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:heavy_check_mark: Rollback Dynamic Segment Tree
(ds/segtree/rollback_dynamic_segtree.hpp)

Overview

RollbackDynamicSegtree<Monoid, Index> is a sparse segment tree over an integral half-open domain with point assignment and rollback. Unvisited ranges retain the configured initial value.

Methods

Constructors and read-only methods follow DynamicSegtree<Monoid, Index>.

Method Description Complexity
void set(Index pos, T value), void set_inplace(Index pos, T value) Assigns one point. $O(\log U)$
int snapshot() Registers the current state and returns its token. $O(1)$
int snapshot_count() const Returns the number of active snapshots. $O(1)$
void reserve_snapshots(int count) Reserves snapshot tokens. $O(H)$
void rollback(int state) Restores a current-path snapshot. $O(F)$ total
void clear_history(), void release() Releases saved states, or all materialized nodes. $O(F)$

$U$ is the domain width and $F = O(\log U)$ per assignment.

Snapshot semantics

Updates made before the first snapshot() retain no rollback data. A snapshot token is positive and valid only on the current path. rollback(state) restores that registered state, keeps it active, and invalidates newer snapshots. clear_history() commits the current state and invalidates every token. No per-update reversal operation is provided.

Within one snapshot interval, a materialized node is saved only before its first mutation; newly allocated nodes are truncated directly by rollback.

Example

#include "ds/segtree/rollback_dynamic_segtree.hpp"
#include "monoid/add.hpp"

using Add = m1une::monoid::Add<long long>;
m1une::ds::RollbackDynamicSegtree<Add> seg(-100, 100);
int state = seg.snapshot();
seg.set(-4, 7);
seg.rollback(state);
assert(seg.all_prod() == 0);

Depends on

Verified with

Code

#ifndef M1UNE_DS_SEGTREE_ROLLBACK_DYNAMIC_SEGTREE_HPP
#define M1UNE_DS_SEGTREE_ROLLBACK_DYNAMIC_SEGTREE_HPP 1

#include <array>
#include <cassert>
#include <concepts>
#include <limits>
#include <numeric>
#include <type_traits>
#include <utility>

#include "../../monoid/concept.hpp"
#include "../detail/rollback_journal.hpp"
#include "dynamic_segtree_common.hpp"

namespace m1une {
namespace ds {

template <m1une::monoid::IsMonoid Monoid, std::integral Index = long long>
    requires(!std::same_as<std::remove_cv_t<Index>, bool>)
struct RollbackDynamicSegtree {
    using T = typename Monoid::value_type;
    using index_type = Index;
    using size_type = detail::dynamic_size_type<Index>;

   private:
    struct Node {
        T value = Monoid::id();
        int left = 0;
        int right = 0;
    };

    static constexpr int path_capacity = std::numeric_limits<size_type>::digits + 1;
    detail::UniformMonoidDomain<Monoid, Index> _domain;
    detail::RollbackJournal<Node> _journal;

    int root() const { return _journal[0].left; }

    int new_node() { return _journal.emplace(); }

    const T& value(int node, Index left, Index right, int depth) const {
        if (node) return _journal[node].value;
        return _domain.default_product(depth, left, right);
    }

    void update(int node, Index left, Index right, int depth) {
        Index middle = std::midpoint(left, right);
        _journal.touch(node);
        _journal[node].value = Monoid::op(
            value(_journal[node].left, left, middle, depth + 1),
            value(_journal[node].right, middle, right, depth + 1)
        );
    }

    T prod_node(int node, Index left, Index right, int depth, Index query_left, Index query_right) const {
        if (query_right <= left || right <= query_left) return Monoid::id();
        if (query_left <= left && right <= query_right) return value(node, left, right, depth);
        Index middle = std::midpoint(left, right);
        return Monoid::op(
            prod_node(node ? _journal[node].left : 0, left, middle, depth + 1, query_left, query_right),
            prod_node(node ? _journal[node].right : 0, middle, right, depth + 1, query_left, query_right)
        );
    }

