), inv41 = inv42 / mint4(m1), inv40 = inv41 / mint4(m0); int n = d0.size(); std::vector<u64> res(n); for (int i = 0; i < n; i++) { i64 x0 = d0[i].val(); i64 x1 = ((d1[i] - x0) * inv10).val(); i64 x2 = (((d2[i] - x0)) * inv20 - mint2(x1) * inv21).val(); i64 x3 = ((d3[i] - x0) * inv30 - mint3(x1) * inv31 - mint3(x2) * inv32) .val(); i64 x4 = ((d4[i] - x0) * inv40 - mint4(x1) * inv41 - mint4(x2) * inv42 - mint4(x3) * inv43) .val(); res[i] = x0 + m0 * (x1 + m1 * (x2 + m2 * (x3 + m3 * (u64(x4))))); } return res; } } // namespace ebi #line 2 "graph/base.hpp" #line 5 "graph/base.hpp" #include <ranges> #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 6 "data_structure/simple_csr.hpp" namespace ebi { template <class E> struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector<std::pair<int, E>>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector<std::vector<E>>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector<int> start; std::vector<E> elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template <class T> struct Edge { int from, to; T cost; int id; }; template <class E> struct Graph { using cost_type = E; using edge_type = Edge<cost_type>; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr<edge_type>(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector<edge_type> get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector<std::pair<int,edge_type>> buff; std::vector<edge_type> edges; simple_csr<edge_type> csr; bool prepared = false; }; } // namespace ebi #line 1 "template/template.hpp" #include <bits/stdc++.h> #define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++) #define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--) #define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++) #define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() #line 2 "template/debug_template.hpp" #line 4 "template/debug_template.hpp" namespace ebi { #ifdef LOCAL #define debug(...) \ std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \ debug_out(__VA_ARGS__) #else #define debug(...) #endif void debug_out() { std::cerr << std::endl; } template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) { std::cerr << " " << h; if (sizeof...(t) > 0) std::cerr << " :"; debug_out(t...); } } // namespace ebi #line 2 "template/int_alias.hpp" #line 4 "template/int_alias.hpp" namespace ebi { using ld = long double; using std::size_t; using i8 = std::int8_t; using u8 = std::uint8_t; using i16 = std::int16_t; using u16 = std::uint16_t; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using i128 = __int128_t; using u128 = __uint128_t; } // namespace ebi #line 2 "template/io.hpp" #line 5 "template/io.hpp" #include <optional> #line 7 "template/io.hpp" namespace ebi { template <typename T1, typename T2> std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) { return os << pa.first << " " << pa.second; } template <typename T1, typename T2> std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) { return os >> pa.first >> pa.second; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) { for (std::size_t i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " "); return os; } template <typename T> std::istream &operator>>(std::istream &os, std::vector<T> &vec) { for (T &e : vec) std::cin >> e; return os; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) { if (opt) { os << opt.value(); } else { os << "invalid value"; } return os; } void fast_io() { std::cout << std::fixed << std::setprecision(15); std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } } // namespace ebi #line 2 "template/utility.hpp" #line 5 "template/utility.hpp" #line 8 "template/utility.hpp" namespace ebi { template <class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template <class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template <class T> T safe_ceil(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return (a / b) + 1; else return -((-a) / b); } template <class T> T safe_floor(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return a / b; else return -((-a) / b) - 1; } constexpr i64 LNF = std::numeric_limits<i64>::max() / 4; constexpr int INF = std::numeric_limits<int>::max() / 