verify/ds/dsu/persistent_potentialized_dsu.test.cpp

View this file on GitHub
Last update: 2026-10-06 01:57:24+09:00
Problem: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_1_B

Depends on

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_1_B"

#include "../../../ds/dsu/persistent_potentialized_dsu.hpp"
#include "../../../monoid/add.hpp"
#include "../../../monoid/xor.hpp"

#include <algorithm>
#include <array>
#include <cassert>
#include "../../../utilities/fast_io.hpp"
#include <random>
#include <utility>
#include <vector>

struct Permutation3Group {
    using value_type = std::array<int, 3>;

    static value_type id() {
        return {0, 1, 2};
    }

    static value_type op(const value_type& first, const value_type& second) {
        value_type result;
        for (int i = 0; i < 3; i++) result[i] = second[first[i]];
        return result;
    }

    static value_type inv(const value_type& value) {
        value_type result;
        for (int i = 0; i < 3; i++) result[value[i]] = i;
        return result;
    }
};

static_assert(m1une::monoid::IsGroup<Permutation3Group>);

template <class Group>
struct NaivePotentializedDsu {
    using T = typename Group::value_type;

    std::vector<int> parent_or_size;
    std::vector<T> diff_to_parent;

    explicit NaivePotentializedDsu(int n = 0) : parent_or_size(n, -1), diff_to_parent(n, Group::id()) {}

    std::pair<int, T> leader_and_potential(int a) const {
        T res = Group::id();
        while (parent_or_size[a] >= 0) {
            res = Group::op(diff_to_parent[a], res);
            a = parent_or_size[a];
        }
        return {a, res};
    }

    int leader(int a) const {
        return leader_and_potential(a).first;
    }

    bool same(int a, int b) const {
        return leader(a) == leader(b);
    }

    int group_size(int a) const {
        return -parent_or_size[leader(a)];
    }

    T potential(int a) const {
        return leader_and_potential(a).second;
    }

    T diff(int a, int b) const {
        assert(same(a, b));
        return Group::op(Group::inv(potential(a)), potential(b));
    }

    std::pair<NaivePotentializedDsu, bool> merge(int a, int b, const T& w) const {
        NaivePotentializedDsu res = *this;
        auto [x, pa] = res.leader_and_potential(a);
        auto [y, pb] = res.leader_and_potential(b);
        if (x == y) return {res, Group::op(Group::inv(pa), pb) == w};

        int sx = -res.parent_or_size[x];
        int sy = -res.parent_or_size[y];
        T y_from_x = Group::op(Group::op(pa, w), Group::inv(pb));
        if (sx < sy) {
            std::swap(x, y);
            std::swap(sx, sy);
            y_from_x = Group::inv(y_from_x);
        }
        res.parent_or_size[x] += res.parent_or_size[y];
        res.parent_or_size[y] = x;
        res.diff_to_parent[y] = y_from_x;
        return {res, true};
    }

    std::vector<std::vector<int>> groups() const {
        int n = int(parent_or_size.size());
        std::vector<int> leader_buf(n), group_size(n);
        for (int i = 0; i < n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(n);
        for (int i = 0; i < n; i++) result[i].reserve(group_size[i]);
        for (int i = 0; i < n; i++) result[leader_buf[i]].push_back(i);
        result.erase(std::remove_if(result.begin(), result.end(), [](const std::vector<int>& v) { return v.empty(); }),
                     result.end());
        return result;
    }
};

void self_test() {
    using Add = m1une::monoid::Add<long long>;
    using AddDsu = m1une::ds::PersistentPotentializedDsu<Add>;

    AddDsu base(5);
    auto [a, ok1] = base.merge(0, 1, 3);
    auto [b, ok2] = a.merge(1, 2, 4);
    auto [c, ok3] = b.merge(3, 4, -2);
    auto [d, ok4] = b.merge(2, 3, 5);
    auto [bad, ok_bad] = b.merge(0, 2, 8);

    assert(ok1);
    assert(ok2);
    assert(ok3);
    assert(ok4);
    assert(!ok_bad);
    assert(base.size() == 5);
    assert(!base.empty());
    assert(!base.same(0, 2));
    assert(a.same(0, 1));
    assert(!a.same(0, 2));
    assert(b.diff(0, 2) == 7);
    assert(b.diff(2, 0) == -7);
    assert(c.diff(3, 4) == -2);
    assert(!c.same(0, 4));
    assert(d.diff(0, 3) == 12);
    assert(bad.diff(0, 2) == 7);
    assert(d.group_size(0) == 4);
    assert(d.size(0) == 4);
    assert(base.group_size(0) == 1);
    assert(base.parent_or_size(0) == -1);

    std::vector<std::vector<int>> base_groups;
    base_groups.emplace_back(std::vector<int>{0});
    base_groups.emplace_back(std::vector<int>{1});
    base_groups.emplace_back(std::vector<int>{2});
    base_groups.emplace_back(std::vector<int>{3});
    base_groups.emplace_back(std::vector<int>{4});
    assert(base.groups() == base_groups);

    using Xor = m1une::monoid::Xor<int>;
    m1une::ds::PersistentPotentializedDsu<Xor> xor_base(4);
    auto [xor_a, xor_ok1] = xor_base.merge(0, 1, 5);
    auto [xor_b, xor_ok2] = xor_a.merge(1, 2, 6);
    auto [xor_bad, xor_ok_bad] = xor_b.merge(0, 2, 2);
    assert(xor_ok1);
    assert(xor_ok2);
    assert(!xor_ok_bad);
    assert(xor_b.diff(0, 2) == (5 ^ 6));
    assert(xor_bad.diff(0, 2) == (5 ^ 6));

    using Permutation = Permutation3Group::value_type;
    using PermutationDsu =
        m1une::ds::PersistentPotentializedDsu<Permutation3Group>;
    Permutation rotate = {1, 2, 0};
    Permutation swap_last = {0, 2, 1};
    Permutation swap_first = {1, 0, 2};
    assert(Permutation3Group::op(rotate, swap_last) !=
           Permutation3Group::op(swap_last, rotate));