    template <class Predicate>
    Index max_right_node(int node, Index left, Index right, int depth, Index query_left, T& product,
                         Predicate& predicate) const {
        if (right <= query_left) return right;
        if (query_left <= left) {
            T next = Monoid::op(product, value(node, left, right, depth));
            if (predicate(next)) {
                product = std::move(next);
                return right;
            }
            Index middle = std::midpoint(left, right);
            if (middle == left) return left;
        }
        Index middle = std::midpoint(left, right);
        Index result = max_right_node(node ? _journal[node].left : 0, left, middle, depth + 1,
                                      query_left, product, predicate);
        if (result < middle) return result;
        return max_right_node(node ? _journal[node].right : 0, middle, right, depth + 1,
                              query_left, product, predicate);
    }

    template <class Predicate>
    Index min_left_node(int node, Index left, Index right, int depth, Index query_right, T& product,
                        Predicate& predicate) const {
        if (query_right <= left) return left;
        if (right <= query_right) {
            T next = Monoid::op(value(node, left, right, depth), product);
            if (predicate(next)) {
                product = std::move(next);
                return left;
            }
            Index middle = std::midpoint(left, right);
            if (middle == left) return right;
        }
        Index middle = std::midpoint(left, right);
        Index result = min_left_node(node ? _journal[node].right : 0, middle, right, depth + 1,
                                     query_right, product, predicate);
        if (middle < result) return result;
        return min_left_node(node ? _journal[node].left : 0, left, middle, depth + 1,
                             query_right, product, predicate);
    }

   public:
    RollbackDynamicSegtree() : RollbackDynamicSegtree(Index(0), Index(0)) {}
    explicit RollbackDynamicSegtree(Index n) : RollbackDynamicSegtree(Index(0), n) {
        if constexpr (std::signed_integral<Index>) assert(Index(0) <= n);
    }
    RollbackDynamicSegtree(Index left, Index right)
        : RollbackDynamicSegtree(left, right, Monoid::id()) {}
    RollbackDynamicSegtree(Index left, Index right, T initial_value)
        : _domain(left, right, std::move(initial_value)) {
        _journal.emplace();
    }

    size_type size() const { return _domain.size(); }
    bool empty() const { return _domain.empty(); }
    Index left_bound() const { return _domain.left_bound(); }
    Index right_bound() const { return _domain.right_bound(); }
    const T& initial_value() const { return _domain.initial_value(); }

    void reserve(std::size_t node_capacity) {
        _journal.nodes.reserve(node_capacity + 1);
        _journal.saved_epoch.reserve(node_capacity + 1);
    }

    std::size_t node_count() const { return _journal.nodes.size() - 1; }

    void set(Index pos, T x) {
        assert(left_bound() <= pos && pos < right_bound());
        if (!root()) {
            int node = new_node();
            _journal.touch(0);
            _journal[0].left = node;
        }

        std::array<int, path_capacity> path;
        std::array<Index, path_capacity> path_left;
        std::array<Index, path_capacity> path_right;
        int depth = 0;
        int node = root();
        Index left = left_bound();
        Index right = right_bound();

        while (true) {
            path[depth] = node;
            path_left[depth] = left;
            path_right[depth] = right;
            ++depth;
            Index middle = std::midpoint(left, right);
            if (middle == left) break;
            if (pos < middle) {
                if (!_journal[node].left) {
                    int child = new_node();
                    _journal.touch(node);
                    _journal[node].left = child;
                }
                node = _journal[node].left;
                right = middle;
            } else {
                if (!_journal[node].right) {
                    int child = new_node();
                    _journal.touch(node);
                    _journal[node].right = child;
                }
                node = _journal[node].right;
                left = middle;
            }
        }
        _journal.touch(node);
        _journal[node].value = std::move(x);
        for (int index = depth - 2; index >= 0; --index) {
            update(path[index], path_left[index], path_right[index], index);
        }
    }

    void set_inplace(Index pos, T x) { set(pos, std::move(x)); }

    T get(Index pos) const {
        assert(left_bound() <= pos && pos < right_bound());
        int node = root();
        Index left = left_bound();
        Index right = right_bound();
        int depth = 0;
        while (node) {
            Index middle = std::midpoint(left, right);
            if (middle == left) return value(node, left, right, depth);
            if (pos < middle) {
                node = _journal[node].left;
                right = middle;
            } else {
                node = _journal[node].right;
                left = middle;
            }
            ++depth;
        }
        return initial_value();
    }

