TreeCentroid(木の重心)
(graph/tree/TreeCentroid.hpp)

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Last update: 2024-05-12 17:35:55+09:00
Include: #include "graph/tree/TreeCentroid.hpp"

概要

木の重心を求めるアルゴリズム。

重心とは、ある頂点とその頂点に接続する辺を全て削除したとき、各連結成分の頂点数が元の木の頂点数の半分以下になる頂点を言う。多くの場合重心は 1 つだが、ある辺を削除するとちょうど元の木の半分の頂点数の連結成分が 2 つできる場合、その辺の端点 2 つが重心となる。その場合は辺(の中点)を重心とする流儀もあるらしい？

TreeCentroids(Graph<T> G) : 木の重心を求める。 $\Theta(N)$ 。
vector<int> get() : 重心を返す。 $\Theta(1)$ 。
bool has_one_centroid() : 重心が 1 つであるか否かを返す。 $\Theta(1)$ 。

また、木の重心とそれに接続する辺を全て削除し、各連結成分に対し同じように重心を求めていくと、その再帰の深さはたかだか $\lceil\log N\rceil$ となる。一度の再帰で連結成分の頂点数の最大値が半分以下になることによる。

よって、各再帰の深さで各連結成分の頂点数に対し線形や準線形の時間計算量の操作を行うとき、全体での時間計算量はそれが $\log N$ 倍になるだけである。これがいわゆる重心分解。 Frequency Table of Tree Distance や Contour Query など。

TreeDecomposition(Graph<T> G) : 木を重心分解する。 $\Theta(N \log N)$ 。
int get_root() : 最初の重心を返す。 $\Theta(1)$ 。
UnweightedGraph get() : 有向木を返す。この木は、各重心について、それを削除した後にできた各連結成分の重心が子となっている。 $\Theta(N)$ 。

Depends on

Required by

Verified with

Code

#pragma once

#include "../../other/template.hpp"
#include "../Graph.hpp"

template<class T> class TreeCentroids {
private:
    int n;
    const Graph<T>& G;
    std::vector<int> sz;
    std::vector<int> cent;
    int dfs(int v, int p) {
        for (const auto& e : G[v]) {
            if (e.to == p) continue;
            sz[v] += dfs(e.to, v);
        }
        return sz[v];
    }
    void init() {
        n = G.size();
        sz.assign(n, 1);
        int s = dfs(0, -1);
        int v = 0, p = -1;
        while (true) {
            bool ok = true;
            for (const auto& e : G[v]) {
                if (e.to == p) continue;
                if (sz[e.to] * 2 > s) {
                    p = v;
                    v = e.to;
                    ok = false;
                    break;
                }
                if (sz[e.to] * 2 == s) {
                    cent = {v, e.to};
                    return;
                }
            }
            if (ok) {
                cent = {v};
                return;
            }
        }
    }

public:
    TreeCentroids(const Graph<T>& G) : G(G) { init(); }
    bool has_one_centroid() const { return cent.size() == 1; }
    std::vector<int> get() { return cent; }
};

template<class T> class CentroidDecomposition {
private:
    int n;
    const Graph<T>& G;
    std::vector<bool> seen;
    std::vector<int> sz;
    int root;
    UnweightedGraph C;
    int dfs(int v, int p) {
        sz[v] = 1;
        for (const auto& e : G[v]) {
            if (e.to == p) continue;
            if (seen[e.to]) continue;
            sz[v] += dfs(e.to, v);
        }
        return sz[v];
    }
    void init() {
        n = G.size();
        seen.assign(n, false);
        sz.assign(n, 1);
        std::vector<std::pair<int, int>> st = {{0, -1}};
        st.reserve(n);
        C = UnweightedGraph(n);
        while (!st.empty()) {
            int v = st.back().first, vp = st.back().second;
            st.pop_back();
            int s = dfs(v, -1);
            int p = -1;
            while (true) {
                bool ok = true;
                for (const auto& e : G[v]) {
                    if (e.to == p) continue;
                    if (seen[e.to]) continue;
                    if (sz[e.to] * 2 > s) {
                        p = v;
                        v = e.to;
                        ok = false;
                        break;
                    }
                }
                if (ok) break;
            }
            seen[v] = true;
            if (vp != -1) C.add_edge(vp, v, true);
            else root = v;
            for (const auto& e : G[v]) {
                if (seen[e.to]) continue;
                st.emplace_back(e.to, v);
            }
        }
    }

public:
    CentroidDecomposition(const Graph<T>& G) : G(G) { init(); }
    int get_root() { return root; }
    const UnweightedGraph& get() const& { return C; }
    UnweightedGraph get() && { return std::move(C); }
};

/**
 * @brief TreeCentroid(木の重心)
 * @docs docs/graph/tree/TreeCentroid.md
 */

#line 2 "graph/tree/TreeCentroid.hpp"

#line 2 "other/template.hpp"

#include <bits/stdc++.h>
#line 2 "template/macros.hpp"

#line 4 "template/macros.hpp"