    PermutationDsu permutation_base(4);
    auto [permutation_a, permutation_ok1] =
        permutation_base.merge(0, 1, rotate);
    auto [permutation_b, permutation_ok2] =
        permutation_a.merge(1, 2, swap_last);
    auto [permutation_c, permutation_ok3] =
        permutation_b.merge(3, 2, swap_first);
    Permutation composed = Permutation3Group::op(rotate, swap_last);
    auto [permutation_bad, permutation_bad_ok] =
        permutation_c.merge(0, 2, Permutation3Group::op(swap_last, rotate));
    assert(permutation_ok1);
    assert(permutation_ok2);
    assert(permutation_ok3);
    assert(!permutation_bad_ok);
    assert(!permutation_base.same(0, 1));
    assert(permutation_b.diff(0, 2) == composed);
    assert(permutation_b.diff(2, 0) == Permutation3Group::inv(composed));
    assert(permutation_c.diff(3, 2) == swap_first);
    assert(permutation_c.diff(3, 0) == Permutation3Group::op(
        swap_first, Permutation3Group::inv(composed)
    ));
    assert(permutation_bad.diff(0, 2) == composed);

    AddDsu empty;
    assert(empty.size() == 0);
    assert(empty.empty());

    std::mt19937 rng(0);
    constexpr int N = 25;
    std::vector<std::pair<AddDsu, NaivePotentializedDsu<Add>>> versions;
    versions.emplace_back(AddDsu(N), NaivePotentializedDsu<Add>(N));

    for (int step = 0; step < 400; step++) {
        int id = int(rng() % versions.size());
        AddDsu cur = versions[id].first;
        NaivePotentializedDsu<Add> expected = versions[id].second;

        for (int i = 0; i < N; i++) {
            assert(cur.group_size(i) == expected.group_size(i));
            assert(cur.parent_or_size(i) == expected.parent_or_size[i]);
            for (int j = 0; j < N; j++) {
                assert(cur.same(i, j) == expected.same(i, j));
                if (cur.same(i, j)) assert(cur.diff(i, j) == expected.diff(i, j));
            }
        }
        assert(cur.groups() == expected.groups());

        int u = int(rng() % N);
        int v = int(rng() % N);
        long long w = int(rng() % 21) - 10;
        if (expected.same(u, v) && (rng() & 1)) w = expected.diff(u, v);

        auto [next, ok] = cur.merge(u, v, w);
        auto [next_expected, expected_ok] = expected.merge(u, v, w);
        assert(ok == expected_ok);

        for (int i = 0; i < N; i++) {
            assert(cur.group_size(i) == expected.group_size(i));
            assert(next.group_size(i) == next_expected.group_size(i));
            assert(next.parent_or_size(i) == next_expected.parent_or_size[i]);
        }

        versions.emplace_back(next, next_expected);
    }
}

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    self_test();

    using Add = m1une::monoid::Add<long long>;
    using Dsu = m1une::ds::PersistentPotentializedDsu<Add>;
    int n, q;
    fast_input >> n >> q;
    Dsu dsu(n);

    while (q--) {
        int type, x, y;
        fast_input >> type >> x >> y;
        if (type == 0) {
            long long z;
            fast_input >> z;
            auto [next, ok] = dsu.merge(x, y, z);
            (void)ok;
            dsu = next;
        } else {
            if (dsu.same(x, y)) {
                fast_output << dsu.diff(x, y) << '\n';
            } else {
                fast_output << "?\n";
            }
        }
    }
}

#line 1 "verify/ds/dsu/persistent_potentialized_dsu.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_1_B"

#line 1 "ds/dsu/persistent_potentialized_dsu.hpp"



#include <algorithm>
#include <cassert>
#include <concepts>
#include <cstddef>
#include <memory>
#include <utility>
#include <vector>

#line 1 "monoid/concept.hpp"



#line 5 "monoid/concept.hpp"

namespace m1une {
namespace monoid {

// Concept to check if a type satisfies the requirements of a Monoid.
// A Monoid must have a `value_type`, an identity element `id()`, and an associative binary operation `op()`.
template <typename M>
concept IsMonoid = requires(typename M::value_type a, typename M::value_type b) {
    // 1. Must define `value_type`
    typename M::value_type;

    // 2. Must have a static method `id()` returning `value_type`
    { M::id() } -> std::same_as<typename M::value_type>;

    // 3. Must have a static method `op(a, b)` returning `value_type`
    { M::op(a, b) } -> std::same_as<typename M::value_type>;
};

// Concept for groups. A type satisfying this concept must also obey the group
// laws; concepts can check the interface but not the algebraic properties.
template <typename M>
concept IsGroup = IsMonoid<M> && requires(typename M::value_type a) {
    { M::inv(a) } -> std::same_as<typename M::value_type>;
};

// Concept for commutative groups. Commutativity is a semantic requirement and
// cannot be checked by a C++ concept.
template <typename M>
concept IsCommutativeGroup = IsGroup<M>;

}  // namespace monoid
}  // namespace m1une


#line 1 "ds/detail/persistent_binary_node_pool.hpp"



#line 6 "ds/detail/persistent_binary_node_pool.hpp"
#include <deque>
#include <limits>
#include <optional>
#line 11 "ds/detail/persistent_binary_node_pool.hpp"

namespace m1une {
namespace ds {
namespace detail {

// Node must have integer `l` and `r` members. New nodes initially have no
// owner; discard_unreferenced() removes temporary path-copy nodes after the
// result roots have been retained.
template <class Node, int null_node = -1>
struct PersistentBinaryNodePool {
   private:
    std::deque<std::optional<Node>> _nodes;
    std::vector<int> _references;
    std::vector<int> _next_free;
    std::vector<int> _unowned;
    int _first_free = -1;
    std::size_t _live_nodes = 0;

    void release_zero(int node) {
        assert(node != null_node && _nodes[node].has_value());
        int left = (*_nodes[node]).l;
        int right = (*_nodes[node]).r;
        _nodes[node].reset();
        _next_free[node] = _first_free;
        _first_free = node;
        --_live_nodes;
        if (left != null_node && --_references[left] == 0) release_zero(left);
        if (right != null_node && --_references[right] == 0) release_zero(right);
    }

   public:
    PersistentBinaryNodePool() {
        if constexpr (null_node == 0) {
            _nodes.emplace_back();
            _references.push_back(0);
            _next_free.push_back(-1);
        }
    }