2; const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1}; const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1}; } // namespace ebi #line 2 "tree/centroid_decomposition.hpp" #line 7 "tree/centroid_decomposition.hpp" namespace ebi { namespace internal { template <class F> void centroid_decomposition_dfs_naive(const std::vector<int> &par, const std::vector<int> &original_vs, F f) { const int n = (int)par.size(); assert(par.size() == original_vs.size()); int center = -1; std::vector<int> sz(n, 1); for (const int v : std::views::iota(0, n) | std::views::reverse) { if (sz[v] >= (n + 1) / 2) { center = v; break; } sz[par[v]] += sz[v]; } std::vector<int> color(n, -1); std::vector<int> vs = {center}; color[center] = 0; int c = 1; for (const int v : std::views::iota(1, n)) { if (par[v] == center) { vs.emplace_back(v); color[v] = c++; } } if (center > 0) { for (int v = par[center]; v != -1; v = par[v]) { vs.emplace_back(v); color[v] = c; } c++; } for (const int v : std::views::iota(0, n)) { if (color[v] == -1) { vs.emplace_back(v); color[v] = color[par[v]]; } } std::vector<int> index_ptr(c + 1, 0); for (const int v : std::views::iota(0, n)) { index_ptr[color[v] + 1]++; } for (const int i : std::views::iota(0, c)) { index_ptr[i + 1] += index_ptr[i]; } auto counter = index_ptr; std::vector<int> ord(n); for (auto v : vs) { ord[counter[color[v]]++] = v; } std::vector<int> relabel(n); for (const int v : std::views::iota(0, n)) { relabel[ord[v]] = v; } std::vector<int> original_vs2(n); for (const int v : std::views::iota(0, n)) { original_vs2[relabel[v]] = original_vs[v]; } std::vector<int> relabel_par(n, -1); for (int v : std::views::iota(1, n)) { int a = relabel[v]; int b = relabel[par[v]]; if (a > b) std::swap(a, b); relabel_par[b] = a; } f(relabel_par, original_vs2, index_ptr); for (const int i : std::views::iota(1, c)) { int l = index_ptr[i], r = index_ptr[i + 1]; std::vector<int> par1(r - l, -1); std::vector<int> original_vs1(r - l, -1); for (int v : std::views::iota(l, r)) { par1[v - l] = (relabel_par[v] == 0 ? -1 : relabel_par[v] - l); original_vs1[v - l] = original_vs2[v]; } centroid_decomposition_dfs_naive(par1, original_vs1, f); } return; } template <class F> void one_third_centroid_decomposition(const std::vector<int> &par, const std::vector<int> &original_vs, F f) { const int n = (int)par.size(); assert(n > 1); if (n == 2) return; int center = -1; std::vector<int> sz(n, 1); for (const int v : std::views::iota(0, n) | std::views::reverse) { if (sz[v] >= (n + 1) / 2) { center = v; break; } sz[par[v]] += sz[v]; } std::vector<int> color(n, -1); std::vector<int> ord(n, -1); ord[center] = 0; int t = 1; int red = n - sz[center]; for (int v = par[center]; v != -1; v = par[v]) { ord[v] = t++; color[v] = 0; } for (const int v : std::views::iota(1, n)) { if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) { red += sz[v]; ord[v] = t++; color[v] = 0; } } for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1 && color[par[v]] == 0) { ord[v] = t++; color[v] = 0; } } const int n0 = t - 1; for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1) { ord[v] = t++; color[v] = 1; } } assert(t == n); const int n1 = n - 1 - n0; std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1); std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1), original_vs2(n); for (const int i : std::views::iota(0, n)) { int v = ord[i]; original_vs2[v] = original_vs[i]; if (color[i] != 1) { original_vs0[v] = original_vs[i]; } if (color[i] != 0) { int idx = std::max(v - n0, 0); original_vs1[idx] = original_vs[i]; } } for (const int v : std::views::iota(1, n)) { int a = ord[v], b = ord[par[v]]; if (a > b) std::swap(a, b); par2[b] = a; if (color[v] != 1 && color[par[v]] != 1) { par0[b] = a; } if (color[v] != 0 && color[par[v]] != 0) { par1[b - n0] = std::max(a - n0, 0); } } f(par2, original_vs2, n0, n1); one_third_centroid_decomposition(par0, original_vs0, f); one_third_centroid_decomposition(par1, original_vs1, f); return; } template <class F> void one_third_centroid_decomposition_virtual_real( const std::vector<int> &par, const std::vector<int> &original_vs, const std::vector<int> &is_real, F f) { const int n = (int)par.size(); assert(n > 1); if (n == 2) { if (is_real[0] && is_real[1]) { f(par, original_vs, {0, 