Library

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:heavy_check_mark: test/tree/Rooted_Tree_Isomorphism_Classification.test.cpp

Depends on

Code

#define PROBLEM \
    "https://judge.yosupo.jp/problem/rooted_tree_isomorphism_classification"

#include <iostream>
#include <map>
#include <vector>

#include "../../tree/rooted_tree_hash.hpp"
#include "../../utility/hash.hpp"
#include "../../graph/base.hpp"

int main() {
    int n;
    std::cin >> n;
    ebi::Graph<int> g(n);
    g.read_parents(0);
    auto hash = ebi::rooted_tree_hash<2>::subtree_hash(g, 0);
    int k = 0;
    std::map<ebi::Hash<2>, int> map;
    for (auto h : hash) {
        if (map.find(h) == map.end()) map[h] = k++;
    }
    std::cout << k << '\n';
    for (int i = 0; i < n; i++) {
        std::cout << map[hash[i]] << " \n"[i == n - 1];
    }
}
#line 1 "test/tree/Rooted_Tree_Isomorphism_Classification.test.cpp"
#define PROBLEM \
    "https://judge.yosupo.jp/problem/rooted_tree_isomorphism_classification"

#include <iostream>
#include <map>
#include <vector>

#line 2 "tree/rooted_tree_hash.hpp"

#line 4 "tree/rooted_tree_hash.hpp"

#line 2 "graph/base.hpp"

#include <cassert>
#line 5 "graph/base.hpp"
#include <ranges>
#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#line 4 "data_structure/simple_csr.hpp"
#include <utility>
#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 2 "utility/hash.hpp"

#include <array>

#line 2 "modint/modint61.hpp"

#line 4 "modint/modint61.hpp"
#include <cstdint>
#line 6 "modint/modint61.hpp"

#line 2 "modint/base.hpp"

#include <concepts>
#line 6 "modint/base.hpp"

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 8 "modint/modint61.hpp"

namespace ebi {

struct modint61 {
  private:
    using mint = modint61;
    using u64 = std::uint64_t;
    constexpr static u64 m = (1ull << 61) - 1;
    constexpr static u64 MASK31 = (1ull << 31) - 1;
    constexpr static u64 MASK30 = (1ull << 30) - 1;

  public:
    constexpr static u64 mod() {
        return m;
    }

    constexpr modint61() : _v(0) {}

    constexpr modint61(long long v) {
        v %= (long long)umod();
        if (v < 0) v += (long long)umod();
        _v = u64(v);
    }

    constexpr u64 val() const {
        return _v;
    }

    constexpr u64 value() const {
        return val();
    }

    constexpr mint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }

    constexpr mint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }

    constexpr mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        _v = safe_mod(_v);
        return *this;
    }

    constexpr mint &operator-=(const mint &rhs) {
        if (_v < rhs._v) _v += umod();
        assert(_v >= rhs._v);
        _v -= rhs._v;
        return *this;
    }

    constexpr mint &operator*=(const mint &rhs) {
        u64 au = _v >> 31, ad = _v & MASK31;
        u64 bu = rhs._v >> 31, bd = rhs._v & MASK31;
        u64 mid = ad * bu + au * bd;
        u64 midu = mid >> 30;
        u64 midd = mid & MASK30;
        _v = (au * bu * 2 + midu + (midd << 31) + ad * bd);
        _v = safe_mod(_v);
        return *this;
    }

    constexpr mint &operator/=(const mint &rhs) {
        return *this *= rhs.inv();
    }

    constexpr mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }

    constexpr mint inv() const {
        assert(_v);
        return pow(umod() - 2);
    }

    friend mint operator+(const mint &lhs, const mint &rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint &lhs, const mint &rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint &lhs, const mint &rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint &lhs, const mint &rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint &lhs, const mint &rhs) {
        return lhs.val() == rhs.val();
    }
    friend bool operator!=(const mint &lhs, const mint &rhs) {
        return !(lhs == rhs);
    }
    friend bool operator<(const mint &lhs, const mint &rhs) {
        return lhs._v < rhs._v;
    }
    friend bool operator>(const mint &lhs, const mint &rhs) {
        return rhs < lhs;
    }

  private:
    u64 _v = 0;

    constexpr static u64 umod() {
        return m;
    }

    constexpr u64 safe_mod(const u64 &a) {
        u64 au = a >> 61;
        u64 ad = a & umod();
        u64 res = au + ad;
        if (res >= umod()) res -= umod();
        return res;
    }
};

}  // namespace ebi
#line 2 "utility/random_number_generator.hpp"

#line 4 "utility/random_number_generator.hpp"
#include <random>


namespace ebi {

struct random_number_generator {
    random_number_generator(int seed = -1) {
        if (seed < 0) seed = rnd();
        mt.seed(seed);
    }

    void set_seed(int seed) {
        mt.seed(seed);
    }

    template <class T> T get(T a, T b) {
        std::uniform_int_distribution<T> dist(a, b - 1);
        return dist(mt);
    }

  private:
    std::mt19937_64 mt;
    std::random_device rnd;
};

