Range Contour Query on Tree
(graph/tree/range_contour_query.hpp)

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Last update: 2026-08-13 01:41:40+09:00
Include: #include "graph/tree/range_contour_query.hpp"

Overview

This header supports commutative-group operations selected by an unweighted distance interval from a vertex. Its generic interfaces are:

VertexApplyRangeContourProduct<Group> applies a group element at one vertex and returns the group product over vertices at distances in [left, right).
VertexGetRangeContourApply<Group> applies a group element to every vertex at distances in [left, right) and retrieves one vertex value.

The additive convenience wrappers preserve the familiar problem-specific API:

VertexAddRangeContourSum<T> supports vertex additions and sums over all vertices at distances in [left, right).
VertexGetRangeContourAdd<T> adds to all vertices at distances in [left, right) and retrieves one vertex value.

Both structures use centroid decomposition, inclusion-exclusion, and Fenwick trees. The input must be a connected undirected tree built with add_edge. Edge costs are ignored; distance means the number of edges. Inactive edges are ignored when validating and building the tree.

Requirements

Group must satisfy m1une::monoid::IsCommutativeGroup:

using value_type = T;
static T id();
static T op(const T&, const T&);
static T inv(const T&);

The operation must be associative and commutative, id() must be its identity, and inv(x) must return the group inverse. m1une::monoid::Add<T> and m1une::monoid::Xor<T> are ready-made policies. Non-invertible operations such as minimum, maximum, GCD, AND, and OR are not supported because centroid inclusion-exclusion requires inverses.

Interfaces

template <m1une::monoid::IsCommutativeGroup Group>
class VertexApplyRangeContourProduct {
public:
    using T = typename Group::value_type;

    VertexApplyRangeContourProduct();

    template <class EdgeCost>
    explicit VertexApplyRangeContourProduct(
        const Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    );

    template <class EdgeCost>
    void build(
        const Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    );

    int size() const;
    bool empty() const;
    T get(int vertex) const;
    void apply(int vertex, const T& value);
    void set(int vertex, const T& value);
    T prod(int vertex, int left_distance, int right_distance) const;
};

template <m1une::monoid::IsCommutativeGroup Group>
class VertexGetRangeContourApply {
public:
    using T = typename Group::value_type;

    VertexGetRangeContourApply();

    template <class EdgeCost>
    explicit VertexGetRangeContourApply(
        const Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    );

    template <class EdgeCost>
    void build(
        const Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    );

    int size() const;
    bool empty() const;
    T get(int vertex) const;
    void point_apply(int vertex, const T& value);
    void set(int vertex, const T& value);
    void apply(
        int vertex,
        int left_distance,
        int right_distance,
        const T& value
    );
};

template <class T>
class VertexAddRangeContourSum;

template <class T>
class VertexGetRangeContourAdd;

VertexAddRangeContourSum<T> is the additive wrapper around VertexApplyRangeContourProduct<m1une::monoid::Add<T>>. It adds add and sum as names for apply and prod. VertexGetRangeContourAdd<T> wraps VertexGetRangeContourApply<m1une::monoid::Add<T>> and adds the point method add as a name for point_apply.

An omitted initial vector initializes every value to T{}. An explicitly provided vector must have one value per vertex. Empty trees are supported. Distance bounds must satisfy 0 <= left_distance <= right_distance; bounds beyond the tree diameter are allowed and are clipped naturally.

Operations

Method	Description	Complexity
`VertexApplyRangeContourProduct()` / `VertexGetRangeContourApply()`	Constructs an empty generic object.	$O(1)$
`template <class EdgeCost> explicit VertexApplyRangeContourProduct(const Graph<EdgeCost>& graph, const std::vector<T>& initial = {})`	Builds the point-apply/range-product structure.	$O(N\log^2 N)$
`template <class EdgeCost> explicit VertexGetRangeContourApply(const Graph<EdgeCost>& graph, const std::vector<T>& initial = {})`	Builds the range-apply/point-get structure.	$O(N\log^2 N)$
`template <class EdgeCost> void build(const Graph<EdgeCost>& graph, const std::vector<T>& initial = {})`	Replaces the current tree and values; available on both classes.	$O(N\log^2 N)$
`int size() const`	Returns the number of vertices.	$O(1)$
`bool empty() const`	Returns whether the structure has no vertices.	$O(1)$
`T VertexApplyRangeContourProduct::get(int vertex) const`	Returns the current vertex value.	$O(1)$
`void VertexApplyRangeContourProduct::apply(int vertex, const T& value)`	Combines one vertex with `value`.	$O(\log^2 N)$
`void VertexApplyRangeContourProduct::set(int vertex, const T& value)`	Replaces one vertex value.	$O(\log^2 N)$
`T VertexApplyRangeContourProduct::prod(int vertex, int left_distance, int right_distance) const`	Returns the group product at distances in `[left_distance, right_distance)`.	$O(\log^2 N)$
`T VertexGetRangeContourApply::get(int vertex) const`	Returns one current vertex value.	$O(\log^2 N)$
`void VertexGetRangeContourApply::point_apply(int vertex, const T& value)`	Combines one vertex with `value`.	$O(1)$
`void VertexGetRangeContourApply::set(int vertex, const T& value)`	Replaces one current vertex value.	$O(\log^2 N)$
`void VertexGetRangeContourApply::apply(int vertex, int left_distance, int right_distance, const T& value)`	Combines every value at distances in `[left_distance, right_distance)` with `value`.	$O(\log^2 N)$
`void VertexAddRangeContourSum::add(int vertex, const T& delta)`	Additive alias of point `apply`.	$O(\log^2 N)$
`T VertexAddRangeContourSum::sum(int vertex, int left_distance, int right_distance) const`	Additive alias of `prod`.	$O(\log^2 N)$
`void VertexGetRangeContourAdd::add(int vertex, const T& delta)`	Additive alias of `point_apply`.	$O(1)$