#ifndef __COUNTER__
#define __COUNTER__ __LINE__
#endif

#define OVERLOAD5(a, b, c, d, e, ...) e
#define REP1_0(b, c) REP1_1(b, c)
#define REP1_1(b, c)                                                           \
    for (ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(b); ++REP_COUNTER_##c)
#define REP1(b) REP1_0(b, __COUNTER__)
#define REP2(i, b) for (ll i = 0; i < (ll)(b); ++i)
#define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define rep(...) OVERLOAD5(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
#define RREP2(i, a) for (ll i = (ll)(a)-1; i >= 0; --i)
#define RREP3(i, a, b) for (ll i = (ll)(a)-1; i >= (ll)(b); --i)
#define RREP4(i, a, b, c) for (ll i = (ll)(a)-1; i >= (ll)(b); i -= (ll)(c))
#define rrep(...) OVERLOAD5(__VA_ARGS__, RREP4, RREP3, RREP2)(__VA_ARGS__)
#define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i)
#define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i)
#define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c))
#define reps(...) OVERLOAD5(__VA_ARGS__, REPS4, REPS3, REPS2)(__VA_ARGS__)
#define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i)
#define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i)
#define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c))
#define rreps(...) OVERLOAD5(__VA_ARGS__, RREPS4, RREPS3, RREPS2)(__VA_ARGS__)

#define each_for(...) for (auto&& __VA_ARGS__)
#define each_const(...) for (const auto& __VA_ARGS__)

#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)

#if __cpp_if_constexpr >= 201606L
#define IF_CONSTEXPR constexpr
#else
#define IF_CONSTEXPR
#endif

#define IO_BUFFER_SIZE (1 << 17)
#line 2 "template/alias.hpp"

#line 4 "template/alias.hpp"

using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using ld = long double;
using PLL = std::pair<ll, ll>;
template<class T>
using prique = std::priority_queue<T, std::vector<T>, std::greater<T>>;

template<class T> struct infinity {
    static constexpr T value = std::numeric_limits<T>::max() / 2;
    static constexpr T mvalue = std::numeric_limits<T>::lowest() / 2;
    static constexpr T max = std::numeric_limits<T>::max();
    static constexpr T min = std::numeric_limits<T>::lowest();
};

#if __cplusplus <= 201402L
template<class T> constexpr T infinity<T>::value;
template<class T> constexpr T infinity<T>::mvalue;
template<class T> constexpr T infinity<T>::max;
template<class T> constexpr T infinity<T>::min;
#endif

#if __cpp_variable_templates >= 201304L
template<class T> constexpr T INF = infinity<T>::value;
#endif

constexpr ll inf = infinity<ll>::value;
constexpr ld EPS = 1e-8;
constexpr ld PI = 3.1415926535897932384626;
#line 2 "template/type_traits.hpp"

#line 5 "template/type_traits.hpp"

template<class T, class... Args> struct function_traits_impl {
    using result_type = T;
    template<std::size_t idx>
    using argument_type =
        typename std::tuple_element<idx, std::tuple<Args...>>::type;
    using argument_tuple = std::tuple<Args...>;
    static constexpr std::size_t arg_size() { return sizeof...(Args); }
};

template<class> struct function_traits_helper;

template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)&> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const&> {
    using type = function_traits_impl<Res, Args...>;
};

#if __cpp_noexcept_function_type >= 201510L
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) noexcept> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)& noexcept> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const noexcept> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const& noexcept> {
    using type = function_traits_impl<Res, Args...>;
};
#endif

template<class F>
using function_traits = typename function_traits_helper<
    decltype(&std::remove_reference<F>::type::operator())>::type;

template<class F>
using function_result_type = typename function_traits<F>::result_type;
template<class F, std::size_t idx>
using function_argument_type =
    typename function_traits<F>::template argument_type<idx>;
template<class F>
using function_argument_tuple = typename function_traits<F>::argument_tuple;

template<class T>
using is_signed_int =
    std::integral_constant<bool, (std::is_integral<T>::value &&
                                  std::is_signed<T>::value) ||
                                     std::is_same<T, i128>::value>;
template<class T>
using is_unsigned_int =
    std::integral_constant<bool, (std::is_integral<T>::value &&
                                  std::is_unsigned<T>::value) ||
                                     std::is_same<T, u128>::value>;
template<class T>
using is_int = std::integral_constant<bool, is_signed_int<T>::value ||
                                                is_unsigned_int<T>::value>;
template<class T>
using make_signed_int = typename std::conditional<
    std::is_same<T, i128>::value || std::is_same<T, u128>::value,
    std::common_type<i128>, std::make_signed<T>>::type;
template<class T>
using make_unsigned_int = typename std::conditional<
    std::is_same<T, i128>::value || std::is_same<T, u128>::value,
    std::common_type<u128>, std::make_unsigned<T>>::type;


template<class T, class = void> struct is_range : std::false_type {};
template<class T>
struct is_range<
    T,
    decltype(all(std::declval<typename std::add_lvalue_reference<T>::type>()),
             (void)0)> : std::true_type {};

template<class T, bool = is_range<T>::value>
struct range_rank : std::integral_constant<std::size_t, 0> {};
template<class T>
struct range_rank<T, true>
    : std::integral_constant<std::size_t,
                             range_rank<typename T::value_type>::value + 1> {};

template<std::size_t size> struct int_least {
    static_assert(size <= 128, "size must be less than or equal to 128");

    using type = typename std::conditional<
        size <= 8, std::int_least8_t,
        typename std::conditional<
            size <= 16, std::int_least16_t,
            typename std::conditional<
                size <= 32, std::int_least32_t,
                typename std::conditional<size <= 64, std::int_least64_t,
                                          i128>::type>::type>::type>::type;
};

template<std::size_t size> using int_least_t = typename int_least<size>::type;