    Node& operator[](int node) {
        assert(node != null_node && _nodes[node].has_value());
        return *_nodes[node];
    }

    const Node& operator[](int node) const {
        assert(node != null_node && _nodes[node].has_value());
        return *_nodes[node];
    }

    template <class... Args>
    int emplace(Args&&... args) {
        int result;
        if (_first_free == -1) {
            assert(_nodes.size() < std::size_t(std::numeric_limits<int>::max()));
            result = int(_nodes.size());
            _nodes.emplace_back(std::in_place, std::forward<Args>(args)...);
            _references.push_back(0);
            _next_free.push_back(-1);
        } else {
            result = _first_free;
            _first_free = _next_free[result];
            _nodes[result].emplace(std::forward<Args>(args)...);
            _references[result] = 0;
        }
        retain((*_nodes[result]).l);
        retain((*_nodes[result]).r);
        _unowned.push_back(result);
        ++_live_nodes;
        return result;
    }

    void retain(int node) {
        if (node != null_node) {
            assert(_nodes[node].has_value());
            ++_references[node];
        }
    }

    void release(int node) {
        if (node == null_node) return;
        assert(_nodes[node].has_value() && _references[node] > 0);
        if (--_references[node] == 0) release_zero(node);
    }

    bool unique(int node) const {
        return node == null_node || _references[node] == 1;
    }

    int clone(int node) {
        assert(node != null_node && _nodes[node].has_value());
        return emplace(*_nodes[node]);
    }

    // Returns node itself when it has one owner, otherwise an unowned clone.
    // A returned clone becomes owned when a root or parent edge retains it.
    int clone_if_shared(int node) {
        if (unique(node)) return node;
        return clone(node);
    }

    void replace(int& edge, int node) {
        if (edge == node) return;
        retain(node);
        int old = edge;
        edge = node;
        release(old);
    }

    void discard_unreferenced() {
        while (!_unowned.empty()) {
            int node = _unowned.back();
            _unowned.pop_back();
            if (_nodes[node].has_value() && _references[node] == 0) release_zero(node);
        }
    }

    void reserve(std::size_t) {}

    int next_index() const { return _first_free == -1 ? int(_nodes.size()) : _first_free; }

    std::size_t size() const { return _live_nodes; }
};

}  // namespace detail
}  // namespace ds
}  // namespace m1une


#line 14 "ds/dsu/persistent_potentialized_dsu.hpp"

namespace m1une {
namespace ds {

template <m1une::monoid::IsGroup Group>
    requires std::equality_comparable<typename Group::value_type>
struct PersistentPotentializedDsu {
    using T = typename Group::value_type;

    struct Value {
        int parent_or_size;
        T diff_to_parent;

        Value() : parent_or_size(0), diff_to_parent(Group::id()) {}
        Value(int parent_or_size_, const T& diff_to_parent_)
            : parent_or_size(parent_or_size_), diff_to_parent(diff_to_parent_) {}
        Value(int parent_or_size_, T&& diff_to_parent_)
            : parent_or_size(parent_or_size_), diff_to_parent(std::move(diff_to_parent_)) {}
    };

   private:
    struct Node {
        Value val;
        int l, r;

        Node() : val(), l(0), r(0) {}
        explicit Node(const Value& value) : val(value), l(0), r(0) {}
        explicit Node(Value&& value) : val(std::move(value)), l(0), r(0) {}
        Node(const Value& value, int left, int right) : val(value), l(left), r(right) {}
        Node(Value&& value, int left, int right) : val(std::move(value)), l(left), r(right) {}
    };

    int _n;
    int _root;
    using Pool = detail::PersistentBinaryNodePool<Node, 0>;

    std::shared_ptr<Pool> _pool;

    explicit PersistentPotentializedDsu(int n, int root, std::shared_ptr<Pool> pool)
        : _n(n), _root(root), _pool(std::move(pool)) {
        _pool->retain(_root);
    }

    int new_node(const Node& node) const {
        return _pool->emplace(node);
    }

    int new_node(Node&& node) const {
        return _pool->emplace(std::move(node));
    }

    int build(int l, int r) const {
        if (l == r) return 0;
        if (r - l == 1) return new_node(Node(Value(-1, Group::id())));
        int m = (l + r) >> 1;
        int left = build(l, m);
        int right = build(m, r);
        return new_node(Node(Value(), left, right));
    }

    int set_node(int t, int l, int r, int p, Value value, bool copy_on_write = false) const {
        if (copy_on_write) t = _pool->clone_if_shared(t);
        if (r - l == 1) {
            if (copy_on_write) {
                (*_pool)[t].val = std::move(value);
                return t;
            }
            return new_node(Node(std::move(value)));
        }
        int m = (l + r) >> 1;
        int left = (*_pool)[t].l;
        int right = (*_pool)[t].r;
        if (p < m) {
            left = set_node(left, l, m, p, std::move(value), copy_on_write);
        } else {
            right = set_node(right, m, r, p, std::move(value), copy_on_write);
        }
        if (copy_on_write) {
            _pool->replace((*_pool)[t].l, left);
            _pool->replace((*_pool)[t].r, right);
            return t;
        }
        return new_node(Node(Value(), left, right));
    }