Both structures use $O(N\log N)$ memory. Operations mutate the structure; queries do not.

Example

#include "graph/graph.hpp"
#include "graph/tree/range_contour_query.hpp"
#include "monoid/xor.hpp"

#include <cassert>
#include <vector>

int main() {
    m1une::graph::Graph<> graph(4);
    graph.add_edge(0, 1);
    graph.add_edge(1, 2);
    graph.add_edge(1, 3);

    std::vector<long long> values = {1, 2, 3, 4};
    m1une::tree::VertexAddRangeContourSum<long long> sums(graph, values);
    assert(sums.sum(0, 1, 3) == 9);
    sums.add(2, 5);
    assert(sums.sum(0, 2, 3) == 12);

    m1une::tree::VertexGetRangeContourAdd<long long> additions(graph, values);
    additions.apply(0, 1, 3, 10);
    assert(additions.get(0) == 1);
    assert(additions.get(3) == 14);

    using Xor = m1une::monoid::Xor<unsigned>;
    m1une::tree::VertexApplyRangeContourProduct<Xor> xor_query(
        graph,
        std::vector<unsigned>{1, 2, 4, 8}
    );
    assert(xor_query.prod(0, 1, 3) == (2U ^ 4U ^ 8U));
}

Depends on

Required by

Verified with

Code

#ifndef M1UNE_TREE_RANGE_CONTOUR_QUERY_HPP
#define M1UNE_TREE_RANGE_CONTOUR_QUERY_HPP 1

#include <algorithm>
#include <cassert>
#include <vector>

#include "../../monoid/add.hpp"
#include "../../monoid/concept.hpp"
#include "../graph.hpp"
#include "centroid_decomposition.hpp"
#include "rooted_tree.hpp"

namespace m1une {
namespace tree {

namespace internal {

struct RangeContourPathEntry {
    int centroid;
    int distance;
    int subtree;
};

struct RangeContourLayout {
    int n = 0;
    std::vector<std::vector<RangeContourPathEntry>> path;
    std::vector<int> all_size;
    std::vector<int> subtree_size;

    template <class EdgeCost>
    void build(const m1une::graph::Graph<EdgeCost>& graph) {
        n = graph.size();
        path.assign(n, {});
        all_size.assign(n, 0);
        subtree_size.assign(n, 0);
        if (n == 0) return;

#ifndef NDEBUG
        std::vector<int> incidence(graph.edge_count(), 0);
        for (int vertex = 0; vertex < n; vertex++) {
            for (const auto& edge : graph[vertex]) {
                if (!edge.alive) continue;
                assert(0 <= edge.id && edge.id < graph.edge_count());
                incidence[edge.id]++;
            }
        }
        int active_edges = 0;
        for (int count : incidence) {
            if (count == 0) continue;
            assert(count == 2);
            active_edges++;
        }
        assert(active_edges == n - 1);
#endif

        RootedTree<EdgeCost> rooted(graph, 0);
        assert(int(rooted.order.size()) == n);
        CentroidDecomposition<EdgeCost> decomposition(graph);

        for (int vertex = 0; vertex < n; vertex++) {
            int previous = -1;
            for (
                int centroid = vertex;
                centroid != -1;
                centroid = decomposition.parent[centroid]
            ) {
                int distance = rooted.dist_edges(vertex, centroid);
                path[vertex].push_back(
                    RangeContourPathEntry{centroid, distance, previous}
                );
                all_size[centroid] = std::max(
                    all_size[centroid],
                    distance + 1
                );
                if (previous != -1) {
                    subtree_size[previous] = std::max(
                        subtree_size[previous],
                        distance + 1
                    );
                }
                previous = centroid;
            }
        }
    }
};

template <m1une::monoid::IsCommutativeGroup Group>
class RangeContourFenwick {
   public:
    using T = typename Group::value_type;

   private:
    int _n = 0;
    std::vector<T> _data;

    T prefix_product(int right) const {
        T result = Group::id();
        while (right > 0) {
            result = Group::op(result, _data[right]);
            right -= right & -right;
        }
        return result;
    }

   public:
    RangeContourFenwick() : _data(1, Group::id()) {}

    explicit RangeContourFenwick(int n)
        : _n(n), _data(n + 1, Group::id()) {
        assert(0 <= n);
    }

    int size() const {
        return _n;
    }

    void apply(int index, const T& value) {
        assert(0 <= index && index < _n);
        for (index++; index <= _n; index += index & -index) {
            _data[index] = Group::op(_data[index], value);
        }
    }