template<std::size_t size> struct uint_least {
    static_assert(size <= 128, "size must be less than or equal to 128");

    using type = typename std::conditional<
        size <= 8, std::uint_least8_t,
        typename std::conditional<
            size <= 16, std::uint_least16_t,
            typename std::conditional<
                size <= 32, std::uint_least32_t,
                typename std::conditional<size <= 64, std::uint_least64_t,
                                          u128>::type>::type>::type>::type;
};

template<std::size_t size> using uint_least_t = typename uint_least<size>::type;

template<class T>
using double_size_int = int_least<std::numeric_limits<T>::digits * 2 + 1>;
template<class T> using double_size_int_t = typename double_size_int<T>::type;
template<class T>
using double_size_uint = uint_least<std::numeric_limits<T>::digits * 2>;
template<class T> using double_size_uint_t = typename double_size_uint<T>::type;

template<class T>
using double_size =
    typename std::conditional<is_signed_int<T>::value, double_size_int<T>,
                              double_size_uint<T>>::type;
template<class T> using double_size_t = typename double_size<T>::type;
#line 2 "template/in.hpp"

#line 4 "template/in.hpp"
#include <unistd.h>
#line 8 "template/in.hpp"

template<std::size_t buf_size = IO_BUFFER_SIZE,
         std::size_t decimal_precision = 16>
class Scanner {
private:
    template<class, class = void> struct has_scan : std::false_type {};
    template<class T>
    struct has_scan<
        T, decltype(std::declval<T>().scan(std::declval<Scanner&>()), (void)0)>
        : std::true_type {};
    int fd;
    int idx, sz;
    bool state;
    std::array<char, IO_BUFFER_SIZE + 1> buffer;
    inline char cur() {
        if (idx == sz) load();
        if (idx == sz) {
            state = false;
            return '\0';
        }
        return buffer[idx];
    }
    inline void next() {
        if (idx == sz) load();
        if (idx == sz) return;
        ++idx;
    }

public:
    inline void load() {
        int len = sz - idx;
        if (idx < len) return;
        std::memcpy(buffer.begin(), buffer.begin() + idx, len);
        sz = len + read(fd, buffer.data() + len, buf_size - len);
        buffer[sz] = 0;
        idx = 0;
    }

    Scanner(int fd) : fd(fd), idx(0), sz(0), state(true) {}
    Scanner(FILE* fp) : fd(fileno(fp)), idx(0), sz(0), state(true) {}

    inline char scan_char() {
        if (idx == sz) load();
        return idx == sz ? '\0' : buffer[idx++];
    }

    Scanner ignore(int n = 1) {
        if (idx + n > sz) load();
        idx += n;
        return *this;
    }

    inline void discard_space() {
        if (idx == sz) load();
        while (('\t' <= buffer[idx] && buffer[idx] <= '\r') ||
               buffer[idx] == ' ') {
            if (++idx == sz) load();
        }
    }
    void scan(char& a) {
        discard_space();
        a = scan_char();
    }
    void scan(bool& a) {
        discard_space();
        a = scan_char() != '0';
    }
    void scan(std::string& a) {
        discard_space();
        a.clear();
        while (cur() != '\0' && (buffer[idx] < '\t' || '\r' < buffer[idx]) &&
               buffer[idx] != ' ') {
            a += scan_char();
        }
    }
    template<std::size_t len> void scan(std::bitset<len>& a) {
        discard_space();
        if (idx + len > sz) load();
        rrep (i, len) a[i] = buffer[idx++] != '0';
    }
    template<class T,
             typename std::enable_if<is_signed_int<T>::value &&
                                     !has_scan<T>::value>::type* = nullptr>
    void scan(T& a) {
        discard_space();
        if (buffer[idx] == '-') {
            ++idx;
            if (idx + 40 > sz &&
                (idx == sz || ('0' <= buffer[sz - 1] && buffer[sz - 1] <= '9')))
                load();
            a = 0;
            while ('0' <= buffer[idx] && buffer[idx] <= '9') {
                a = a * 10 - (buffer[idx++] - '0');
            }
        }
        else {
            if (idx + 40 > sz && '0' <= buffer[sz - 1] && buffer[sz - 1] <= '9')
                load();
            a = 0;
            while ('0' <= buffer[idx] && buffer[idx] <= '9') {
                a = a * 10 + (buffer[idx++] - '0');
            }
        }
    }
    template<class T,
             typename std::enable_if<is_unsigned_int<T>::value &&
                                     !has_scan<T>::value>::type* = nullptr>
    void scan(T& a) {
        discard_space();
        if (idx + 40 > sz && '0' <= buffer[sz - 1] && buffer[sz - 1] <= '9')
            load();
        a = 0;
        while ('0' <= buffer[idx] && buffer[idx] <= '9') {
            a = a * 10 + (buffer[idx++] - '0');
        }
    }
    template<class T,
             typename std::enable_if<std::is_floating_point<T>::value &&
                                     !has_scan<T>::value>::type* = nullptr>
    void scan(T& a) {
        discard_space();
        bool sgn = false;
        if (cur() == '-') {
            sgn = true;
            next();
        }
        a = 0;
        while ('0' <= cur() && cur() <= '9') {
            a = a * 10 + cur() - '0';
            next();
        }
        if (cur() == '.') {
            next();
            T n = 0, d = 1;
            for (int i = 0;
                 '0' <= cur() && cur() <= '9' && i < (int)decimal_precision;
                 ++i) {
                n = n * 10 + cur() - '0';
                d *= 10;
                next();
            }
            while ('0' <= cur() && cur() <= '9') next();
            a += n / d;
        }
        if (sgn) a = -a;
    }