    Value get_value(int t, int l, int r, int p) const {
        while (r - l > 1) {
            int m = (l + r) >> 1;
            if (p < m) {
                t = (*_pool)[t].l;
                r = m;
            } else {
                t = (*_pool)[t].r;
                l = m;
            }
        }
        return (*_pool)[t].val;
    }

    std::pair<int, T> leader_and_potential(int a) const {
        T res = Group::id();
        while (true) {
            Value cur = get(a);
            if (cur.parent_or_size < 0) return {a, res};
            res = Group::op(cur.diff_to_parent, res);
            a = cur.parent_or_size;
        }
    }

    PersistentPotentializedDsu make_version(int root) const {
        PersistentPotentializedDsu result(_n, root, _pool);
        _pool->discard_unreferenced();
        return result;
    }

   public:
    PersistentPotentializedDsu() : PersistentPotentializedDsu(0) {}

    explicit PersistentPotentializedDsu(int n) : _n(n), _root(0), _pool(std::make_shared<Pool>()) {
        assert(0 <= n);
        _pool->reserve(n * 4 + 1);
        if (_n > 0) _root = build(0, _n);
        _pool->retain(_root);
        _pool->discard_unreferenced();
    }

    PersistentPotentializedDsu(const PersistentPotentializedDsu& other)
        : _n(other._n), _root(other._root), _pool(other._pool) {
        if (_pool) _pool->retain(_root);
    }

    PersistentPotentializedDsu(PersistentPotentializedDsu&& other) noexcept
        : _n(other._n), _root(other._root), _pool(std::move(other._pool)) {
        other._n = 0;
        other._root = 0;
    }

    PersistentPotentializedDsu& operator=(const PersistentPotentializedDsu& other) {
        if (this == &other) return *this;
        if (other._pool) other._pool->retain(other._root);
        if (_pool) _pool->release(_root);
        _n = other._n;
        _root = other._root;
        _pool = other._pool;
        return *this;
    }

    PersistentPotentializedDsu& operator=(PersistentPotentializedDsu&& other) noexcept {
        if (this == &other) return *this;
        if (_pool) _pool->release(_root);
        _n = other._n;
        _root = other._root;
        _pool = std::move(other._pool);
        other._n = 0;
        other._root = 0;
        return *this;
    }

    ~PersistentPotentializedDsu() {
        if (_pool) _pool->release(_root);
    }

    int size() const {
        return _n;
    }

    bool empty() const {
        return _n == 0;
    }

    void release() {
        if (_pool) _pool->release(_root);
        _n = 0;
        _root = 0;
        _pool = std::make_shared<Pool>();
    }

    std::size_t node_count() const { return _pool ? _pool->size() : 0; }

    int leader(int a) const {
        assert(0 <= a && a < _n);
        return leader_and_potential(a).first;
    }

    bool same(int a, int b) const {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int group_size(int a) const {
        assert(0 <= a && a < _n);
        return -get(leader(a)).parent_or_size;
    }

    int size(int a) const {
        return group_size(a);
    }

    T potential(int a) const {
        assert(0 <= a && a < _n);
        return leader_and_potential(a).second;
    }

    T diff(int a, int b) const {
        assert(same(a, b));
        return Group::op(Group::inv(potential(a)), potential(b));
    }

    Value get(int p) const {
        assert(0 <= p && p < _n);
        return get_value(_root, 0, _n, p);
    }

    int parent_or_size(int p) const {
        return get(p).parent_or_size;
    }

    std::pair<PersistentPotentializedDsu, bool> merge(int a, int b, const T& w) const {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        auto [x, pa] = leader_and_potential(a);
        auto [y, pb] = leader_and_potential(b);
        if (x == y) return {*this, Group::op(Group::inv(pa), pb) == w};

        int sx = -get(x).parent_or_size;
        int sy = -get(y).parent_or_size;
        T y_from_x = Group::op(Group::op(pa, w), Group::inv(pb));
        if (sx < sy) {
            std::swap(x, y);
            std::swap(sx, sy);
            y_from_x = Group::inv(y_from_x);
        }
        int root = set_node(_root, 0, _n, x, Value(-(sx + sy), Group::id()));
        root = set_node(root, 0, _n, y, Value(x, std::move(y_from_x)));
        return {make_version(root), true};
    }

    bool merge_inplace(int a, int b, const T& w) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        auto [x, pa] = leader_and_potential(a);
        auto [y, pb] = leader_and_potential(b);
        if (x == y) return Group::op(Group::inv(pa), pb) == w;

        int sx = -get(x).parent_or_size;
        int sy = -get(y).parent_or_size;
        T y_from_x = Group::op(Group::op(pa, w), Group::inv(pb));
        if (sx < sy) {
            std::swap(x, y);
            std::swap(sx, sy);
            y_from_x = Group::inv(y_from_x);
        }
        int root = set_node(_root, 0, _n, x, Value(-(sx + sy), Group::id()), true);
        _pool->replace(_root, root);
        root = set_node(_root, 0, _n, y, Value(x, std::move(y_from_x)), true);
        _pool->replace(_root, root);
        _pool->discard_unreferenced();
        return true;
    }

    std::vector<std::vector<int>> groups() const {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(std::remove_if(result.begin(), result.end(), [&](const std::vector<int>& v) { return v.empty(); }),
                     result.end());
        return result;
    }
};

}  // namespace ds
}  // namespace m1une


#line 1 "monoid/add.hpp"



namespace m1une {
namespace monoid {

// Monoid for addition (Range Sum).
template <typename T>
struct Add {
    using value_type = T;
    static constexpr bool commutative = true;

    // Returns the identity element for addition, which is 0.
    static constexpr T id() {
        return T(0);
    }

    // Returns the sum of a and b.
    static constexpr T op(const T& a, const T& b) {
        return a + b;
    }

    static constexpr T inv(const T& x) {
        return -x;
    }
};

}  // namespace monoid
}  // namespace m1une


#line 1 "monoid/xor.hpp"



namespace m1une {
namespace monoid {

// Monoid for bitwise XOR (Range XOR).
template <typename T>
struct Xor {
    using value_type = T;
    static constexpr bool commutative = true;

    // Returns the identity element for bitwise XOR, which is 0.
    static constexpr T id() {
        return T(0);
    }