    T product(int left, int right) const {
        left = std::max(left, 0);
        right = std::min(right, _n);
        if (right <= left) return Group::id();
        return Group::op(
            Group::inv(prefix_product(left)),
            prefix_product(right)
        );
    }

    void range_apply(int left, int right, const T& value) {
        left = std::max(left, 0);
        right = std::min(right, _n);
        if (right <= left) return;
        apply(left, value);
        if (right < _n) apply(right, Group::inv(value));
    }

    T get(int index) const {
        assert(0 <= index && index < _n);
        return prefix_product(index + 1);
    }
};

}  // namespace internal

template <m1une::monoid::IsCommutativeGroup Group>
class VertexApplyRangeContourProduct {
   public:
    using T = typename Group::value_type;

   private:
    internal::RangeContourLayout _layout;
    std::vector<T> _value;
    std::vector<internal::RangeContourFenwick<Group>> _all;
    std::vector<internal::RangeContourFenwick<Group>> _subtree;

    void check_vertex(int vertex) const {
        assert(0 <= vertex && vertex < size());
    }

   public:
    VertexApplyRangeContourProduct() = default;

    template <class EdgeCost>
    explicit VertexApplyRangeContourProduct(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        build(graph, initial);
    }

    template <class EdgeCost>
    void build(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        assert(initial.empty() || int(initial.size()) == graph.size());
        _layout.build(graph);
        const int n = _layout.n;
        _value.assign(n, Group::id());
        _all.assign(n, internal::RangeContourFenwick<Group>());
        _subtree.assign(n, internal::RangeContourFenwick<Group>());
        for (int index = 0; index < n; index++) {
            _all[index] =
                internal::RangeContourFenwick<Group>(_layout.all_size[index]);
            _subtree[index] =
                internal::RangeContourFenwick<Group>(
                    _layout.subtree_size[index]
                );
        }
        if (!initial.empty()) {
            for (int vertex = 0; vertex < n; vertex++) {
                apply(vertex, initial[vertex]);
            }
        }
    }

    int size() const {
        return _layout.n;
    }

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

    T get(int vertex) const {
        check_vertex(vertex);
        return _value[vertex];
    }

    void apply(int vertex, const T& value) {
        check_vertex(vertex);
        _value[vertex] = Group::op(_value[vertex], value);
        for (const auto& entry : _layout.path[vertex]) {
            _all[entry.centroid].apply(entry.distance, value);
            if (entry.subtree != -1) {
                _subtree[entry.subtree].apply(entry.distance, value);
            }
        }
    }

    void set(int vertex, const T& value) {
        check_vertex(vertex);
        apply(vertex, Group::op(Group::inv(_value[vertex]), value));
    }

    T prod(int vertex, int left_distance, int right_distance) const {
        check_vertex(vertex);
        assert(0 <= left_distance && left_distance <= right_distance);
        T result = Group::id();
        for (const auto& entry : _layout.path[vertex]) {
            int left = left_distance - entry.distance;
            int right = right_distance - entry.distance;
            result = Group::op(
                result,
                _all[entry.centroid].product(left, right)
            );
            if (entry.subtree != -1) {
                result = Group::op(
                    result,
                    Group::inv(
                        _subtree[entry.subtree].product(left, right)
                    )
                );
            }
        }
        return result;
    }
};

template <m1une::monoid::IsCommutativeGroup Group>
class VertexGetRangeContourApply {
   public:
    using T = typename Group::value_type;

   private:
    internal::RangeContourLayout _layout;
    std::vector<T> _base;
    std::vector<internal::RangeContourFenwick<Group>> _all;
    std::vector<internal::RangeContourFenwick<Group>> _subtree;

    void check_vertex(int vertex) const {
        assert(0 <= vertex && vertex < size());
    }

   public:
    VertexGetRangeContourApply() = default;

    template <class EdgeCost>
    explicit VertexGetRangeContourApply(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        build(graph, initial);
    }

    template <class EdgeCost>
    void build(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        assert(initial.empty() || int(initial.size()) == graph.size());
        _layout.build(graph);
        const int n = _layout.n;
        _base = initial.empty() ? std::vector<T>(n, Group::id()) : initial;
        _all.assign(n, internal::RangeContourFenwick<Group>());
        _subtree.assign(n, internal::RangeContourFenwick<Group>());
        for (int index = 0; index < n; index++) {
            _all[index] =
                internal::RangeContourFenwick<Group>(_layout.all_size[index]);
            _subtree[index] =
                internal::RangeContourFenwick<Group>(
                    _layout.subtree_size[index]
                );
        }
    }

    int size() const {
        return _layout.n;
    }

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

    T get(int vertex) const {
        check_vertex(vertex);
        T result = _base[vertex];
        for (const auto& entry : _layout.path[vertex]) {
            result = Group::op(
                result,
                _all[entry.centroid].get(entry.distance)
            );
            if (entry.subtree != -1) {
                result = Group::op(
                    result,
                    Group::inv(
                        _subtree[entry.subtree].get(entry.distance)
                    )
                );
            }
        }
        return result;
    }