private:
    template<std::size_t i, class... Args> void scan(std::tuple<Args...>& a) {
        if IF_CONSTEXPR (i < sizeof...(Args)) {
            scan(std::get<i>(a));
            scan<i + 1, Args...>(a);
        }
    }

public:
    template<class... Args> void scan(std::tuple<Args...>& a) {
        scan<0, Args...>(a);
    }
    template<class T, class U> void scan(std::pair<T, U>& a) {
        scan(a.first);
        scan(a.second);
    }
    template<class T,
             typename std::enable_if<is_range<T>::value &&
                                     !has_scan<T>::value>::type* = nullptr>
    void scan(T& a) {
        for (auto&& i : a) scan(i);
    }
    template<class T,
             typename std::enable_if<has_scan<T>::value>::type* = nullptr>
    void scan(T& a) {
        a.scan(*this);
    }

    void operator()() {}
    template<class Head, class... Args>
    void operator()(Head& head, Args&... args) {
        scan(head);
        operator()(args...);
    }

    template<class T> Scanner& operator>>(T& a) {
        scan(a);
        return *this;
    }

    explicit operator bool() const { return state; }

    friend Scanner& getline(Scanner& scan, std::string& a) {
        a.erase();
        char c;
        if ((c = scan.scan_char()) == '\n' || c == '\0') return scan;
        a += c;
        while ((c = scan.scan_char()) != '\n' && c != '\0') a += c;
        scan.state = true;
        return scan;
    }
};

Scanner<> scan(0);
#line 2 "template/out.hpp"

#line 8 "template/out.hpp"

struct NumberToString {
    char buf[10000][4];
    constexpr NumberToString() : buf{} {
        rep (i, 10000) {
            int n = i;
            rrep (j, 4) {
                buf[i][j] = (char)('0' + n % 10);
                n /= 10;
            }
        }
    }
} constexpr precalc_number_to_string;

template<std::size_t buf_size = IO_BUFFER_SIZE, bool debug = false>
class Printer {
private:
    template<class, bool = debug, class = void>
    struct has_print : std::false_type {};
    template<class T>
    struct has_print<T, false,
                     decltype(std::declval<T>().print(std::declval<Printer&>()),
                              (void)0)> : std::true_type {};
    template<class T>
    struct has_print<T, true,
                     decltype(std::declval<T>().debug(std::declval<Printer&>()),
                              (void)0)> : std::true_type {};
    int fd;
    std::size_t idx;
    std::array<char, buf_size> buffer;

    std::size_t decimal_precision;

public:
    inline void print_char(char c) {
#if SHIO_LOCAL
        buffer[idx++] = c;
        if (idx == buf_size) flush();
#else
        if IF_CONSTEXPR (!debug) {
            buffer[idx++] = c;
            if (idx == buf_size) flush();
        }
#endif
    }
    inline void flush() {
        idx = write(fd, buffer.begin(), idx);
        idx = 0;
    }

    Printer(int fd) : fd(fd), idx(0), decimal_precision(16) {}
    Printer(FILE* fp) : fd(fileno(fp)), idx(0), decimal_precision(16) {}
    ~Printer() { flush(); }

    void set_decimal_precision(std::size_t decimal_precision) {
        this->decimal_precision = decimal_precision;
    }

    void print(char c) {
        if IF_CONSTEXPR (debug) print_char('\'');
        print_char(c);
        if IF_CONSTEXPR (debug) print_char('\'');
    }
    void print(bool b) { print_char((char)(b + '0')); }
    void print(const char* a) {
        if IF_CONSTEXPR (debug) print_char('"');
        for (; *a != '\0'; ++a) print_char(*a);
        if IF_CONSTEXPR (debug) print_char('"');
    }
    template<std::size_t len> void print(const char (&a)[len]) {
        if IF_CONSTEXPR (debug) print_char('"');
        for (auto i : a) print_char(i);
        if IF_CONSTEXPR (debug) print_char('"');
    }
    void print(const std::string& a) {
        if IF_CONSTEXPR (debug) print_char('"');
        for (auto i : a) print_char(i);
        if IF_CONSTEXPR (debug) print_char('"');
    }
    template<std::size_t len> void print(const std::bitset<len>& a) {
        rrep (i, len) print_char((char)(a[i] + '0'));
    }
    template<class T,
             typename std::enable_if<is_int<T>::value &&
                                     !has_print<T>::value>::type* = nullptr>
    void print(T a) {
        if (!a) {
            print_char('0');
            return;
        }
        if IF_CONSTEXPR (is_signed_int<T>::value) {
            if (a < 0) {
                print_char('-');
                using U = typename make_unsigned_int<T>::type;
                print(static_cast<U>(-static_cast<U>(a)));
                return;
            }
        }
        if (idx + 40 >= buf_size) flush();
        static char s[40];
        int t = 40;
        while (a >= 10000) {
            int i = a % 10000;
            a /= 10000;
            t -= 4;
            std::memcpy(s + t, precalc_number_to_string.buf[i], 4);
        }
        if (a >= 1000) {
            std::memcpy(buffer.begin() + idx, precalc_number_to_string.buf[a],
                        4);
            idx += 4;
        }
        else if (a >= 100) {
            std::memcpy(buffer.begin() + idx,
                        precalc_number_to_string.buf[a] + 1, 3);
            idx += 3;
        }
        else if (a >= 10) {
            std::memcpy(buffer.begin() + idx,
                        precalc_number_to_string.buf[a] + 2, 2);
            idx += 2;
        }
        else {
            buffer[idx++] = '0' | a;
        }
        std::memcpy(buffer.begin() + idx, s + t, 40 - t);
        idx += 40 - t;
    }
    template<class T,
             typename std::enable_if<std::is_floating_point<T>::value &&
                                     !has_print<T>::value>::type* = nullptr>
    void print(T a) {
        if (a == std::numeric_limits<T>::infinity()) {
            print("inf");
            return;
        }
        if (a == -std::numeric_limits<T>::infinity()) {
            print("-inf");
            return;
        }
        if (std::isnan(a)) {
            print("nan");
            return;
        }
        if (a < 0) {
            print_char('-');
            a = -a;
        }
        T b = a;
        if (b < 1) {
            print_char('0');
        }
        else {
            std::string s;
            while (b >= 1) {
                s += (char)('0' + (int)std::fmod(b, 10.0));
                b /= 10;
            }
            for (auto i = s.rbegin(); i != s.rend(); ++i) print_char(*i);
        }
        print_char('.');
        rep (decimal_precision) {
            a *= 10;
            print_char((char)('0' + (int)std::fmod(a, 10.0)));
        }
    }

