Rollback Dynamic Dual Segment Tree
(ds/segtree/rollback_dynamic_dual_segtree.hpp)

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Last update: 2026-08-12 17:21:09+09:00
Include: #include "ds/segtree/rollback_dynamic_dual_segtree.hpp"

Overview

RollbackDynamicDualSegtree<Monoid, Index> is a sparse dual segment tree with range action composition, point assignment, point queries, and rollback over an integral half-open domain.

Methods

Constructors and read-only methods follow the corresponding mutable structure.

Method	Description	Complexity
`void set(Index pos, T value)`, `void set_inplace(Index pos, T value)`	Assigns one point.	$O(\log U)$
`void apply(Index pos, const T& value)`, `void apply(Index left, Index right, const T& value)`	Composes an action on a point or range.	$O(\log U)$
`void apply_inplace(...)`	Aliases of `apply`.	$O(\log U)$
`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.	$O(F)$

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_dual_segtree.hpp"
#include "monoid/add.hpp"

using Add = m1une::monoid::Add<long long>;
m1une::ds::RollbackDynamicDualSegtree<Add> seg(-100, 100, 0);
int state = seg.snapshot();
seg.apply(-5, 6, 3);
seg.rollback(state);
assert(seg.get(0) == 0);

Depends on

Verified with

verify/ds/rollback_counterparts.test.cpp

Code

#ifndef M1UNE_DS_SEGTREE_ROLLBACK_DYNAMIC_DUAL_SEGTREE_HPP
#define M1UNE_DS_SEGTREE_ROLLBACK_DYNAMIC_DUAL_SEGTREE_HPP 1

#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 RollbackDynamicDualSegtree {
    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;
        bool has_value = false;
    };

    Index _left;
    Index _right;
    T _initial_value;
    detail::RollbackJournal<Node> _journal;

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

    int ensure(int node) { return node ? node : new_node(); }

    void all_apply(int node, Index left, Index right, const T& value) {
        _journal.touch(node);
        Node& current = _journal[node];
        if (std::midpoint(left, right) == left) {
            T old = current.has_value ? current.value : _initial_value;
            current.value = Monoid::op(value, old);
        } else {
            current.value = current.has_value ? Monoid::op(value, current.value) : value;
        }
        current.has_value = true;
    }

    void push(int node, Index left, Index right) {
        if (!_journal[node].has_value) return;
        Index middle = std::midpoint(left, right);
        if (middle == left) return;
        T lazy = _journal[node].value;
        int left_child = ensure(_journal[node].left);
        int right_child = ensure(_journal[node].right);
        all_apply(left_child, left, middle, lazy);
        all_apply(right_child, middle, right, lazy);
        _journal.touch(node);
        _journal[node].left = left_child;
        _journal[node].right = right_child;
        _journal[node].value = Monoid::id();
        _journal[node].has_value = false;
    }

    int set_node(int node, Index left, Index right, Index pos, T value) {
        node = ensure(node);
        Index middle = std::midpoint(left, right);
        if (middle == left) {
            _journal.touch(node);
            _journal[node].value = std::move(value);
            _journal[node].has_value = true;
            return node;
        }
        push(node, left, right);
        if (pos < middle) {
            int child = set_node(_journal[node].left, left, middle, pos, std::move(value));
            _journal.touch(node);
            _journal[node].left = child;
        } else {
            int child = set_node(_journal[node].right, middle, right, pos, std::move(value));
            _journal.touch(node);
            _journal[node].right = child;
        }
        return node;
    }

    int apply_node(int node, Index left, Index right, Index query_left, Index query_right, const T& value) {
        if (query_right <= left || right <= query_left) return node;
        node = ensure(node);
        if (query_left <= left && right <= query_right) {
            all_apply(node, left, right, value);
            return node;
        }
        push(node, left, right);
        Index middle = std::midpoint(left, right);
        int left_child = apply_node(_journal[node].left, left, middle, query_left, query_right, value);
        int right_child = apply_node(_journal[node].right, middle, right, query_left, query_right, value);
        _journal.touch(node);
        _journal[node].left = left_child;
        _journal[node].right = right_child;
        return node;
    }

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

    size_type size() const { return detail::dynamic_distance(_left, _right); }
    bool empty() const { return _left == _right; }
    Index left_bound() const { return _left; }
    Index right_bound() const { return _right; }
    const T& initial_value() const { return _initial_value; }
    std::size_t node_count() const { return _journal.nodes.size() - 1; }

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

    void set(Index pos, T value) {
        assert(_left <= pos && pos < _right);
        int next_root = set_node(root(), _left, _right, pos, std::move(value));
        if (next_root != root()) {
            _journal.touch(0);
            _journal[0].left = next_root;
        }
    }
    void set_inplace(Index pos, T value) { set(pos, std::move(value)); }

    T get(Index pos) const {
        assert(_left <= pos && pos < _right);
        int node = root();
        Index left = _left;
        Index right = _right;
        T inherited = Monoid::id();
        while (node) {
            Index middle = std::midpoint(left, right);
            if (middle == left) {
                T value = _journal[node].has_value ? _journal[node].value : _initial_value;
                return Monoid::op(inherited, value);
            }
            if (_journal[node].has_value) inherited = Monoid::op(inherited, _journal[node].value);
            if (pos < middle) {
                node = _journal[node].left;
                right = middle;
            } else {
                node = _journal[node].right;
                left = middle;
            }
        }
        return Monoid::op(inherited, _initial_value);
    }
    T operator[](Index pos) const { return get(pos); }

    void apply(Index pos, const T& value) { apply(pos, pos + 1, value); }
    void apply(Index left, Index right, const T& value) {
        assert(_left <= left && left <= right && right <= _right);
        if (left == right) return;
        int next_root = apply_node(root(), _left, _right, left, right, value);
        if (next_root != root()) {
            _journal.touch(0);
            _journal[0].left = next_root;
        }
    }
    void apply_inplace(Index pos, const T& value) { apply(pos, value); }
    void apply_inplace(Index left, Index right, const T& value) { apply(left, right, value); }