    void point_apply(int vertex, const T& value) {
        check_vertex(vertex);
        _base[vertex] = Group::op(_base[vertex], value);
    }

    void set(int vertex, const T& value) {
        check_vertex(vertex);
        _base[vertex] = Group::op(
            _base[vertex],
            Group::op(Group::inv(get(vertex)), value)
        );
    }

    void apply(
        int vertex,
        int left_distance,
        int right_distance,
        const T& value
    ) {
        check_vertex(vertex);
        assert(0 <= left_distance && left_distance <= right_distance);
        for (const auto& entry : _layout.path[vertex]) {
            int left = left_distance - entry.distance;
            int right = right_distance - entry.distance;
            _all[entry.centroid].range_apply(left, right, value);
            if (entry.subtree != -1) {
                _subtree[entry.subtree].range_apply(left, right, value);
            }
        }
    }
};

template <class T>
class VertexAddRangeContourSum
    : public VertexApplyRangeContourProduct<m1une::monoid::Add<T>> {
   private:
    using Base = VertexApplyRangeContourProduct<m1une::monoid::Add<T>>;

   public:
    using Base::Base;

    void add(int vertex, const T& delta) {
        Base::apply(vertex, delta);
    }

    T sum(int vertex, int left_distance, int right_distance) const {
        return Base::prod(vertex, left_distance, right_distance);
    }
};

template <class T>
class VertexGetRangeContourAdd
    : public VertexGetRangeContourApply<m1une::monoid::Add<T>> {
   private:
    using Base = VertexGetRangeContourApply<m1une::monoid::Add<T>>;

   public:
    using Base::Base;

    void add(int vertex, const T& delta) {
        Base::point_apply(vertex, delta);
    }
};

}  // namespace tree
}  // namespace m1une

#endif  // M1UNE_TREE_RANGE_CONTOUR_QUERY_HPP

#line 1 "graph/tree/range_contour_query.hpp"



#include <algorithm>
#include <cassert>
#include <vector>

#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/concept.hpp"



#include <concepts>

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 "graph/graph.hpp"



#include <array>
#line 6 "graph/graph.hpp"
#include <utility>
#line 8 "graph/graph.hpp"

namespace m1une {
namespace graph {

template <class T = int>
struct Edge {
    using cost_type = T;

    int from;
    int to;
    T cost;
    int id;
    bool alive;

    Edge() : from(-1), to(-1), cost(T()), id(-1), alive(true) {}
    Edge(int from_, int to_, T cost_ = T(1), int id_ = -1, bool alive_ = true)
        : from(from_), to(to_), cost(cost_), id(id_), alive(alive_) {}

    int other(int v) const {
        assert(v == from || v == to);
        return from ^ to ^ v;
    }
};

template <class T = int>
struct Graph {
    using edge_type = Edge<T>;
    using cost_type = T;

   private:
    struct EdgePositions {
        std::array<std::pair<int, int>, 2> value{};
        int size = 0;

        void push_back(std::pair<int, int> position) {
            assert(size < 2);
            value[size++] = position;
        }
    };

    int _n;
    int _edge_count;
    std::vector<std::vector<edge_type>> _g;
    std::vector<EdgePositions> _edge_positions;

   public:
    Graph() : _n(0), _edge_count(0) {}
    explicit Graph(int n) : _n(n), _edge_count(0), _g(n) {
        assert(0 <= n);
    }

    int size() const {
        return _n;
    }

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

    int edge_count() const {
        return _edge_count;
    }

    int add_vertex() {
        _g.emplace_back();
        return _n++;
    }

    int add_directed_edge(int from, int to, T cost = T(1)) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        int id = _edge_count++;
        int idx = int(_g[from].size());
        _g[from].push_back(edge_type(from, to, cost, id));
        _edge_positions.emplace_back();
        _edge_positions.back().push_back({from, idx});
        return id;
    }

    int add_edge(int u, int v, T cost = T(1)) {
        assert(0 <= u && u < _n);
        assert(0 <= v && v < _n);
        int id = _edge_count++;
        int u_idx = int(_g[u].size());
        _g[u].push_back(edge_type(u, v, cost, id));
        int v_idx = int(_g[v].size());
        _g[v].push_back(edge_type(v, u, cost, id));
        _edge_positions.emplace_back();
        _edge_positions.back().push_back({u, u_idx});
        _edge_positions.back().push_back({v, v_idx});
        return id;
    }

    void set_edge_alive(int id, bool alive) {
        assert(0 <= id && id < _edge_count);
        for (int i = 0; i < _edge_positions[id].size; ++i) {
            auto [v, idx] = _edge_positions[id].value[i];
            _g[v][idx].alive = alive;
        }
    }

    void erase_edge(int id) {
        set_edge_alive(id, false);
    }

    void revive_edge(int id) {
        set_edge_alive(id, true);
    }

    bool is_edge_alive(int id) const {
        assert(0 <= id && id < _edge_count);
        assert(_edge_positions[id].size != 0);
        auto [v, idx] = _edge_positions[id].value[0];
        return _g[v][idx].alive;
    }

    const std::vector<edge_type>& operator[](int v) const {
        assert(0 <= v && v < _n);
        return _g[v];
    }