private:
    template<std::size_t i, class... Args>
    void print(const std::tuple<Args...>& a) {
        if IF_CONSTEXPR (i < sizeof...(Args)) {
            if IF_CONSTEXPR (debug) print_char(',');
            print_char(' ');
            print(std::get<i>(a));
            print<i + 1, Args...>(a);
        }
    }

public:
    template<class... Args> void print(const std::tuple<Args...>& a) {
        if IF_CONSTEXPR (debug) print_char('(');
        if IF_CONSTEXPR (sizeof...(Args) != 0) print(std::get<0>(a));
        print<1, Args...>(a);
        if IF_CONSTEXPR (debug) print_char(')');
    }
    template<class T, class U> void print(const std::pair<T, U>& a) {
        if IF_CONSTEXPR (debug) print_char('(');
        print(a.first);
        if IF_CONSTEXPR (debug) print_char(',');
        print_char(' ');
        print(a.second);
        if IF_CONSTEXPR (debug) print_char(')');
    }
    template<class T,
             typename std::enable_if<is_range<T>::value &&
                                     !has_print<T>::value>::type* = nullptr>
    void print(const T& a) {
        if IF_CONSTEXPR (debug) print_char('{');
        for (auto i = std::begin(a); i != std::end(a); ++i) {
            if (i != std::begin(a)) {
                if IF_CONSTEXPR (debug) print_char(',');
                print_char(' ');
            }
            print(*i);
        }
        if IF_CONSTEXPR (debug) print_char('}');
    }
    template<class T, typename std::enable_if<has_print<T>::value &&
                                              !debug>::type* = nullptr>
    void print(const T& a) {
        a.print(*this);
    }
    template<class T, typename std::enable_if<has_print<T>::value &&
                                              debug>::type* = nullptr>
    void print(const T& a) {
        a.debug(*this);
    }

    void operator()() {}
    template<class Head, class... Args>
    void operator()(const Head& head, const Args&... args) {
        print(head);
        operator()(args...);
    }

    template<class T> Printer& operator<<(const T& a) {
        print(a);
        return *this;
    }

    Printer& operator<<(Printer& (*pf)(Printer&)) { return pf(*this); }
};

template<std::size_t buf_size, bool debug>
Printer<buf_size, debug>& endl(Printer<buf_size, debug>& pr) {
    pr.print_char('\n');
    pr.flush();
    return pr;
}
template<std::size_t buf_size, bool debug>
Printer<buf_size, debug>& flush(Printer<buf_size, debug>& pr) {
    pr.flush();
    return pr;
}

struct SetPrec {
    int n;
    template<class Pr> void print(Pr& pr) const { pr.set_decimal_precision(n); }
    template<class Pr> void debug(Pr& pr) const { pr.set_decimal_precision(n); }
};
SetPrec setprec(int n) { return SetPrec{n}; };

Printer<> print(1), eprint(2);

void prints() { print.print_char('\n'); }

template<class T> auto prints(const T& v) -> decltype(print << v, (void)0) {
    print << v;
    print.print_char('\n');
}

template<class Head, class... Tail>
auto prints(const Head& head, const Tail&... tail)
    -> decltype(print << head, (void)0) {
    print << head;
    print.print_char(' ');
    prints(tail...);
}

Printer<IO_BUFFER_SIZE, true> debug(1), edebug(2);

void debugs() { debug.print_char('\n'); }

template<class T> auto debugs(const T& v) -> decltype(debug << v, (void)0) {
    debug << v;
    debug.print_char('\n');
}

template<class Head, class... Tail>
auto debugs(const Head& head, const Tail&... tail)
    -> decltype(debug << head, (void)0) {
    debug << head;
    debug.print_char(' ');
    debugs(tail...);
}
#line 2 "template/bitop.hpp"