    T operator[](Index pos) const { return get(pos); }
    T prod(Index left, Index right) const {
        assert(left_bound() <= left && left <= right && right <= right_bound());
        if (left == right) return Monoid::id();
        return prod_node(root(), left_bound(), right_bound(), 0, left, right);
    }
    T all_prod() const { return value(root(), left_bound(), right_bound(), 0); }

    template <class Predicate>
    Index max_right(Index left, Predicate predicate) const {
        assert(left_bound() <= left && left <= right_bound());
        assert(predicate(Monoid::id()));
        if (left == right_bound()) return right_bound();
        T product = Monoid::id();
        return max_right_node(root(), left_bound(), right_bound(), 0, left, product, predicate);
    }

    template <class Predicate>
    Index min_left(Index right, Predicate predicate) const {
        assert(left_bound() <= right && right <= right_bound());
        assert(predicate(Monoid::id()));
        if (right == left_bound()) return left_bound();
        T product = Monoid::id();
        return min_left_node(root(), left_bound(), right_bound(), 0, right, product, predicate);
    }

    int snapshot() { return _journal.snapshot(); }
    int snapshot_count() const { return _journal.snapshot_count(); }
    void reserve_snapshots(int count) { _journal.reserve_snapshots(count); }
    void rollback(int state) { _journal.rollback(state); }
    void clear_history() { _journal.clear_history(); }
    void release() { _journal.clear(); _journal.emplace(); }
};

}  // namespace ds
}  // namespace m1une

#endif  // M1UNE_DS_SEGTREE_ROLLBACK_DYNAMIC_SEGTREE_HPP
#line 1 "ds/segtree/rollback_dynamic_segtree.hpp"



#include <array>
#include <cassert>
#include <concepts>
#include <limits>
#include <numeric>
#include <type_traits>
#include <utility>

#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/rollback_journal.hpp"



#include <algorithm>
#line 6 "ds/detail/rollback_journal.hpp"
#include <cstddef>
#include <cstdint>
#line 10 "ds/detail/rollback_journal.hpp"
#include <vector>

namespace m1une {
namespace ds {
namespace detail {

template <class Node>
struct RollbackJournal {
    struct Change {
        int index;
        Node value;
    };

    struct Checkpoint {
        std::size_t change_size;
        std::size_t node_size;
        std::uint64_t epoch;
    };

    std::vector<Node> nodes;
    std::vector<Change> changes;
    std::vector<Checkpoint> checkpoints;
    std::vector<std::uint64_t> saved_epoch;
    std::uint64_t next_epoch = 1;

    std::uint64_t new_epoch() {
        if (next_epoch == 0) {
            std::fill(saved_epoch.begin(), saved_epoch.end(), 0);
            next_epoch = 1;
        }
        return next_epoch++;
    }

    int size() const { return int(nodes.size()); }

    Node& operator[](int index) { return nodes[index]; }
    const Node& operator[](int index) const { return nodes[index]; }

    template <class... Args>
    int emplace(Args&&... args) {
        assert(nodes.size() < std::size_t(std::numeric_limits<int>::max()));
        int index = int(nodes.size());
        nodes.emplace_back(std::forward<Args>(args)...);
        saved_epoch.push_back(0);
        return index;
    }

    int snapshot() {
        assert(checkpoints.size() < std::size_t(std::numeric_limits<int>::max()));
        checkpoints.push_back(Checkpoint{changes.size(), nodes.size(), new_epoch()});
        return int(checkpoints.size());
    }

    void touch(int index) {
        assert(0 <= index && index < size());
        if (checkpoints.empty()) return;
        const Checkpoint& checkpoint = checkpoints.back();
        if (std::size_t(index) >= checkpoint.node_size) return;
        if (saved_epoch[index] == checkpoint.epoch) return;
        saved_epoch[index] = checkpoint.epoch;
        changes.push_back(Change{index, nodes[index]});
    }

    int snapshot_count() const { return int(checkpoints.size()); }

    void reserve_snapshots(int count) {
        assert(0 <= count);
        checkpoints.reserve(count);
    }