    std::vector<edge_type>& operator[](int v) {
        assert(0 <= v && v < _n);
        return _g[v];
    }

    const std::vector<std::vector<edge_type>>& adjacency() const {
        return _g;
    }

    std::vector<std::vector<edge_type>>& adjacency() {
        return _g;
    }

    std::vector<edge_type> edges(bool include_inactive = false) const {
        std::vector<edge_type> result;
        result.reserve(_edge_count);
        std::vector<char> used(_edge_count, false);
        for (int v = 0; v < _n; v++) {
            for (const auto& e : _g[v]) {
                if (!include_inactive && !e.alive) continue;
                if (0 <= e.id && e.id < _edge_count) {
                    if (used[e.id]) continue;
                    used[e.id] = true;
                }
                result.push_back(e);
            }
        }
        return result;
    }

    Graph reversed() const {
        Graph result(_n);
        result._edge_count = _edge_count;
        result._edge_positions.assign(_edge_count, {});
        for (int v = 0; v < _n; v++) {
            for (const auto& e : _g[v]) {
                int idx = int(result._g[e.to].size());
                result._g[e.to].push_back(edge_type(e.to, e.from, e.cost, e.id, e.alive));
                if (0 <= e.id && e.id < _edge_count) result._edge_positions[e.id].push_back({e.to, idx});
            }
        }
        return result;
    }
};

}  // namespace graph
}  // namespace m1une


#line 1 "graph/tree/centroid_decomposition.hpp"



#line 6 "graph/tree/centroid_decomposition.hpp"

#line 8 "graph/tree/centroid_decomposition.hpp"

namespace m1une {
namespace tree {

template <class T = int>
struct CentroidDecomposition {
    int n;
    std::vector<int> parent;
    std::vector<int> depth;
    std::vector<int> order;
    std::vector<int> roots;
    std::vector<std::vector<int>> children;

   private:
    std::vector<int> _subtree_size;
    std::vector<int> _work_parent;
    std::vector<char> _removed;

    void build_component(const m1une::graph::Graph<T>& g, int start, int p, int d) {
        std::vector<int> nodes;
        std::vector<int> stack = {start};
        _work_parent[start] = -2;
        while (!stack.empty()) {
            int v = stack.back();
            stack.pop_back();
            nodes.push_back(v);
            for (const auto& e : g[v]) {
                if (!e.alive || _removed[e.to]) continue;
                if (_work_parent[e.to] != -1) continue;
                _work_parent[e.to] = v;
                stack.push_back(e.to);
            }
        }

        for (int v : nodes) _subtree_size[v] = 1;
        for (int i = int(nodes.size()) - 1; i >= 0; i--) {
            int v = nodes[i];
            if (_work_parent[v] >= 0) _subtree_size[_work_parent[v]] += _subtree_size[v];
        }

        int total = int(nodes.size());
        int centroid = start;
        int best = total + 1;
        for (int v : nodes) {
            int largest = total - _subtree_size[v];
            for (const auto& e : g[v]) {
                if (!e.alive || _removed[e.to]) continue;
                if (_work_parent[e.to] == v) largest = std::max(largest, _subtree_size[e.to]);
            }
            if (largest < best) {
                best = largest;
                centroid = v;
            }
        }

        for (int v : nodes) _work_parent[v] = -1;

        parent[centroid] = p;
        depth[centroid] = d;
        order.push_back(centroid);
        if (p == -1) {
            roots.push_back(centroid);
        } else {
            children[p].push_back(centroid);
        }
        _removed[centroid] = true;

        for (const auto& e : g[centroid]) {
            if (!e.alive || _removed[e.to]) continue;
            build_component(g, e.to, centroid, d + 1);
        }
    }

   public:
    CentroidDecomposition() : n(0) {}
    explicit CentroidDecomposition(const m1une::graph::Graph<T>& g) {
        build(g);
    }

    void build(const m1une::graph::Graph<T>& g) {
        n = g.size();
        parent.assign(n, -1);
        depth.assign(n, -1);
        order.clear();
        order.reserve(n);
        roots.clear();
        children.assign(n, {});
        _subtree_size.assign(n, 0);
        _work_parent.assign(n, -1);
        _removed.assign(n, false);

        for (int v = 0; v < n; v++) {
            if (depth[v] == -1) build_component(g, v, -1, 0);
        }
    }

    int size() const {
        return n;
    }

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

    int root() const {
        return roots.empty() ? -1 : roots[0];
    }
};

}  // namespace tree
}  // namespace m1une


#line 1 "graph/tree/rooted_tree.hpp"



#line 7 "graph/tree/rooted_tree.hpp"

