Euler Tour
(graph/tree/euler_tour.hpp)

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

Overview

m1une::tree::EulerTour<T> roots an undirected tree and flattens each rooted subtree into one contiguous interval. It is the lightweight choice when you only need parent/depth metadata and subtree ranges for a Fenwick tree, segment tree, or direct iteration.

The input uses m1une::graph::Graph<T> and should be built with add_edge. Inactive graph edges are ignored.

Construction

m1une::graph::Graph<int> g(n);
g.add_edge(u, v);

m1une::tree::EulerTour<int> tour(g, 0);

The graph is expected to be an undirected tree. If the graph is disconnected, only the component reachable from the selected root is represented; unreachable vertices keep tin[v] == -1.

Public Members

For a connected tree, all arrays have size N, and order also contains N vertices.

Member	Type	Description
`root`	`int`	Root vertex, or `-1` for an empty tree.
`parent`	`std::vector<int>`	Parent vertex, or `-1` at the root.
`parent_edge`	`std::vector<int>`	Edge id connecting the vertex to its parent, or `-1`.
`depth`	`std::vector<int>`	Number of edges from the root.
`dist`	`std::vector<T>`	Sum of edge costs from the root.
`subtree_size`	`std::vector<int>`	Number of vertices in each rooted subtree.
`tin`, `tout`	`std::vector<int>`	Subtree interval `[tin[v], tout[v])` in preorder.
`order`	`std::vector<int>`	Vertices in DFS preorder.
`children`	`std::vector<std::vector<int>>`	Children in the rooted tree.

Important relationships:

Vertex v is stored at base-array index tin[v].
order[i] converts a base-array index back to the original vertex.
The rooted subtree of v is exactly order[tin[v]..tout[v]).
If edge values are stored at the child vertex position, the subtree edge interval is [tin[v] + 1, tout[v]).

Methods

Method	Description	Complexity
`EulerTour(const Graph<T>& g, int root = 0)`	Builds Euler-tour metadata.	$O(N)$
`void build(const Graph<T>& g, int root = 0)`	Rebuilds the structure.	$O(N)$
`int size() const`	Returns the number of vertices in the source graph.	$O(1)$
`int visited_size() const`	Returns the number of vertices reached from `root`.	$O(1)$
`bool empty() const`	Returns whether the source graph is empty.	$O(1)$
`bool is_ancestor(int u, int v) const`	Returns whether `u` is an ancestor of `v`.	$O(1)$
`bool in_subtree(int v, int u) const`	Returns whether `v` is in the subtree of `u`.	$O(1)$
`std::pair<int, int> subtree_range(int v, bool edge = false) const`	Returns `[tin[v], tout[v])`; with `edge=true`, excludes `v`.	$O(1)$
`std::vector<int> subtree_vertices(int v) const`	Returns vertices in the rooted subtree of `v`.	$O(\text{subtree size})$
`template <class F> void for_each_subtree(int v, F f) const`	Calls `f(vertex)` for each vertex in the subtree.	$O(\text{subtree size})$

T must be default-constructible and support addition with edge costs if dist is used.

Example

#include "ds/range_query/fenwick_tree.hpp"
#include "graph/graph.hpp"
#include "graph/tree/euler_tour.hpp"
#include <iostream>
#include <vector>

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

    std::vector<long long> value = {10, 20, 30, 40};
    m1une::tree::EulerTour<int> tour(g, 0);

    std::vector<long long> base(4);
    for (int v = 0; v < 4; ++v) {
        base[tour.tin[v]] = value[v];
    }
    m1une::ds::FenwickTree<long long> fenwick(base);

    auto [l, r] = tour.subtree_range(1);
    std::cout << fenwick.sum(l, r) << "\n"; // 60
}

Depends on

Graph (graph/graph.hpp)

Required by

Verified with

Code

#ifndef M1UNE_TREE_EULER_TOUR_HPP
#define M1UNE_TREE_EULER_TOUR_HPP 1

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

#include "../graph.hpp"

namespace m1une {
namespace tree {

template <class T = int>
struct EulerTour {
    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>> children;

   private:
    int _n;