1}); } return; } int center = -1; std::vector<int> sz(n, 1); for (const int v : std::views::iota(0, n) | std::views::reverse) { if (sz[v] >= (n + 1) / 2) { center = v; break; } sz[par[v]] += sz[v]; } std::vector<int> color(n, -1); std::vector<int> ord(n, -1); ord[center] = 0; int t = 1; int red = n - sz[center]; for (int v = par[center]; v != -1; v = par[v]) { ord[v] = t++; color[v] = 0; } for (const int v : std::views::iota(1, n)) { if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) { red += sz[v]; ord[v] = t++; color[v] = 0; } } for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1 && color[par[v]] == 0) { ord[v] = t++; color[v] = 0; } } const int n0 = t - 1; for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1) { ord[v] = t++; color[v] = 1; } } assert(t == n); const int n1 = n - 1 - n0; std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1); std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1), original_vs2(n); std::vector<int> is_real0(n0 + 1), is_real1(n1 + 1), is_real2(n); for (const int i : std::views::iota(0, n)) { int v = ord[i]; original_vs2[v] = original_vs[i]; is_real2[v] = is_real[i]; if (color[i] != 1) { original_vs0[v] = original_vs[i]; is_real0[v] = is_real[i]; } if (color[i] != 0) { int idx = std::max(v - n0, 0); original_vs1[idx] = original_vs[i]; is_real1[idx] = is_real[i]; } } for (const int v : std::views::iota(1, n)) { int a = ord[v], b = ord[par[v]]; if (a > b) std::swap(a, b); par2[b] = a; if (color[v] != 1 && color[par[v]] != 1) { par0[b] = a; } if (color[v] != 0 && color[par[v]] != 0) { par1[b - n0] = std::max(a - n0, 0); } } if (is_real[center]) { color.assign(n, -1); color[0] = 0; for (const int v : std::views::iota(1, n)) { if (is_real2[v]) color[v] = 1; } f(par2, original_vs2, color); is_real0[0] = is_real1[0] = is_real2[0] = 0; } color.assign(n, -1); for (const int v : std::views::iota(1, n)) { if (is_real2[v]) { color[v] = int(v > n0); } } f(par2, original_vs2, color); one_third_centroid_decomposition_virtual_real(par0, original_vs0, is_real0, f); one_third_centroid_decomposition_virtual_real(par1, original_vs1, is_real1, f); return; } } // namespace internal template <int MODE, class T, class F> void centroid_decomposition(const Graph<T> &tree, F f) { int n = (int)tree.size(); if (n == 1) return; std::vector<int> bfs_order(n), par(n, -1); bfs_order[0] = 0; int l = 0, r = 1; while (l < r) { int v = bfs_order[l++]; for (auto e : tree[v]) { int nv = e.to; if (nv == par[v]) continue; bfs_order[r++] = nv; par[nv] = v; } } assert(l == n && r == n); { std::vector<int> relabel(n); for (int i : std::views::iota(0, n)) { relabel[bfs_order[i]] = i; } std::vector<int> relabel_par(n, -1); for (int i : std::views::iota(1, n)) { relabel_par[relabel[i]] = relabel[par[i]]; } std::swap(par, relabel_par); } static_assert(MODE == 0 || MODE == 1 || MODE == 2); if constexpr (MODE == 0) { internal::centroid_decomposition_dfs_naive(par, bfs_order, f); } else if constexpr (MODE == 1) { internal::one_third_centroid_decomposition(par, bfs_order, f); } else { internal::one_third_centroid_decomposition_virtual_real( par, bfs_order, std::vector<int>(n, 1), f); } } } // namespace ebi #line 8 "test/tree/Frequency_Table_of_Tree_Distance_MODE_0.test.cpp" namespace ebi { void main_() { int n; std::cin >> n; Graph<int> g(n); g.read_tree(0); std::vector<i64> ans(n, 0); auto f = [&](const std::vector<int> &par, const std::vector<int> &vs, const std::vector<int> &index_ptr) -> void { int sz = par.size(); std::vector<int> dist(sz, 0); rep(v, 1, sz) { dist[v] = dist[par[v]] + 1; } auto calc = [&](int l, int r, int sgn) -> void { int max = *std::max_element(dist.begin() + l, dist.begin() + r); std::vector<u64> table(max + 1, 0); rep(v, l, r) { table[dist[v]]++; } auto a = convolution_mod_2_64(table, table); rep(i, 1, a.size()) { ans[i] += sgn * i64(a[i]); } }; calc(0, sz, 1); rep(c, 1, index_ptr.size() - 1) { int l = index_ptr[c]; int r = index_ptr[c + 1]; calc(l, r, -1); } }; centroid_decomposition<0>(g, f); ans.erase(ans.begin()); for (auto &x : ans) { x /= 2; } std::cout << ans << '\n'; } } // namespace ebi int main() { ebi::fast_io(); int t = 1; // std::cin >> t; while (t--) { ebi::main_(); } return 0; }