#line 9 "graph/tree/rooted_tree.hpp"

namespace m1une {
namespace tree {

template <class T = int>
struct RootedTree {
    using cost_type = T;
    using edge_type = m1une::graph::Edge<T>;

    int root;
    std::vector<int> parent;
    std::vector<int> parent_edge;
    std::vector<int> depth;
    std::vector<T> dist;
    std::vector<int> subtree_size;
    std::vector<int> tin;
    std::vector<int> tout;
    std::vector<int> order;
    std::vector<std::vector<int>> up;

   private:
    int _n;
    int _log;

    void check_vertex(int v) const {
        assert(0 <= v && v < _n);
        assert(tin[v] != -1);
    }

   public:
    RootedTree() : root(-1), _n(0), _log(0) {}
    explicit RootedTree(const m1une::graph::Graph<T>& g, int root_ = 0) {
        build(g, root_);
    }

    void build(const m1une::graph::Graph<T>& g, int root_ = 0) {
        _n = g.size();
        root = _n == 0 ? -1 : root_;
        _log = 1;
        while ((1U << _log) <= (unsigned int)(std::max(1, _n))) _log++;

        parent.assign(_n, -1);
        parent_edge.assign(_n, -1);
        depth.assign(_n, 0);
        dist.assign(_n, T(0));
        subtree_size.assign(_n, 0);
        tin.assign(_n, -1);
        tout.assign(_n, -1);
        order.clear();
        order.reserve(_n);
        up.assign(_log, std::vector<int>(_n, -1));

        if (_n == 0) return;
        assert(0 <= root && root < _n);

        struct Frame {
            int v;
            int state;
        };

        std::vector<char> visited(_n, false);
        std::vector<Frame> stack;
        stack.push_back({root, 0});
        visited[root] = true;
        int timer = 0;

        while (!stack.empty()) {
            Frame frame = stack.back();
            stack.pop_back();
            int v = frame.v;
            if (frame.state == 0) {
                tin[v] = timer++;
                order.push_back(v);
                up[0][v] = parent[v];
                for (int k = 1; k < _log; k++) {
                    int p = up[k - 1][v];
                    up[k][v] = p == -1 ? -1 : up[k - 1][p];
                }

                stack.push_back({v, 1});
                const auto& adj = g[v];
                for (int i = int(adj.size()) - 1; i >= 0; i--) {
                    const auto& e = adj[i];
                    if (!e.alive) continue;
                    if (visited[e.to]) continue;
                    visited[e.to] = true;
                    parent[e.to] = v;
                    parent_edge[e.to] = e.id;
                    depth[e.to] = depth[v] + 1;
                    dist[e.to] = dist[v] + e.cost;
                    stack.push_back({e.to, 0});
                }
            } else {
                subtree_size[v]++;
                if (parent[v] != -1) subtree_size[parent[v]] += subtree_size[v];
                tout[v] = timer;
            }
        }
    }

    int size() const {
        return _n;
    }

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

    int log() const {
        return _log;
    }

    bool is_ancestor(int u, int v) const {
        check_vertex(u);
        check_vertex(v);
        return tin[u] <= tin[v] && tout[v] <= tout[u];
    }

    bool in_subtree(int v, int u) const {
        return is_ancestor(u, v);
    }

    int kth_ancestor(int v, int k) const {
        check_vertex(v);
        assert(0 <= k);
        int bit = 0;
        while (k > 0 && v != -1) {
            if (k & 1) {
                if (_log <= bit) return -1;
                v = up[bit][v];
            }
            k >>= 1;
            bit++;
        }
        return v;
    }

    int lca(int u, int v) const {
        check_vertex(u);
        check_vertex(v);
        if (depth[u] < depth[v]) std::swap(u, v);
        u = kth_ancestor(u, depth[u] - depth[v]);
        if (u == v) return u;
        for (int k = _log - 1; k >= 0; k--) {
            if (up[k][u] != up[k][v]) {
                u = up[k][u];
                v = up[k][v];
            }
        }
        return parent[u];
    }

    int dist_edges(int u, int v) const {
        int w = lca(u, v);
        return depth[u] + depth[v] - 2 * depth[w];
    }

    T dist_cost(int u, int v) const {
        int w = lca(u, v);
        return dist[u] + dist[v] - dist[w] - dist[w];
    }

    int jump(int from, int to, int k) const {
        check_vertex(from);
        check_vertex(to);
        assert(0 <= k);
        int w = lca(from, to);
        int up_len = depth[from] - depth[w];
        int down_len = depth[to] - depth[w];
        if (up_len + down_len < k) return -1;
        if (k <= up_len) return kth_ancestor(from, k);
        return kth_ancestor(to, down_len - (k - up_len));
    }

    std::vector<int> path(int u, int v) const {
        check_vertex(u);
        check_vertex(v);
        int w = lca(u, v);
        std::vector<int> a, b;
        for (int x = u; x != w; x = parent[x]) a.push_back(x);
        a.push_back(w);
        for (int x = v; x != w; x = parent[x]) b.push_back(x);
        std::reverse(b.begin(), b.end());
        a.insert(a.end(), b.begin(), b.end());
        return a;
    }

    std::vector<int> path_edges(int u, int v) const {
        check_vertex(u);
        check_vertex(v);
        int w = lca(u, v);
        std::vector<int> a, b;
        for (int x = u; x != w; x = parent[x]) a.push_back(parent_edge[x]);
        for (int x = v; x != w; x = parent[x]) b.push_back(parent_edge[x]);
        std::reverse(b.begin(), b.end());
        a.insert(a.end(), b.begin(), b.end());
        return a;
    }

    std::pair<int, int> subtree_range(int v) const {
        check_vertex(v);
        return {tin[v], tout[v]};
    }

    std::vector<int> subtree_vertices(int v) const {
        check_vertex(v);
        return std::vector<int>(order.begin() + tin[v], order.begin() + tout[v]);
    }
};