    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_DUAL_SEGTREE_HPP

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



#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 14 "ds/segtree/rollback_dynamic_dual_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 RollbackDynamicDualSegtree {
    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;
        bool has_value = false;
    };

    Index _left;
    Index _right;
    T _initial_value;
    detail::RollbackJournal<Node> _journal;

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

    int ensure(int node) { return node ? node : new_node(); }

    void all_apply(int node, Index left, Index right, const T& value) {
        _journal.touch(node);
        Node& current = _journal[node];
        if (std::midpoint(left, right) == left) {
            T old = current.has_value ? current.value : _initial_value;
            current.value = Monoid::op(value, old);
        } else {
            current.value = current.has_value ? Monoid::op(value, current.value) : value;
        }
        current.has_value = true;
    }

    void push(int node, Index left, Index right) {
        if (!_journal[node].has_value) return;
        Index middle = std::midpoint(left, right);
        if (middle == left) return;
        T lazy = _journal[node].value;
        int left_child = ensure(_journal[node].left);
        int right_child = ensure(_journal[node].right);
        all_apply(left_child, left, middle, lazy);
        all_apply(right_child, middle, right, lazy);
        _journal.touch(node);
        _journal[node].left = left_child;
        _journal[node].right = right_child;
        _journal[node].value = Monoid::id();
        _journal[node].has_value = false;
    }

    int set_node(int node, Index left, Index right, Index pos, T value) {
        node = ensure(node);
        Index middle = std::midpoint(left, right);
        if (middle == left) {
            _journal.touch(node);
            _journal[node].value = std::move(value);
            _journal[node].has_value = true;
            return node;
        }
        push(node, left, right);
        if (pos < middle) {
            int child = set_node(_journal[node].left, left, middle, pos, std::move(value));
            _journal.touch(node);
            _journal[node].left = child;
        } else {
            int child = set_node(_journal[node].right, middle, right, pos, std::move(value));
            _journal.touch(node);
            _journal[node].right = child;
        }
        return node;
    }

    int apply_node(int node, Index left, Index right, Index query_left, Index query_right, const T& value) {
        if (query_right <= left || right <= query_left) return node;
        node = ensure(node);
        if (query_left <= left && right <= query_right) {
            all_apply(node, left, right, value);
            return node;
        }
        push(node, left, right);
        Index middle = std::midpoint(left, right);
        int left_child = apply_node(_journal[node].left, left, middle, query_left, query_right, value);
        int right_child = apply_node(_journal[node].right, middle, right, query_left, query_right, value);
        _journal.touch(node);
        _journal[node].left = left_child;
        _journal[node].right = right_child;
        return node;
    }

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

    size_type size() const { return detail::dynamic_distance(_left, _right); }
    bool empty() const { return _left == _right; }
    Index left_bound() const { return _left; }
    Index right_bound() const { return _right; }
    const T& initial_value() const { return _initial_value; }
    std::size_t node_count() const { return _journal.nodes.size() - 1; }

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

    void set(Index pos, T value) {
        assert(_left <= pos && pos < _right);
        int next_root = set_node(root(), _left, _right, pos, std::move(value));
        if (next_root != root()) {
            _journal.touch(0);
            _journal[0].left = next_root;
        }
    }
    void set_inplace(Index pos, T value) { set(pos, std::move(value)); }

    T get(Index pos) const {
        assert(_left <= pos && pos < _right);
        int node = root();
        Index left = _left;
        Index right = _right;
        T inherited = Monoid::id();
        while (node) {
            Index middle = std::midpoint(left, right);
            if (middle == left) {
                T value = _journal[node].has_value ? _journal[node].value : _initial_value;
                return Monoid::op(inherited, value);
            }
            if (_journal[node].has_value) inherited = Monoid::op(inherited, _journal[node].value);
            if (pos < middle) {
                node = _journal[node].left;
                right = middle;
            } else {
                node = _journal[node].right;
                left = middle;
            }
        }
        return Monoid::op(inherited, _initial_value);
    }
    T operator[](Index pos) const { return get(pos); }

    void apply(Index pos, const T& value) { apply(pos, pos + 1, value); }
    void apply(Index left, Index right, const T& value) {
        assert(_left <= left && left <= right && right <= _right);
        if (left == right) return;
        int next_root = apply_node(root(), _left, _right, left, right, value);
        if (next_root != root()) {
            _journal.touch(0);
            _journal[0].left = next_root;
        }
    }
    void apply_inplace(Index pos, const T& value) { apply(pos, value); }
    void apply_inplace(Index left, Index right, const T& value) { apply(left, right, value); }

    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

m1une's library

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

Rollback Dynamic Dual Segment Tree
(ds/segtree/rollback_dynamic_dual_segtree.hpp)

Overview

Methods

Snapshot semantics

Example

Depends on

Verified with

Code

Rollback Dynamic Dual Segment Tree (ds/segtree/rollback_dynamic_dual_segtree.hpp)

Overview

Methods

Snapshot semantics

Example

Depends on

Verified with

Code

Rollback Dynamic Dual Segment Tree
(ds/segtree/rollback_dynamic_dual_segtree.hpp)