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

   public:
    EulerTour() : root(-1), _n(0) {}
    explicit EulerTour(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_;
        parent.assign(_n, -2);
        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);
        children.assign(_n, {});

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

        struct Frame {
            int v;
            int state;
        };

        std::vector<Frame> stack;
        stack.push_back({root, 0});
        parent[root] = -1;

        while (!stack.empty()) {
            Frame frame = stack.back();
            stack.pop_back();
            int v = frame.v;
            if (frame.state == 0) {
                tin[v] = int(order.size());
                order.push_back(v);
                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 (parent[e.to] != -2) continue;
                    parent[e.to] = v;
                    parent_edge[e.to] = e.id;
                    depth[e.to] = depth[v] + 1;
                    dist[e.to] = dist[v] + e.cost;
                    children[v].push_back(e.to);
                    stack.push_back({e.to, 0});
                }
                std::reverse(children[v].begin(), children[v].end());
            } else {
                subtree_size[v] = 1;
                for (int child : children[v]) subtree_size[v] += subtree_size[child];
                tout[v] = int(order.size());
            }
        }
    }

    int size() const {
        return _n;
    }

    int visited_size() const {
        return int(order.size());
    }

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

    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);
    }

    std::pair<int, int> subtree_range(int v, bool edge = false) const {
        check_vertex(v);
        return {tin[v] + (edge ? 1 : 0), 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]);
    }

    template <class F>
    void for_each_subtree(int v, F f) const {
        auto [l, r] = subtree_range(v);
        for (int i = l; i < r; ++i) f(order[i]);
    }
};

}  // namespace tree
}  // namespace m1une

#endif  // M1UNE_TREE_EULER_TOUR_HPP

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



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

#line 1 "graph/graph.hpp"



#include <array>
#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 10 "graph/tree/euler_tour.hpp"

namespace m1une {
namespace tree {

template <class T = int>
struct EulerTour {
    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>> children;

   private:
    int _n;

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

   public:
    EulerTour() : root(-1), _n(0) {}
    explicit EulerTour(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_;
        parent.assign(_n, -2);
        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);
        children.assign(_n, {});

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

        struct Frame {
            int v;
            int state;
        };

        std::vector<Frame> stack;
        stack.push_back({root, 0});
        parent[root] = -1;

        while (!stack.empty()) {
            Frame frame = stack.back();
            stack.pop_back();
            int v = frame.v;
            if (frame.state == 0) {
                tin[v] = int(order.size());
                order.push_back(v);
                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 (parent[e.to] != -2) continue;
                    parent[e.to] = v;
                    parent_edge[e.to] = e.id;
                    depth[e.to] = depth[v] + 1;
                    dist[e.to] = dist[v] + e.cost;
                    children[v].push_back(e.to);
                    stack.push_back({e.to, 0});
                }
                std::reverse(children[v].begin(), children[v].end());
            } else {
                subtree_size[v] = 1;
                for (int child : children[v]) subtree_size[v] += subtree_size[child];
                tout[v] = int(order.size());
            }
        }
    }

    int size() const {
        return _n;
    }

    int visited_size() const {
        return int(order.size());
    }

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

    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);
    }

    std::pair<int, int> subtree_range(int v, bool edge = false) const {
        check_vertex(v);
        return {tin[v] + (edge ? 1 : 0), 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]);
    }

    template <class F>
    void for_each_subtree(int v, F f) const {
        auto [l, r] = subtree_range(v);
        for (int i = l; i < r; ++i) f(order[i]);
    }
};

}  // namespace tree
}  // namespace m1une

m1une's library

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

Euler Tour
(graph/tree/euler_tour.hpp)

Overview

Construction

Public Members

Methods

Example

Depends on

Required by

Verified with

Code

Euler Tour (graph/tree/euler_tour.hpp)

Overview

Construction

Public Members

Methods

Example

Depends on

Required by

Verified with

Code

Euler Tour
(graph/tree/euler_tour.hpp)