#line 6 "template/bitop.hpp"

namespace bitop {

#define KTH_BIT(b, k) (((b) >> (k)) & 1)
#define POW2(k) (1ull << (k))

inline ull next_combination(int n, ull x) {
    if (n == 0) return 1;
    ull a = x & -x;
    ull b = x + a;
    return (x & ~b) / a >> 1 | b;
}

#define rep_comb(i, n, k)                                                      \
    for (ull i = (1ull << (k)) - 1; i < (1ull << (n));                         \
         i = bitop::next_combination((n), i))

inline constexpr int msb(ull x) {
    int res = x ? 0 : -1;
    if (x & 0xFFFFFFFF00000000) x &= 0xFFFFFFFF00000000, res += 32;
    if (x & 0xFFFF0000FFFF0000) x &= 0xFFFF0000FFFF0000, res += 16;
    if (x & 0xFF00FF00FF00FF00) x &= 0xFF00FF00FF00FF00, res += 8;
    if (x & 0xF0F0F0F0F0F0F0F0) x &= 0xF0F0F0F0F0F0F0F0, res += 4;
    if (x & 0xCCCCCCCCCCCCCCCC) x &= 0xCCCCCCCCCCCCCCCC, res += 2;
    return res + ((x & 0xAAAAAAAAAAAAAAAA) ? 1 : 0);
}

inline constexpr int ceil_log2(ull x) { return x ? msb(x - 1) + 1 : 0; }

inline constexpr ull reverse(ull x) {
    x = ((x & 0xAAAAAAAAAAAAAAAA) >> 1) | ((x & 0x5555555555555555) << 1);
    x = ((x & 0xCCCCCCCCCCCCCCCC) >> 2) | ((x & 0x3333333333333333) << 2);
    x = ((x & 0xF0F0F0F0F0F0F0F0) >> 4) | ((x & 0x0F0F0F0F0F0F0F0F) << 4);
    x = ((x & 0xFF00FF00FF00FF00) >> 8) | ((x & 0x00FF00FF00FF00FF) << 8);
    x = ((x & 0xFFFF0000FFFF0000) >> 16) | ((x & 0x0000FFFF0000FFFF) << 16);
    return (x >> 32) | (x << 32);
}

inline constexpr ull reverse(ull x, int n) { return reverse(x) >> (64 - n); }

} // namespace bitop

inline constexpr int popcnt(ull x) noexcept {
#if __cplusplus >= 202002L
    return std::popcount(x);
#endif
    x = (x & 0x5555555555555555) + ((x >> 1) & 0x5555555555555555);
    x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333);
    x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f0f0f0f0f);
    x = (x & 0x00ff00ff00ff00ff) + ((x >> 8) & 0x00ff00ff00ff00ff);
    x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff);
    return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff);
}
#line 2 "template/func.hpp"

#line 6 "template/func.hpp"

template<class T, class U, class Comp = std::less<>>
inline constexpr bool chmin(T& a, const U& b,
                            Comp cmp = Comp()) noexcept(noexcept(cmp(b, a))) {
    return cmp(b, a) ? a = b, true : false;
}
template<class T, class U, class Comp = std::less<>>
inline constexpr bool chmax(T& a, const U& b,
                            Comp cmp = Comp()) noexcept(noexcept(cmp(a, b))) {
    return cmp(a, b) ? a = b, true : false;
}

inline constexpr ll gcd(ll a, ll b) {
    if (a < 0) a = -a;
    if (b < 0) b = -b;
    while (b) {
        const ll c = a;
        a = b;
        b = c % b;
    }
    return a;
}
inline constexpr ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

inline constexpr bool is_prime(ll N) {
    if (N <= 1) return false;
    for (ll i = 2; i * i <= N; ++i) {
        if (N % i == 0) return false;
    }
    return true;
}
inline std::vector<ll> prime_factor(ll N) {
    std::vector<ll> res;
    for (ll i = 2; i * i <= N; ++i) {
        while (N % i == 0) {
            res.push_back(i);
            N /= i;
        }
    }
    if (N != 1) res.push_back(N);
    return res;
}

inline constexpr ll my_pow(ll a, ll b) {
    ll res = 1;
    while (b) {
        if (b & 1) res *= a;
        b >>= 1;
        a *= a;
    }
    return res;
}
inline constexpr ll mod_pow(ll a, ll b, ll mod) {
    assert(mod > 0);
    if (mod == 1) return 0;
    a %= mod;
    ll res = 1;
    while (b) {
        if (b & 1) (res *= a) %= mod;
        b >>= 1;
        (a *= a) %= mod;
    }
    return res;
}

inline PLL extGCD(ll a, ll b) {
    const ll n = a, m = b;
    ll x = 1, y = 0, u = 0, v = 1;
    ll t;
    while (b) {
        t = a / b;
        std::swap(a -= t * b, b);
        std::swap(x -= t * u, u);
        std::swap(y -= t * v, v);
    }
    if (x < 0) {
        x += m;
        y -= n;
    }
    return {x, y};
}
inline ll mod_inv(ll a, ll mod) {
    ll b = mod;
    ll x = 1, u = 0;
    ll t;
    while (b) {
        t = a / b;
        std::swap(a -= t * b, b);
        std::swap(x -= t * u, u);
    }
    if (x < 0) x += mod;
    assert(a == 1);
    return x;
}
#line 2 "template/util.hpp"