    void reserve_changes(std::size_t count) { changes.reserve(count); }

    void rollback(int state) {
        assert(1 <= state && state <= snapshot_count());
        Checkpoint checkpoint = checkpoints[state - 1];
        while (changes.size() > checkpoint.change_size) {
            Change change = std::move(changes.back());
            changes.pop_back();
            nodes[change.index] = std::move(change.value);
        }
        nodes.erase(nodes.begin() + checkpoint.node_size, nodes.end());
        saved_epoch.resize(checkpoint.node_size);
        checkpoints.resize(state);
        checkpoints.back().change_size = changes.size();
        checkpoints.back().node_size = nodes.size();
        checkpoints.back().epoch = new_epoch();
    }

    void clear_history() {
        changes.clear();
        checkpoints.clear();
        std::fill(saved_epoch.begin(), saved_epoch.end(), 0);
    }

    void clear() {
        nodes.clear();
        changes.clear();
        checkpoints.clear();
        saved_epoch.clear();
        next_epoch = 1;
    }
};

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


#line 1 "ds/segtree/dynamic_segtree_common.hpp"



#line 11 "ds/segtree/dynamic_segtree_common.hpp"

namespace m1une {
namespace ds {
namespace detail {

template <std::integral Index>
using dynamic_size_type = std::make_unsigned_t<Index>;

template <std::integral Index>
constexpr dynamic_size_type<Index> dynamic_distance(Index left, Index right) {
    return static_cast<dynamic_size_type<Index>>(right) - static_cast<dynamic_size_type<Index>>(left);
}

template <class Monoid, class Size>
typename Monoid::value_type monoid_repeat(typename Monoid::value_type value, Size count) {
    typename Monoid::value_type result = Monoid::id();
    while (count != 0) {
        if (count & 1) result = Monoid::op(result, value);
        count >>= 1;
        if (count != 0) value = Monoid::op(value, value);
    }
    return result;
}

template <class ActedMonoid>
typename ActedMonoid::value_type dynamic_mapping(
    const typename ActedMonoid::operator_type& f,
    const typename ActedMonoid::value_type& value
) {
    using F = typename ActedMonoid::operator_type;
    using T = typename ActedMonoid::value_type;
    if constexpr (requires(F g, T x, long long ord) { ActedMonoid::mapping(g, x, ord); }) {
        return ActedMonoid::mapping(f, value, 0);
    } else {
        return ActedMonoid::mapping(f, value);
    }
}

template <class ActedMonoid, class Size>
typename ActedMonoid::operator_type dynamic_shift(
    const typename ActedMonoid::operator_type& f,
    Size offset
) {
    using F = typename ActedMonoid::operator_type;
    if constexpr (requires(F g, long long ord) { ActedMonoid::op_shift(g, ord); }) {
        assert(offset <= static_cast<Size>(std::numeric_limits<long long>::max()));
        return ActedMonoid::op_shift(f, static_cast<long long>(offset));
    } else {
        return f;
    }
}

template <class Monoid, std::integral Index>
class UniformMonoidDomain {
   public:
    using T = typename Monoid::value_type;
    using size_type = dynamic_size_type<Index>;

   private:
    struct Level {
        size_type small_length;
        T small_value;
        T large_value;
    };

    Index _left;
    Index _right;
    T _initial_value;
    std::vector<Level> _levels;

   public:
    UniformMonoidDomain(Index left, Index right, T initial_value)
        : _left(left), _right(right), _initial_value(std::move(initial_value)) {
        assert(left <= right);
        size_type n = size();
        constexpr int digits = std::numeric_limits<size_type>::digits;
        _levels.reserve(digits + 1);
        for (int depth = 0; depth <= digits; depth++) {
            size_type small = depth == digits ? 0 : n >> depth;
            size_type large = small;
            if (depth != 0) {
                bool has_remainder;
                if (depth == digits) {
                    has_remainder = n != 0;
                } else {
                    size_type mask = (size_type(1) << depth) - 1;
                    has_remainder = (n & mask) != 0;
                }
                if (has_remainder) large++;
            }
            _levels.push_back(Level{
                small,
                monoid_repeat<Monoid>(_initial_value, small),
                monoid_repeat<Monoid>(_initial_value, large),
            });
        }
    }