    // Returns the bitwise XOR of a and b.
    static constexpr T op(const T& a, const T& b) {
        return a ^ b;
    }

    static constexpr T inv(const T& x) {
        return x;
    }
};

}  // namespace monoid
}  // namespace m1une


#line 6 "verify/ds/dsu/persistent_potentialized_dsu.test.cpp"

#line 8 "verify/ds/dsu/persistent_potentialized_dsu.test.cpp"
#include <array>
#line 1 "utilities/fast_io.hpp"



#line 6 "utilities/fast_io.hpp"
#include <cerrno>
#include <charconv>
#line 9 "utilities/fast_io.hpp"
#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"

namespace m1une {
namespace utilities {

struct FastOutput;

namespace internal {

// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;

// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};

template <class T>
struct is_range<T, std::void_t<
    decltype(std::begin(std::declval<T&>())),
    decltype(std::end(std::declval<T&>()))
>> : std::true_type {};

template <class T>
inline constexpr bool is_range_v = is_range<T>::value;

template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));

template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;

template <class T, class = void>
struct range_stored_value {
    using type = range_value_t<T>;
};

template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
    using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};

template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;

// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};

template <class T, std::size_t N>
struct is_char_array<T[N]>
    : std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};

template <class T>
struct is_string_like
    : std::bool_constant<
          std::is_same_v<std::decay_t<T>, std::string>
          || std::is_same_v<std::decay_t<T>, const char*>
          || std::is_same_v<std::decay_t<T>, char*>
          || is_char_array<std::remove_reference_t<T>>::value
      > {};

template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;

// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};

template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
    : std::true_type {};

template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;

template <class T, class = void>
struct has_static_mod_raw : std::false_type {};

template <class T>
struct has_static_mod_raw<
    T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
    : std::true_type {};

template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;

// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
    std::is_integral_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>
    || std::is_same_v<std::remove_cv_t<T>, __uint128_t>;

template <class T>
inline constexpr bool is_signed_v =
    std::is_signed_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>;

template <class T>
struct make_unsigned {
    using type = std::make_unsigned_t<T>;
};

template <>
struct make_unsigned<__int128_t> {
    using type = __uint128_t;
};

template <>
struct make_unsigned<__uint128_t> {
    using type = __uint128_t;
};

template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;

}  // namespace internal

struct FastInput {
    static constexpr int buffer_size = 1 << 20;

   private:
    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _length;
    int _file_descriptor;
    bool _streaming;

    bool refill() {
        _position = 0;
        if (_streaming) {
            ssize_t length;
            do {
                length = ::read(_file_descriptor, _buffer, buffer_size);
            } while (length < 0 && errno == EINTR);
            if (length <= 0) {
                _length = 0;
                return false;
            }
            _length = int(length);
        } else {
            _length = int(std::fread(_buffer, 1, buffer_size, _stream));
        }
        return _length != 0;
    }

    template <class T>
    bool read_integer_from_stream(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = read_char_raw();
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = negative ? result * 10 - (c - '0')
                                  : result * 10 + (c - '0');
                c = read_char_raw();
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = result * 10 + T(c - '0');
                c = read_char_raw();
            }
            value = negative ? T(0) - result : result;
        }
        return true;
    }

    bool prepare_number() {
        if (_length - _position >= 64) return true;
        const int remaining = _length - _position;
        if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
        const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
        _position = 0;
        _length = remaining + added;
        if (_length < buffer_size) _buffer[_length] = '\0';
        return _length != 0;
    }

   public:
    explicit FastInput(std::FILE* stream = stdin)
        : _stream(stream),
          _position(0),
          _length(0),
          _file_descriptor(::fileno(stream)),
          _streaming([&] {
              struct stat status;
              return _file_descriptor >= 0
                     && ::fstat(_file_descriptor, &status) == 0
                     && !S_ISREG(status.st_mode);
          }()) {}

    FastInput(const FastInput&) = delete;
    FastInput& operator=(const FastInput&) = delete;

    int read_char_raw() {
        if (_position == _length && !refill()) return EOF;
        return _buffer[_position++];
    }

    bool skip_spaces() {
        int c = read_char_raw();
        while (c != EOF && c <= ' ') c = read_char_raw();
        if (c == EOF) return false;
        --_position;
        return true;
    }

    bool read(char& value) {
        if (!skip_spaces()) return false;
        value = char(read_char_raw());
        return true;
    }

    bool read(std::string& value) {
        if (!skip_spaces()) return false;
        value.clear();
        while (true) {
            const int begin = _position;
            while (_position < _length &&
                   static_cast<unsigned char>(_buffer[_position]) > ' ') {
                ++_position;
            }
            value.append(_buffer + begin, _position - begin);
            if (_position < _length) {
                ++_position;
                return true;
            }
            if (!refill()) return true;
        }
    }

    bool read(bool& value) {
        int x;
        if (!read(x)) return false;
        value = x != 0;
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>,
        bool
    >
    read(T& value) {
        if (_streaming) return read_integer_from_stream(value);
        if (!prepare_number()) return false;
        int c = static_cast<unsigned char>(_buffer[_position++]);
        while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = static_cast<unsigned char>(_buffer[_position++]);
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const int first = c - '0';
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = negative ? result * 100 - (first * 10 + second)
                                      : result * 100 + (first * 10 + second);
                    ++_position;
                } else {
                    result = negative ? result * 10 - first : result * 10 + first;
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const unsigned first = unsigned(c - '0');
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = result * 100 + T(first * 10 + unsigned(second));
                    ++_position;
                } else {
                    result = result * 10 + T(first);
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = negative ? T(0) - result : result;
        }
        if (_position > _length) _position = _length;
        return true;
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>, bool>
    read(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();
        bool negative = false;
        if (c == '-' || c == '+') {
            negative = c == '-';
            c = read_char_raw();
        }