}  // namespace tree
}  // namespace m1une


#line 13 "graph/tree/range_contour_query.hpp"

namespace m1une {
namespace tree {

namespace internal {

struct RangeContourPathEntry {
    int centroid;
    int distance;
    int subtree;
};

struct RangeContourLayout {
    int n = 0;
    std::vector<std::vector<RangeContourPathEntry>> path;
    std::vector<int> all_size;
    std::vector<int> subtree_size;

    template <class EdgeCost>
    void build(const m1une::graph::Graph<EdgeCost>& graph) {
        n = graph.size();
        path.assign(n, {});
        all_size.assign(n, 0);
        subtree_size.assign(n, 0);
        if (n == 0) return;

#ifndef NDEBUG
        std::vector<int> incidence(graph.edge_count(), 0);
        for (int vertex = 0; vertex < n; vertex++) {
            for (const auto& edge : graph[vertex]) {
                if (!edge.alive) continue;
                assert(0 <= edge.id && edge.id < graph.edge_count());
                incidence[edge.id]++;
            }
        }
        int active_edges = 0;
        for (int count : incidence) {
            if (count == 0) continue;
            assert(count == 2);
            active_edges++;
        }
        assert(active_edges == n - 1);
#endif

        RootedTree<EdgeCost> rooted(graph, 0);
        assert(int(rooted.order.size()) == n);
        CentroidDecomposition<EdgeCost> decomposition(graph);

        for (int vertex = 0; vertex < n; vertex++) {
            int previous = -1;
            for (
                int centroid = vertex;
                centroid != -1;
                centroid = decomposition.parent[centroid]
            ) {
                int distance = rooted.dist_edges(vertex, centroid);
                path[vertex].push_back(
                    RangeContourPathEntry{centroid, distance, previous}
                );
                all_size[centroid] = std::max(
                    all_size[centroid],
                    distance + 1
                );
                if (previous != -1) {
                    subtree_size[previous] = std::max(
                        subtree_size[previous],
                        distance + 1
                    );
                }
                previous = centroid;
            }
        }
    }
};

template <m1une::monoid::IsCommutativeGroup Group>
class RangeContourFenwick {
   public:
    using T = typename Group::value_type;

   private:
    int _n = 0;
    std::vector<T> _data;

    T prefix_product(int right) const {
        T result = Group::id();
        while (right > 0) {
            result = Group::op(result, _data[right]);
            right -= right & -right;
        }
        return result;
    }

   public:
    RangeContourFenwick() : _data(1, Group::id()) {}

    explicit RangeContourFenwick(int n)
        : _n(n), _data(n + 1, Group::id()) {
        assert(0 <= n);
    }

    int size() const {
        return _n;
    }

    void apply(int index, const T& value) {
        assert(0 <= index && index < _n);
        for (index++; index <= _n; index += index & -index) {
            _data[index] = Group::op(_data[index], value);
        }
    }

    T product(int left, int right) const {
        left = std::max(left, 0);
        right = std::min(right, _n);
        if (right <= left) return Group::id();
        return Group::op(
            Group::inv(prefix_product(left)),
            prefix_product(right)
        );
    }

    void range_apply(int left, int right, const T& value) {
        left = std::max(left, 0);
        right = std::min(right, _n);
        if (right <= left) return;
        apply(left, value);
        if (right < _n) apply(right, Group::inv(value));
    }

    T get(int index) const {
        assert(0 <= index && index < _n);
        return prefix_product(index + 1);
    }
};

}  // namespace internal

template <m1une::monoid::IsCommutativeGroup Group>
class VertexApplyRangeContourProduct {
   public:
    using T = typename Group::value_type;

   private:
    internal::RangeContourLayout _layout;
    std::vector<T> _value;
    std::vector<internal::RangeContourFenwick<Group>> _all;
    std::vector<internal::RangeContourFenwick<Group>> _subtree;

    void check_vertex(int vertex) const {
        assert(0 <= vertex && vertex < size());
    }

   public:
    VertexApplyRangeContourProduct() = default;

    template <class EdgeCost>
    explicit VertexApplyRangeContourProduct(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        build(graph, initial);
    }

    template <class EdgeCost>
    void build(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        assert(initial.empty() || int(initial.size()) == graph.size());
        _layout.build(graph);
        const int n = _layout.n;
        _value.assign(n, Group::id());
        _all.assign(n, internal::RangeContourFenwick<Group>());
        _subtree.assign(n, internal::RangeContourFenwick<Group>());
        for (int index = 0; index < n; index++) {
            _all[index] =
                internal::RangeContourFenwick<Group>(_layout.all_size[index]);
            _subtree[index] =
                internal::RangeContourFenwick<Group>(
                    _layout.subtree_size[index]
                );
        }
        if (!initial.empty()) {
            for (int vertex = 0; vertex < n; vertex++) {
                apply(vertex, initial[vertex]);
            }
        }
    }

    int size() const {
        return _layout.n;
    }

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

    T get(int vertex) const {
        check_vertex(vertex);
        return _value[vertex];
    }

    void apply(int vertex, const T& value) {
        check_vertex(vertex);
        _value[vertex] = Group::op(_value[vertex], value);
        for (const auto& entry : _layout.path[vertex]) {
            _all[entry.centroid].apply(entry.distance, value);
            if (entry.subtree != -1) {
                _subtree[entry.subtree].apply(entry.distance, value);
            }
        }
    }

    void set(int vertex, const T& value) {
        check_vertex(vertex);
        apply(vertex, Group::op(Group::inv(_value[vertex]), value));
    }