}  // namespace ebi
#line 7 "utility/hash.hpp"

namespace ebi {

template <int BASE_NUM = 2> struct Hash : std::array<modint61, BASE_NUM> {
  private:
    using std::array<modint61, BASE_NUM>::array;
    using std::array<modint61, BASE_NUM>::operator=;

  public:
    Hash() : std::array<modint61, BASE_NUM>() {}

    constexpr static Hash set(const modint61 &a) {
        Hash res;
        std::fill(res.begin(), res.end(), a);
        return res;
    }

    constexpr Hash &operator+=(const Hash &rhs) {
        for (int i = 0; i < BASE_NUM; i++) {
            (*this)[i] += rhs[i];
        }
        return *this;
    }
    constexpr Hash &operator-=(const Hash &rhs) {
        for (int i = 0; i < BASE_NUM; i++) {
            (*this)[i] -= rhs[i];
        }
        return *this;
    }
    constexpr Hash &operator*=(const Hash &rhs) {
        for (int i = 0; i < BASE_NUM; i++) {
            (*this)[i] *= rhs[i];
        }
        return *this;
    }

    constexpr Hash &operator+=(const modint61 &rhs) {
        for (int i = 0; i < BASE_NUM; i++) {
            (*this)[i] += rhs;
        }
        return *this;
    }
    constexpr Hash &operator-=(const modint61 &rhs) {
        for (int i = 0; i < BASE_NUM; i++) {
            (*this)[i] -= rhs;
        }
        return *this;
    }
    constexpr Hash &operator*=(const modint61 &rhs) {
        for (int i = 0; i < BASE_NUM; i++) {
            (*this)[i] *= rhs;
        }
        return *this;
    }

    Hash operator+(const Hash &rhs) const {
        return Hash(*this) += rhs;
    }
    Hash operator-(const Hash &rhs) const {
        return Hash(*this) -= rhs;
    }
    Hash operator*(const Hash &rhs) const {
        return Hash(*this) *= rhs;
    }

    Hash operator+(const modint61 &rhs) const {
        return Hash(*this) += rhs;
    }
    Hash operator-(const modint61 &rhs) const {
        return Hash(*this) -= rhs;
    }
    Hash operator*(const modint61 &rhs) const {
        return Hash(*this) *= rhs;
    }

    Hash pow(long long n) const {
        Hash a = *this, res = set(1);
        while (n) {
            if (n & 1) res *= a;
            a *= a;
            n >>= 1;
        }
        return res;
    }

    static Hash get_basis() {
        static random_number_generator rng;
        Hash h;
        for (int i = 0; i < BASE_NUM; i++) {
            h[i] = rng.get<std::uint64_t>(0, modint61::mod() - 1) + 1;
        }
        return h;
    }

    Hash inv() const {
        Hash h;
        for (int i = 0; i < BASE_NUM; i++) {
            h[i] = (*this)[i].inv();
        }
        return h;
    }

    static Hash get_basis_primitive() {
        static random_number_generator rng;
        Hash h;
        for (int i = 0; i < BASE_NUM; i++) {
            while (!is_primitive(
                (h[i] = rng.get<std::uint64_t>(0, modint61::mod() - 1) + 1)
                    .val()))
                ;
        }
        return h;
    }

  private:
    static bool is_primitive(long long x) {
        for (long long d : {2, 3, 5, 7, 11, 13, 31, 41, 61, 151, 331, 1321}) {
            if (modint61(x).pow((modint61::mod() - 1) / d).val() <= 1)
                return false;
        }
        return true;
    }
};

}  // namespace ebi
#line 7 "tree/rooted_tree_hash.hpp"

namespace ebi {

template <int BASE_NUM = 2> struct rooted_tree_hash {
  private:
    using H = Hash<BASE_NUM>;

    static H get_basis(int d) {
        if (int(_basis.size()) <= d) _basis.emplace_back(H::get_basis());
        return _basis[d];
    }

  public:
    rooted_tree_hash() = default;

    template <class T>
    static std::vector<H> subtree_hash(const Graph<T> &g, int root = 0) {
        int n = g.size();
        std::vector<H> hash(n, H::set(1));
        std::vector<int> depth(n, 0);
        auto dfs = [&](auto &&self, int v, int par = -1) -> void {
            for (auto e : g[v]) {
                if (e.to == par) continue;
                self(self, e.to, v);
                depth[v] = std::max(depth[v], depth[e.to] + 1);
            }
            for (auto e : g[v]) {
                if (e.to == par) continue;
                hash[v] *= hash[e.to];
            }
            if (hash[v] == H::set(1)) hash[v] = H::set(0);
            hash[v] += get_basis(depth[v]);
            return;
        };
        dfs(dfs, root);
        return hash;
    }

    static std::vector<H> basis() {
        return _basis;
    }

  private:
    static std::vector<H> _basis;
};

template <int BASE_NUM>
std::vector<Hash<BASE_NUM>> rooted_tree_hash<BASE_NUM>::_basis = {};

}  // namespace ebi
#line 11 "test/tree/Rooted_Tree_Isomorphism_Classification.test.cpp"

int main() {
    int n;
    std::cin >> n;
    ebi::Graph<int> g(n);
    g.read_parents(0);
    auto hash = ebi::rooted_tree_hash<2>::subtree_hash(g, 0);
    int k = 0;
    std::map<ebi::Hash<2>, int> map;
    for (auto h : hash) {
        if (map.find(h) == map.end()) map[h] = k++;
    }
    std::cout << k << '\n';
    for (int i = 0; i < n; i++) {
        std::cout << map[hash[i]] << " \n"[i == n - 1];
    }
}
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