        long double result = 0;
        while ('0' <= c && c <= '9') {
            result = result * 10 + (c - '0');
            c = read_char_raw();
        }
        if (c == '.') {
            long double place = 0.1L;
            c = read_char_raw();
            while ('0' <= c && c <= '9') {
                result += (c - '0') * place;
                place *= 0.1L;
                c = read_char_raw();
            }
        }
        if (c == 'e' || c == 'E') {
            c = read_char_raw();
            bool exponent_negative = false;
            if (c == '-' || c == '+') {
                exponent_negative = c == '-';
                c = read_char_raw();
            }
            int exponent = 0;
            while ('0' <= c && c <= '9') {
                exponent = exponent * 10 + (c - '0');
                c = read_char_raw();
            }
            long double scale = 1;
            long double power = 10;
            while (exponent > 0) {
                if (exponent & 1) scale *= power;
                power *= power;
                exponent >>= 1;
            }
            result = exponent_negative ? result / scale : result * scale;
        }
        value = static_cast<T>(negative ? -result : result);
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>,
        bool
    >
    read(T& value) {
        long long x;
        if (!read(x)) return false;
        if constexpr (internal::has_static_mod_raw_v<T>) {
            if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
                value = T::raw(uint32_t(x));
            } else {
                value = T(x);
            }
        } else {
            value = T(x);
        }
        return true;
    }

    template <class First, class Second>
    bool read(std::pair<First, Second>& value) {
        if (!read(value.first)) return false;
        return read(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>,
        bool
    >
    read(Range& range) {
        using StoredValue = internal::range_stored_value_t<Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        for (auto&& value : range) {
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                bool x;
                if (!read(x)) return false;
                value = x;
            } else {
                if (!read(value)) return false;
            }
        }
        return true;
    }

    template <class First, class Second, class... Rest>
    bool read(First& first, Second& second, Rest&... rest) {
        if (!read(first)) return false;
        return read(second, rest...);
    }

    template <class T>
    FastInput& operator>>(T& value) {
        if (!read(value)) std::abort();
        return *this;
    }
};

struct FastOutput {
    static constexpr int buffer_size = 1 << 20;

   private:
    inline static const auto digit_quads = [] {
        std::array<char, 40000> result{};
        for (int i = 0; i < 10000; i++) {
            int value = i;
            for (int j = 3; j >= 0; j--) {
                result[4 * i + j] = char('0' + value % 10);
                value /= 10;
            }
        }
        return result;
    }();

    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _precision;
    std::chars_format _float_format;
    char _range_separator;
    std::string* _capture = nullptr;

    template <class T>
    std::string format_cell(const T& value) {
        std::string result;
        struct CaptureGuard {
            std::string*& target;
            std::string* previous;
            ~CaptureGuard() { target = previous; }
        } guard{_capture, _capture};
        _capture = &result;
        write(value);
        return result;
    }

    template <class Matrix>
    void write_aligned_matrix(const Matrix& matrix) {
        std::vector<std::vector<std::string>> rows;
        std::vector<std::size_t> widths;
        for (const auto& row : matrix) {
            auto& cells = rows.emplace_back();
            std::size_t column = 0;
            for (const auto& value : row) {
                cells.push_back(format_cell(value));
                if (column == widths.size()) widths.push_back(0);
                widths[column] = std::max(widths[column], cells.back().size());
                ++column;
            }
        }
        bool first = true;
        for (const auto& row : rows) {
            if (!first) write_char('\n');
            first = false;
            for (std::size_t column = 0; column < row.size(); ++column) {
                if (column != 0) write_char(_range_separator);
                for (std::size_t padding = row[column].size();
                     padding < widths[column]; ++padding) {
                    write_char(' ');
                }
                write(row[column]);
            }
        }
    }

   public:
    explicit FastOutput(std::FILE* stream = stdout)
        : _stream(stream),
          _position(0),
          _precision(6),
          _float_format(std::chars_format::general),
          _range_separator(' ') {
        if (_stream == stdout
            && internal::standard_output_instance == nullptr) {
            internal::standard_output_instance = this;
        }
    }

    FastOutput(const FastOutput&) = delete;
    FastOutput& operator=(const FastOutput&) = delete;

    ~FastOutput() {
        flush();
        if (internal::standard_output_instance == this) {
            internal::standard_output_instance = nullptr;
        }
    }

    void flush() {
        if (_position != 0) {
            std::fwrite(_buffer, 1, _position, _stream);
            _position = 0;
        }
        std::fflush(_stream);
    }

    void write_char(char c) {
        if (_capture != nullptr) {
            _capture->push_back(c);
            return;
        }
        if (_position == buffer_size) flush();
        _buffer[_position++] = c;
    }

    void write(const char* s) {
        while (*s != '\0') write_char(*s++);
    }

    void write(const std::string& s) {
        if (_capture != nullptr) {
            _capture->append(s);
            return;
        }
        std::size_t position = 0;
        while (position < s.size()) {
            if (_position == buffer_size) flush();
            const std::size_t copied =
                std::min<std::size_t>(buffer_size - _position, s.size() - position);
            std::memcpy(_buffer + _position, s.data() + position, copied);
            _position += int(copied);
            position += copied;
        }
    }

    void write(char c) {
        write_char(c);
    }

    void write(bool value) {
        write_char(value ? '1' : '0');
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>>
    write(T value) {
        char digits[128];
        auto [end, error] = std::to_chars(
            digits,
            digits + sizeof(digits),
            value,
            _float_format,
            _precision
        );
        if (error != std::errc()) std::abort();
        for (const char* pointer = digits; pointer != end; pointer++) {
            write_char(*pointer);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>
    >
    write(T value) {
        using Raw = std::remove_cv_t<T>;
        using Unsigned = internal::make_unsigned_t<Raw>;