    T prod(int vertex, int left_distance, int right_distance) const {
        check_vertex(vertex);
        assert(0 <= left_distance && left_distance <= right_distance);
        T result = Group::id();
        for (const auto& entry : _layout.path[vertex]) {
            int left = left_distance - entry.distance;
            int right = right_distance - entry.distance;
            result = Group::op(
                result,
                _all[entry.centroid].product(left, right)
            );
            if (entry.subtree != -1) {
                result = Group::op(
                    result,
                    Group::inv(
                        _subtree[entry.subtree].product(left, right)
                    )
                );
            }
        }
        return result;
    }
};

template <m1une::monoid::IsCommutativeGroup Group>
class VertexGetRangeContourApply {
   public:
    using T = typename Group::value_type;

   private:
    internal::RangeContourLayout _layout;
    std::vector<T> _base;
    std::vector<internal::RangeContourFenwick<Group>> _all;
    std::vector<internal::RangeContourFenwick<Group>> _subtree;

    void check_vertex(int vertex) const {
        assert(0 <= vertex && vertex < size());
    }

   public:
    VertexGetRangeContourApply() = default;

    template <class EdgeCost>
    explicit VertexGetRangeContourApply(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        build(graph, initial);
    }

    template <class EdgeCost>
    void build(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        assert(initial.empty() || int(initial.size()) == graph.size());
        _layout.build(graph);
        const int n = _layout.n;
        _base = initial.empty() ? std::vector<T>(n, Group::id()) : initial;
        _all.assign(n, internal::RangeContourFenwick<Group>());
        _subtree.assign(n, internal::RangeContourFenwick<Group>());
        for (int index = 0; index < n; index++) {
            _all[index] =
                internal::RangeContourFenwick<Group>(_layout.all_size[index]);
            _subtree[index] =
                internal::RangeContourFenwick<Group>(
                    _layout.subtree_size[index]
                );
        }
    }

    int size() const {
        return _layout.n;
    }

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

    T get(int vertex) const {
        check_vertex(vertex);
        T result = _base[vertex];
        for (const auto& entry : _layout.path[vertex]) {
            result = Group::op(
                result,
                _all[entry.centroid].get(entry.distance)
            );
            if (entry.subtree != -1) {
                result = Group::op(
                    result,
                    Group::inv(
                        _subtree[entry.subtree].get(entry.distance)
                    )
                );
            }
        }
        return result;
    }

    void point_apply(int vertex, const T& value) {
        check_vertex(vertex);
        _base[vertex] = Group::op(_base[vertex], value);
    }

    void set(int vertex, const T& value) {
        check_vertex(vertex);
        _base[vertex] = Group::op(
            _base[vertex],
            Group::op(Group::inv(get(vertex)), value)
        );
    }

    void apply(
        int vertex,
        int left_distance,
        int right_distance,
        const T& value
    ) {
        check_vertex(vertex);
        assert(0 <= left_distance && left_distance <= right_distance);
        for (const auto& entry : _layout.path[vertex]) {
            int left = left_distance - entry.distance;
            int right = right_distance - entry.distance;
            _all[entry.centroid].range_apply(left, right, value);
            if (entry.subtree != -1) {
                _subtree[entry.subtree].range_apply(left, right, value);
            }
        }
    }
};

template <class T>
class VertexAddRangeContourSum
    : public VertexApplyRangeContourProduct<m1une::monoid::Add<T>> {
   private:
    using Base = VertexApplyRangeContourProduct<m1une::monoid::Add<T>>;

   public:
    using Base::Base;

    void add(int vertex, const T& delta) {
        Base::apply(vertex, delta);
    }

    T sum(int vertex, int left_distance, int right_distance) const {
        return Base::prod(vertex, left_distance, right_distance);
    }
};

template <class T>
class VertexGetRangeContourAdd
    : public VertexGetRangeContourApply<m1une::monoid::Add<T>> {
   private:
    using Base = VertexGetRangeContourApply<m1une::monoid::Add<T>>;

   public:
    using Base::Base;

    void add(int vertex, const T& delta) {
        Base::point_apply(vertex, delta);
    }
};

}  // namespace tree
}  // namespace m1une

m1une's library

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

Range Contour Query on Tree
(graph/tree/range_contour_query.hpp)

Overview

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Interfaces

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Example

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Range Contour Query on Tree (graph/tree/range_contour_query.hpp)

Overview

Requirements

Interfaces

Operations

Example

Depends on

Required by

Verified with

Code

Range Contour Query on Tree
(graph/tree/range_contour_query.hpp)