#line 6 "template/util.hpp"

template<class F> class RecLambda {
private:
    F f;

public:
    explicit constexpr RecLambda(F&& f_) : f(std::forward<F>(f_)) {}
    template<class... Args>
    constexpr auto operator()(Args&&... args)
        -> decltype(f(*this, std::forward<Args>(args)...)) {
        return f(*this, std::forward<Args>(args)...);
    }
};

template<class F> inline constexpr RecLambda<F> rec_lambda(F&& f) {
    return RecLambda<F>(std::forward<F>(f));
}


template<class Head, class... Tail> struct multi_dim_vector {
    using type = std::vector<typename multi_dim_vector<Tail...>::type>;
};
template<class T> struct multi_dim_vector<T> { using type = T; };

template<class T, class Arg>
constexpr std::vector<T> make_vec(int n, Arg&& arg) {
    return std::vector<T>(n, std::forward<Arg>(arg));
}
template<class T, class... Args>
constexpr typename multi_dim_vector<Args..., T>::type make_vec(int n,
                                                               Args&&... args) {
    return typename multi_dim_vector<Args..., T>::type(
        n, make_vec<T>(std::forward<Args>(args)...));
}


template<class T, class Comp = std::less<T>> class compressor {
private:
    std::vector<T> dat;
    Comp cmp;
    bool sorted = false;

public:
    compressor() : compressor(Comp()) {}
    compressor(const Comp& cmp) : cmp(cmp) {}
    compressor(const std::vector<T>& vec, bool f = false,
               const Comp& cmp = Comp())
        : dat(vec), cmp(cmp) {
        if (f) build();
    }
    compressor(std::vector<T>&& vec, bool f = false, const Comp& cmp = Comp())
        : dat(std::move(vec)), cmp(cmp) {
        if (f) build();
    }
    compressor(std::initializer_list<T> il, bool f = false,
               const Comp& cmp = Comp())
        : dat(all(il)), cmp(cmp) {
        if (f) build();
    }
    void reserve(int n) {
        assert(!sorted);
        dat.reserve(n);
    }
    void push_back(const T& v) {
        assert(!sorted);
        dat.push_back(v);
    }
    void push_back(T&& v) {
        assert(!sorted);
        dat.push_back(std::move(v));
    }
    template<class... Args> void emplace_back(Args&&... args) {
        assert(!sorted);
        dat.emplace_back(std::forward<Args>(args)...);
    }
    void push(const std::vector<T>& vec) {
        assert(!sorted);
        const int n = dat.size();
        dat.resize(n + vec.size());
        rep (i, vec.size()) dat[n + i] = vec[i];
    }
    int build() {
        assert(!sorted);
        sorted = true;
        std::sort(all(dat), cmp);
        dat.erase(std::unique(all(dat),
                              [&](const T& a, const T& b) -> bool {
                                  return !cmp(a, b) && !cmp(b, a);
                              }),
                  dat.end());
        return dat.size();
    }
    const T& operator[](int k) const& {
        assert(sorted);
        assert(0 <= k && k < (int)dat.size());
        return dat[k];
    }
    int get(const T& val) const {
        assert(sorted);
        auto itr = std::lower_bound(all(dat), val, cmp);
        assert(itr != dat.end() && !cmp(val, *itr));
        return itr - dat.begin();
    }
    int lower_bound(const T& val) const {
        assert(sorted);
        auto itr = std::lower_bound(all(dat), val, cmp);
        return itr - dat.begin();
    }
    int upper_bound(const T& val) const {
        assert(sorted);
        auto itr = std::upper_bound(all(dat), val, cmp);
        return itr - dat.begin();
    }
    bool contains(const T& val) const {
        assert(sorted);
        return std::binary_search(all(dat), val, cmp);
    }
    std::vector<int> pressed(const std::vector<T>& vec) const {
        assert(sorted);
        std::vector<int> res(vec.size());
        rep (i, vec.size()) res[i] = get(vec[i]);
        return res;
    }
    void press(std::vector<T>& vec) const {
        assert(sorted);
        for (auto&& i : vec) i = get(i);
    }
    int size() const {
        assert(sorted);
        return dat.size();
    }
};
#line 2 "graph/Graph.hpp"

#line 4 "graph/Graph.hpp"

template<class T = int> struct edge {
    int from, to;
    T cost;
    int idx;
    edge() : from(-1), to(-1) {}
    edge(int f, int t, const T& c = 1, int i = -1)
        : from(f), to(t), cost(c), idx(i) {}
    edge(int f, int t, T&& c, int i = -1)
        : from(f), to(t), cost(std::move(c)), idx(i) {}
    operator int() const { return to; }
    friend bool operator<(const edge<T>& lhs, const edge<T>& rhs) {
        return lhs.cost < rhs.cost;
    }
    friend bool operator>(const edge<T>& lhs, const edge<T>& rhs) {
        return lhs.cost > rhs.cost;
    }
};

template<class T = int> using Edges = std::vector<edge<T>>;
template<class T = int> using GMatrix = std::vector<std::vector<T>>;

template<class T = int> class Graph : public std::vector<std::vector<edge<T>>> {
private:
    using Base = std::vector<std::vector<edge<T>>>;