    Index left_bound() const {
        return _left;
    }

    Index right_bound() const {
        return _right;
    }

    size_type size() const {
        return dynamic_distance(_left, _right);
    }

    bool empty() const {
        return _left == _right;
    }

    const T& initial_value() const {
        return _initial_value;
    }

    const T& default_product(int depth, Index left, Index right) const {
        assert(0 <= depth && depth < int(_levels.size()));
        const Level& level = _levels[depth];
        size_type length = dynamic_distance(left, right);
        if (length == level.small_length) return level.small_value;
        assert(length == level.small_length + 1);
        return level.large_value;
    }
};

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


#line 15 "ds/segtree/rollback_dynamic_segtree.hpp"

namespace m1une {
namespace ds {

template <m1une::monoid::IsMonoid Monoid, std::integral Index = long long>
    requires(!std::same_as<std::remove_cv_t<Index>, bool>)
struct RollbackDynamicSegtree {
    using T = typename Monoid::value_type;
    using index_type = Index;
    using size_type = detail::dynamic_size_type<Index>;

   private:
    struct Node {
        T value = Monoid::id();
        int left = 0;
        int right = 0;
    };

    static constexpr int path_capacity = std::numeric_limits<size_type>::digits + 1;
    detail::UniformMonoidDomain<Monoid, Index> _domain;
    detail::RollbackJournal<Node> _journal;

    int root() const { return _journal[0].left; }

    int new_node() { return _journal.emplace(); }

    const T& value(int node, Index left, Index right, int depth) const {
        if (node) return _journal[node].value;
        return _domain.default_product(depth, left, right);
    }

    void update(int node, Index left, Index right, int depth) {
        Index middle = std::midpoint(left, right);
        _journal.touch(node);
        _journal[node].value = Monoid::op(
            value(_journal[node].left, left, middle, depth + 1),
            value(_journal[node].right, middle, right, depth + 1)
        );
    }

    T prod_node(int node, Index left, Index right, int depth, Index query_left, Index query_right) const {
        if (query_right <= left || right <= query_left) return Monoid::id();
        if (query_left <= left && right <= query_right) return value(node, left, right, depth);
        Index middle = std::midpoint(left, right);
        return Monoid::op(
            prod_node(node ? _journal[node].left : 0, left, middle, depth + 1, query_left, query_right),
            prod_node(node ? _journal[node].right : 0, middle, right, depth + 1, query_left, query_right)
        );
    }

    template <class Predicate>
    Index max_right_node(int node, Index left, Index right, int depth, Index query_left, T& product,
                         Predicate& predicate) const {
        if (right <= query_left) return right;
        if (query_left <= left) {
            T next = Monoid::op(product, value(node, left, right, depth));
            if (predicate(next)) {
                product = std::move(next);
                return right;
            }
            Index middle = std::midpoint(left, right);
            if (middle == left) return left;
        }
        Index middle = std::midpoint(left, right);
        Index result = max_right_node(node ? _journal[node].left : 0, left, middle, depth + 1,
                                      query_left, product, predicate);
        if (result < middle) return result;
        return max_right_node(node ? _journal[node].right : 0, middle, right, depth + 1,
                              query_left, product, predicate);
    }

    template <class Predicate>
    Index min_left_node(int node, Index left, Index right, int depth, Index query_right, T& product,
                        Predicate& predicate) const {
        if (query_right <= left) return left;
        if (right <= query_right) {
            T next = Monoid::op(value(node, left, right, depth), product);
            if (predicate(next)) {
                product = std::move(next);
                return left;
            }
            Index middle = std::midpoint(left, right);
            if (middle == left) return right;
        }
        Index middle = std::midpoint(left, right);
        Index result = min_left_node(node ? _journal[node].right : 0, middle, right, depth + 1,
                                     query_right, product, predicate);
        if (middle < result) return result;
        return min_left_node(node ? _journal[node].left : 0, left, middle, depth + 1,
                             query_right, product, predicate);
    }