        Unsigned magnitude;
        if constexpr (internal::is_signed_v<Raw>) {
            if (value < 0) {
                write_char('-');
                magnitude = Unsigned(0) - Unsigned(value);
            } else {
                magnitude = Unsigned(value);
            }
        } else {
            magnitude = value;
        }

        if (magnitude == 0) {
            write_char('0');
            return;
        }

        unsigned chunks[16];
        int count = 0;
        while (magnitude >= 10000) {
            const Unsigned quotient = magnitude / 10000;
            chunks[count++] = unsigned(magnitude - quotient * 10000);
            magnitude = quotient;
        }
        if (_capture == nullptr && _position > buffer_size - 64) flush();
        char captured[64];
        char* const begin = _capture != nullptr ? captured : _buffer + _position;
        char* destination = begin;
        const unsigned leading = unsigned(magnitude);
        const char* first = digit_quads.data() + 4 * leading;
        int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
        for (; skip < 4; skip++) *destination++ = first[skip];
        while (count--) {
            const char* digits = digit_quads.data() + 4 * chunks[count];
            std::memcpy(destination, digits, 4);
            destination += 4;
        }
        if (_capture != nullptr) {
            _capture->append(begin, destination - begin);
        } else {
            _position += int(destination - begin);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>
    >
    write(const T& value) {
        write(value.val());
    }

    template <class First, class Second>
    void write(const std::pair<First, Second>& value) {
        write(value.first);
        write_char(' ');
        write(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>
    >
    write(const Range& range) {
        using StoredValue = internal::range_stored_value_t<const Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        bool first = true;
        for (const auto& value : range) {
            if (!first) write_char(nested ? '\n' : _range_separator);
            first = false;
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                write(static_cast<bool>(value));
            } else {
                write(value);
            }
        }
    }

    template <class First, class... Rest>
    void print(const First& first, const Rest&... rest) {
        write(first);
        ((write_char(' '), write(rest)), ...);
    }

    void println() {
        write_char('\n');
    }

    void set_precision(int precision) {
        _precision = precision;
    }

    void set_fixed(int precision = 6) {
        _float_format = std::chars_format::fixed;
        _precision = precision;
    }

    void set_general(int precision = 6) {
        _float_format = std::chars_format::general;
        _precision = precision;
    }

    void set_range_separator(char separator) {
        _range_separator = separator;
    }

    template <class Matrix>
    void write_aligned(const Matrix& matrix) {
        using Row = internal::range_stored_value_t<const Matrix>;
        using Cell = internal::range_stored_value_t<const Row>;
        static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
                      "write_aligned requires a two-dimensional range");
        static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
                      "write_aligned requires scalar cells");
        write_aligned_matrix(matrix);
    }

    template <class Matrix>
    void println_aligned(const Matrix& matrix) {
        write_aligned(matrix);
        write_char('\n');
    }

    template <class... Args>
    void println(const Args&... args) {
        print(args...);
        write_char('\n');
    }

    template <class T>
    FastOutput& operator<<(const T& value) {
        write(value);
        return *this;
    }
};

}  // namespace utilities
}  // namespace m1une


#line 11 "verify/ds/dsu/persistent_potentialized_dsu.test.cpp"
#include <random>
#line 14 "verify/ds/dsu/persistent_potentialized_dsu.test.cpp"

struct Permutation3Group {
    using value_type = std::array<int, 3>;

    static value_type id() {
        return {0, 1, 2};
    }

    static value_type op(const value_type& first, const value_type& second) {
        value_type result;
        for (int i = 0; i < 3; i++) result[i] = second[first[i]];
        return result;
    }

    static value_type inv(const value_type& value) {
        value_type result;
        for (int i = 0; i < 3; i++) result[value[i]] = i;
        return result;
    }
};

static_assert(m1une::monoid::IsGroup<Permutation3Group>);

template <class Group>
struct NaivePotentializedDsu {
    using T = typename Group::value_type;

    std::vector<int> parent_or_size;
    std::vector<T> diff_to_parent;

    explicit NaivePotentializedDsu(int n = 0) : parent_or_size(n, -1), diff_to_parent(n, Group::id()) {}

    std::pair<int, T> leader_and_potential(int a) const {
        T res = Group::id();
        while (parent_or_size[a] >= 0) {
            res = Group::op(diff_to_parent[a], res);
            a = parent_or_size[a];
        }
        return {a, res};
    }

    int leader(int a) const {
        return leader_and_potential(a).first;
    }

    bool same(int a, int b) const {
        return leader(a) == leader(b);
    }

    int group_size(int a) const {
        return -parent_or_size[leader(a)];
    }

    T potential(int a) const {
        return leader_and_potential(a).second;
    }

    T diff(int a, int b) const {
        assert(same(a, b));
        return Group::op(Group::inv(potential(a)), potential(b));
    }

    std::pair<NaivePotentializedDsu, bool> merge(int a, int b, const T& w) const {
        NaivePotentializedDsu res = *this;
        auto [x, pa] = res.leader_and_potential(a);
        auto [y, pb] = res.leader_and_potential(b);
        if (x == y) return {res, Group::op(Group::inv(pa), pb) == w};

        int sx = -res.parent_or_size[x];
        int sy = -res.parent_or_size[y];
        T y_from_x = Group::op(Group::op(pa, w), Group::inv(pb));
        if (sx < sy) {
            std::swap(x, y);
            std::swap(sx, sy);
            y_from_x = Group::inv(y_from_x);
        }
        res.parent_or_size[x] += res.parent_or_size[y];
        res.parent_or_size[y] = x;
        res.diff_to_parent[y] = y_from_x;
        return {res, true};
    }

    std::vector<std::vector<int>> groups() const {
        int n = int(parent_or_size.size());
        std::vector<int> leader_buf(n), group_size(n);
        for (int i = 0; i < n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(n);
        for (int i = 0; i < n; i++) result[i].reserve(group_size[i]);
        for (int i = 0; i < n; i++) result[leader_buf[i]].push_back(i);
        result.erase(std::remove_if(result.begin(), result.end(), [](const std::vector<int>& v) { return v.empty(); }),
                     result.end());
        return result;
    }
};

void self_test() {
    using Add = m1une::monoid::Add<long long>;
    using AddDsu = m1une::ds::PersistentPotentializedDsu<Add>;