public:
    int edge_id = 0;
    using Base::Base;
    int edge_size() const { return edge_id; }
    int add_edge(int a, int b, const T& c, bool is_directed = false) {
        assert(0 <= a && a < (int)this->size());
        assert(0 <= b && b < (int)this->size());
        (*this)[a].emplace_back(a, b, c, edge_id);
        if (!is_directed) (*this)[b].emplace_back(b, a, c, edge_id);
        return edge_id++;
    }
    int add_edge(int a, int b, bool is_directed = false) {
        assert(0 <= a && a < (int)this->size());
        assert(0 <= b && b < (int)this->size());
        (*this)[a].emplace_back(a, b, 1, edge_id);
        if (!is_directed) (*this)[b].emplace_back(b, a, 1, edge_id);
        return edge_id++;
    }
};

template<class T> GMatrix<T> ListToMatrix(const Graph<T>& G) {
    const int N = G.size();
    auto res = make_vec<T>(N, N, infinity<T>::value);
    rep (i, N) res[i][i] = 0;
    rep (i, N) {
        for (const auto& e : G[i]) res[i][e.to] = e.cost;
    }
    return res;
}

template<class T> Edges<T> UndirectedListToEdges(const Graph<T>& G) {
    const int V = G.size();
    const int E = G.edge_size();
    Edges<T> Ed(E);
    rep (i, V) {
        for (const auto& e : G[i]) Ed[e.idx] = e;
    }
    return Ed;
}

template<class T> Edges<T> DirectedListToEdges(const Graph<T>& G) {
    const int V = G.size();
    const int E = std::accumulate(
        all(G), 0, [](int a, const std::vector<edge<T>>& v) -> int {
            return a + v.size();
        });
    Edges<T> Ed(G.edge_size());
    Ed.reserve(E);
    rep (i, V) {
        for (const auto& e : G[i]) {
            if (Ed[e.idx] == -1) Ed[e.idx] = e;
            else Ed.push_back(e);
        }
    }
    return Ed;
}

template<class T> Graph<T> ReverseGraph(const Graph<T>& G) {
    const int V = G.size();
    Graph<T> res(V);
    rep (i, V) {
        for (const auto& e : G[i]) {
            res[e.to].emplace_back(e.to, e.from, e.cost, e.idx);
        }
    }
    res.edge_id = G.edge_size();
    return res;
}


struct unweighted_edge {
    template<class... Args> unweighted_edge(const Args&...) {}
    operator int() { return 1; }
};

using UnweightedGraph = Graph<unweighted_edge>;

/**
 * @brief Graph-template
 * @docs docs/graph/Graph.md
 */
#line 5 "graph/tree/TreeCentroid.hpp"

template<class T> class TreeCentroids {
private:
    int n;
    const Graph<T>& G;
    std::vector<int> sz;
    std::vector<int> cent;
    int dfs(int v, int p) {
        for (const auto& e : G[v]) {
            if (e.to == p) continue;
            sz[v] += dfs(e.to, v);
        }
        return sz[v];
    }
    void init() {
        n = G.size();
        sz.assign(n, 1);
        int s = dfs(0, -1);
        int v = 0, p = -1;
        while (true) {
            bool ok = true;
            for (const auto& e : G[v]) {
                if (e.to == p) continue;
                if (sz[e.to] * 2 > s) {
                    p = v;
                    v = e.to;
                    ok = false;
                    break;
                }
                if (sz[e.to] * 2 == s) {
                    cent = {v, e.to};
                    return;
                }
            }
            if (ok) {
                cent = {v};
                return;
            }
        }
    }

public:
    TreeCentroids(const Graph<T>& G) : G(G) { init(); }
    bool has_one_centroid() const { return cent.size() == 1; }
    std::vector<int> get() { return cent; }
};

template<class T> class CentroidDecomposition {
private:
    int n;
    const Graph<T>& G;
    std::vector<bool> seen;
    std::vector<int> sz;
    int root;
    UnweightedGraph C;
    int dfs(int v, int p) {
        sz[v] = 1;
        for (const auto& e : G[v]) {
            if (e.to == p) continue;
            if (seen[e.to]) continue;
            sz[v] += dfs(e.to, v);
        }
        return sz[v];
    }
    void init() {
        n = G.size();
        seen.assign(n, false);
        sz.assign(n, 1);
        std::vector<std::pair<int, int>> st = {{0, -1}};
        st.reserve(n);
        C = UnweightedGraph(n);
        while (!st.empty()) {
            int v = st.back().first, vp = st.back().second;
            st.pop_back();
            int s = dfs(v, -1);
            int p = -1;
            while (true) {
                bool ok = true;
                for (const auto& e : G[v]) {
                    if (e.to == p) continue;
                    if (seen[e.to]) continue;
                    if (sz[e.to] * 2 > s) {
                        p = v;
                        v = e.to;
                        ok = false;
                        break;
                    }
                }
                if (ok) break;
            }
            seen[v] = true;
            if (vp != -1) C.add_edge(vp, v, true);
            else root = v;
            for (const auto& e : G[v]) {
                if (seen[e.to]) continue;
                st.emplace_back(e.to, v);
            }
        }
    }

public:
    CentroidDecomposition(const Graph<T>& G) : G(G) { init(); }
    int get_root() { return root; }
    const UnweightedGraph& get() const& { return C; }
    UnweightedGraph get() && { return std::move(C); }
};

/**
 * @brief TreeCentroid(木の重心)
 * @docs docs/graph/tree/TreeCentroid.md
 */

TreeCentroid(木の重心) (graph/tree/TreeCentroid.hpp)

概要

Depends on

Required by

Verified with

Code

TreeCentroid(木の重心)
(graph/tree/TreeCentroid.hpp)