   public:
    RollbackDynamicSegtree() : RollbackDynamicSegtree(Index(0), Index(0)) {}
    explicit RollbackDynamicSegtree(Index n) : RollbackDynamicSegtree(Index(0), n) {
        if constexpr (std::signed_integral<Index>) assert(Index(0) <= n);
    }
    RollbackDynamicSegtree(Index left, Index right)
        : RollbackDynamicSegtree(left, right, Monoid::id()) {}
    RollbackDynamicSegtree(Index left, Index right, T initial_value)
        : _domain(left, right, std::move(initial_value)) {
        _journal.emplace();
    }

    size_type size() const { return _domain.size(); }
    bool empty() const { return _domain.empty(); }
    Index left_bound() const { return _domain.left_bound(); }
    Index right_bound() const { return _domain.right_bound(); }
    const T& initial_value() const { return _domain.initial_value(); }

    void reserve(std::size_t node_capacity) {
        _journal.nodes.reserve(node_capacity + 1);
        _journal.saved_epoch.reserve(node_capacity + 1);
    }

    std::size_t node_count() const { return _journal.nodes.size() - 1; }

    void set(Index pos, T x) {
        assert(left_bound() <= pos && pos < right_bound());
        if (!root()) {
            int node = new_node();
            _journal.touch(0);
            _journal[0].left = node;
        }

        std::array<int, path_capacity> path;
        std::array<Index, path_capacity> path_left;
        std::array<Index, path_capacity> path_right;
        int depth = 0;
        int node = root();
        Index left = left_bound();
        Index right = right_bound();

        while (true) {
            path[depth] = node;
            path_left[depth] = left;
            path_right[depth] = right;
            ++depth;
            Index middle = std::midpoint(left, right);
            if (middle == left) break;
            if (pos < middle) {
                if (!_journal[node].left) {
                    int child = new_node();
                    _journal.touch(node);
                    _journal[node].left = child;
                }
                node = _journal[node].left;
                right = middle;
            } else {
                if (!_journal[node].right) {
                    int child = new_node();
                    _journal.touch(node);
                    _journal[node].right = child;
                }
                node = _journal[node].right;
                left = middle;
            }
        }
        _journal.touch(node);
        _journal[node].value = std::move(x);
        for (int index = depth - 2; index >= 0; --index) {
            update(path[index], path_left[index], path_right[index], index);
        }
    }

    void set_inplace(Index pos, T x) { set(pos, std::move(x)); }

    T get(Index pos) const {
        assert(left_bound() <= pos && pos < right_bound());
        int node = root();
        Index left = left_bound();
        Index right = right_bound();
        int depth = 0;
        while (node) {
            Index middle = std::midpoint(left, right);
            if (middle == left) return value(node, left, right, depth);
            if (pos < middle) {
                node = _journal[node].left;
                right = middle;
            } else {
                node = _journal[node].right;
                left = middle;
            }
            ++depth;
        }
        return initial_value();
    }

    T operator[](Index pos) const { return get(pos); }
    T prod(Index left, Index right) const {
        assert(left_bound() <= left && left <= right && right <= right_bound());
        if (left == right) return Monoid::id();
        return prod_node(root(), left_bound(), right_bound(), 0, left, right);
    }
    T all_prod() const { return value(root(), left_bound(), right_bound(), 0); }

    template <class Predicate>
    Index max_right(Index left, Predicate predicate) const {
        assert(left_bound() <= left && left <= right_bound());
        assert(predicate(Monoid::id()));
        if (left == right_bound()) return right_bound();
        T product = Monoid::id();
        return max_right_node(root(), left_bound(), right_bound(), 0, left, product, predicate);
    }

    template <class Predicate>
    Index min_left(Index right, Predicate predicate) const {
        assert(left_bound() <= right && right <= right_bound());
        assert(predicate(Monoid::id()));
        if (right == left_bound()) return left_bound();
        T product = Monoid::id();
        return min_left_node(root(), left_bound(), right_bound(), 0, right, product, predicate);
    }

    int snapshot() { return _journal.snapshot(); }
    int snapshot_count() const { return _journal.snapshot_count(); }
    void reserve_snapshots(int count) { _journal.reserve_snapshots(count); }
    void rollback(int state) { _journal.rollback(state); }
    void clear_history() { _journal.clear_history(); }
    void release() { _journal.clear(); _journal.emplace(); }
};

}  // namespace ds
}  // namespace m1une
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