    AddDsu base(5);
    auto [a, ok1] = base.merge(0, 1, 3);
    auto [b, ok2] = a.merge(1, 2, 4);
    auto [c, ok3] = b.merge(3, 4, -2);
    auto [d, ok4] = b.merge(2, 3, 5);
    auto [bad, ok_bad] = b.merge(0, 2, 8);

    assert(ok1);
    assert(ok2);
    assert(ok3);
    assert(ok4);
    assert(!ok_bad);
    assert(base.size() == 5);
    assert(!base.empty());
    assert(!base.same(0, 2));
    assert(a.same(0, 1));
    assert(!a.same(0, 2));
    assert(b.diff(0, 2) == 7);
    assert(b.diff(2, 0) == -7);
    assert(c.diff(3, 4) == -2);
    assert(!c.same(0, 4));
    assert(d.diff(0, 3) == 12);
    assert(bad.diff(0, 2) == 7);
    assert(d.group_size(0) == 4);
    assert(d.size(0) == 4);
    assert(base.group_size(0) == 1);
    assert(base.parent_or_size(0) == -1);

    std::vector<std::vector<int>> base_groups;
    base_groups.emplace_back(std::vector<int>{0});
    base_groups.emplace_back(std::vector<int>{1});
    base_groups.emplace_back(std::vector<int>{2});
    base_groups.emplace_back(std::vector<int>{3});
    base_groups.emplace_back(std::vector<int>{4});
    assert(base.groups() == base_groups);

    using Xor = m1une::monoid::Xor<int>;
    m1une::ds::PersistentPotentializedDsu<Xor> xor_base(4);
    auto [xor_a, xor_ok1] = xor_base.merge(0, 1, 5);
    auto [xor_b, xor_ok2] = xor_a.merge(1, 2, 6);
    auto [xor_bad, xor_ok_bad] = xor_b.merge(0, 2, 2);
    assert(xor_ok1);
    assert(xor_ok2);
    assert(!xor_ok_bad);
    assert(xor_b.diff(0, 2) == (5 ^ 6));
    assert(xor_bad.diff(0, 2) == (5 ^ 6));

    using Permutation = Permutation3Group::value_type;
    using PermutationDsu =
        m1une::ds::PersistentPotentializedDsu<Permutation3Group>;
    Permutation rotate = {1, 2, 0};
    Permutation swap_last = {0, 2, 1};
    Permutation swap_first = {1, 0, 2};
    assert(Permutation3Group::op(rotate, swap_last) !=
           Permutation3Group::op(swap_last, rotate));

    PermutationDsu permutation_base(4);
    auto [permutation_a, permutation_ok1] =
        permutation_base.merge(0, 1, rotate);
    auto [permutation_b, permutation_ok2] =
        permutation_a.merge(1, 2, swap_last);
    auto [permutation_c, permutation_ok3] =
        permutation_b.merge(3, 2, swap_first);
    Permutation composed = Permutation3Group::op(rotate, swap_last);
    auto [permutation_bad, permutation_bad_ok] =
        permutation_c.merge(0, 2, Permutation3Group::op(swap_last, rotate));
    assert(permutation_ok1);
    assert(permutation_ok2);
    assert(permutation_ok3);
    assert(!permutation_bad_ok);
    assert(!permutation_base.same(0, 1));
    assert(permutation_b.diff(0, 2) == composed);
    assert(permutation_b.diff(2, 0) == Permutation3Group::inv(composed));
    assert(permutation_c.diff(3, 2) == swap_first);
    assert(permutation_c.diff(3, 0) == Permutation3Group::op(
        swap_first, Permutation3Group::inv(composed)
    ));
    assert(permutation_bad.diff(0, 2) == composed);

    AddDsu empty;
    assert(empty.size() == 0);
    assert(empty.empty());

    std::mt19937 rng(0);
    constexpr int N = 25;
    std::vector<std::pair<AddDsu, NaivePotentializedDsu<Add>>> versions;
    versions.emplace_back(AddDsu(N), NaivePotentializedDsu<Add>(N));

    for (int step = 0; step < 400; step++) {
        int id = int(rng() % versions.size());
        AddDsu cur = versions[id].first;
        NaivePotentializedDsu<Add> expected = versions[id].second;

        for (int i = 0; i < N; i++) {
            assert(cur.group_size(i) == expected.group_size(i));
            assert(cur.parent_or_size(i) == expected.parent_or_size[i]);
            for (int j = 0; j < N; j++) {
                assert(cur.same(i, j) == expected.same(i, j));
                if (cur.same(i, j)) assert(cur.diff(i, j) == expected.diff(i, j));
            }
        }
        assert(cur.groups() == expected.groups());

        int u = int(rng() % N);
        int v = int(rng() % N);
        long long w = int(rng() % 21) - 10;
        if (expected.same(u, v) && (rng() & 1)) w = expected.diff(u, v);

        auto [next, ok] = cur.merge(u, v, w);
        auto [next_expected, expected_ok] = expected.merge(u, v, w);
        assert(ok == expected_ok);

        for (int i = 0; i < N; i++) {
            assert(cur.group_size(i) == expected.group_size(i));
            assert(next.group_size(i) == next_expected.group_size(i));
            assert(next.parent_or_size(i) == next_expected.parent_or_size[i]);
        }

        versions.emplace_back(next, next_expected);
    }
}

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    self_test();

    using Add = m1une::monoid::Add<long long>;
    using Dsu = m1une::ds::PersistentPotentializedDsu<Add>;
    int n, q;
    fast_input >> n >> q;
    Dsu dsu(n);

    while (q--) {
        int type, x, y;
        fast_input >> type >> x >> y;
        if (type == 0) {
            long long z;
            fast_input >> z;
            auto [next, ok] = dsu.merge(x, y, z);
            (void)ok;
            dsu = next;
        } else {
            if (dsu.same(x, y)) {
                fast_output << dsu.diff(x, y) << '\n';
            } else {
                fast_output << "?\n";
            }
        }
    }
}

m1une's library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/ds/dsu/persistent_potentialized_dsu.test.cpp

Depends on

Code