Euler Trail
(graph/euler_trail.hpp)

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• Last update: 2024-04-02 14:52:16+09:00
• Include: #include "graph/euler_trail.hpp"

説明

与えたグラフに対して、オイラー路を構築する。circuit に true を渡すと、オイラー閉路を構築する。

Depends on

• Simple CSR (data_structure/simple_csr.hpp)
• Graph (CSR format) (graph/base.hpp)

Verified with

• test/graph/Eulerian_Trail_Directed.test.cpp
• test/graph/Eulerian_Trail_Undirected.test.cpp

Code

#pragma once

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

#include "../graph/base.hpp"

namespace ebi {

template <class T>
std::optional<std::pair<std::vector<int>, std::vector<int>>>
euler_trail_undirected(const Graph<T> &g, bool circuit = false) {
    int n = g.node_number();
    int m = g.edge_number();
    int s = -1, t = -1;
    for (int v : std::views::iota(0, n)) {
        if (g[v].size() & 1) {
            if (s < 0)
                s = v;
            else if (t < 0)
                t = v;
            else
                return std::nullopt;
        }
    }
    if (circuit && s != -1) return std::nullopt;
    if (!circuit && (s != -1 && t == -1)) return std::nullopt;
    if (m == 0) return std::pair<std::vector<int>, std::vector<int>>({0}, {});
    if (s < 0) s = g.get_edge(0).from;
    std::vector<int> ids(n, 0);
    std::vector<bool> used(m, false);
    std::vector<int> vs, es;
    auto dfs = [&](auto &&self, int v) -> void {
        while (ids[v] < (int)g[v].size()) {
            auto e = g[v][ids[v]++];
            if (used[e.id]) continue;
            used[e.id] = true;
            self(self, e.to);
            es.emplace_back(e.id);
        }
        vs.emplace_back(v);
    };
    dfs(dfs, s);
    if ((int)es.size() != m) return std::nullopt;
    return std::pair<std::vector<int>, std::vector<int>>(vs, es);
}

template <class T>
std::optional<std::pair<std::vector<int>, std::vector<int>>>
euler_trail_directed(const Graph<T> &g, bool circuit = false) {
    int n = g.node_number();
    int m = g.edge_number();
    std::vector<int> in(n, 0), out(n, 0);
    for (auto e : g.get_edges()) {
        in[e.to]++;
        out[e.from]++;
    }
    int s = -1, t = -1;
    for (auto v : std::views::iota(0, n)) {
        if (in[v] + 1 == out[v]) {
            if (s != -1) return std::nullopt;
            s = v;
        } else if (in[v] == out[v] + 1) {
            if (t != -1) return std::nullopt;
            t = v;
        } else if (in[v] == out[v])
            continue;
        else
            return std::nullopt;
    }
    if (circuit && (s != -1 || t != -1)) return std::nullopt;
    if (!circuit && ((s == -1 && t != -1) || (s != -1 && t == -1)))
        return std::nullopt;
    if (m == 0) return std::pair<std::vector<int>, std::vector<int>>({0}, {});
    if (s == -1) s = g.get_edge(0).from;
    std::vector<int> vs, es;
    std::vector<int> ids(n, 0);
    auto dfs = [&](auto &&self, int v) -> void {
        while (ids[v] < (int)g[v].size()) {
            auto e = g[v][ids[v]++];
            self(self, e.to);
            es.emplace_back(e.id);
        }
        vs.emplace_back(v);
    };
    dfs(dfs, s);
    if ((int)es.size() != m) return std::nullopt;
    std::reverse(vs.begin(), vs.end());
    std::reverse(es.begin(), es.end());
    return std::pair<std::vector<int>, std::vector<int>>(vs, es);
}

}  // namespace ebi

#line 2 "graph/euler_trail.hpp"

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

#line 2 "graph/base.hpp"

#line 4 "graph/base.hpp"
#include <iostream>
#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#line 6 "data_structure/simple_csr.hpp"

namespace ebi {

template <class E> struct simple_csr {
    simple_csr() = default;

    simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
        : start(n + 1, 0), elist(elements.size()) {
        for (auto e : elements) {
            start[e.first + 1]++;
        }
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] += start[i];
        }
        auto counter = start;
        for (auto [i, e] : elements) {
            elist[counter[i]++] = e;
        }
    }

    simple_csr(const std::vector<std::vector<E>>& es)
        : start(es.size() + 1, 0) {
        int n = es.size();
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] = (int)es[i].size() + start[i];
        }
        elist.resize(start.back());
        for (auto i : std::views::iota(0, n)) {
            std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
        }
    }

    int size() const {
        return (int)start.size() - 1;
    }

    const auto operator[](int i) const {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }
    auto operator[](int i) {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }

    const auto operator()(int i, int l, int r) const {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }
    auto operator()(int i, int l, int r) {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }

  private:
    std::vector<int> start;
    std::vector<E> elist;
};

}  // namespace ebi
#line 9 "graph/base.hpp"

namespace ebi {

template <class T> struct Edge {
    int from, to;
    T cost;
    int id;
};

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

    Graph(int n_) : n(n_) {}

    Graph() = default;

    void add_edge(int u, int v, cost_type c) {
        buff.emplace_back(u, edge_type{u, v, c, m});
        edges.emplace_back(edge_type{u, v, c, m++});
    }

    void add_undirected_edge(int u, int v, cost_type c) {
        buff.emplace_back(u, edge_type{u, v, c, m});
        buff.emplace_back(v, edge_type{v, u, c, m});
        edges.emplace_back(edge_type{u, v, c, m});
        m++;
    }

    void read_tree(int offset = 1, bool is_weighted = false) {
        read_graph(n - 1, offset, false, is_weighted);
    }

    void read_parents(int offset = 1) {
        for (auto i : std::views::iota(1, n)) {
            int p;
            std::cin >> p;
            p -= offset;
            add_undirected_edge(p, i, 1);
        }
        build();
    }

    void read_graph(int e, int offset = 1, bool is_directed = false,
                    bool is_weighted = false) {
        for (int i = 0; i < e; i++) {
            int u, v;
            std::cin >> u >> v;
            u -= offset;
            v -= offset;
            if (is_weighted) {
                cost_type c;
                std::cin >> c;
                if (is_directed) {
                    add_edge(u, v, c);
                } else {
                    add_undirected_edge(u, v, c);
                }
            } else {
                if (is_directed) {
                    add_edge(u, v, 1);
                } else {
                    add_undirected_edge(u, v, 1);
                }
            }
        }
        build();
    }

    void build() {
        assert(!prepared);
        csr = simple_csr<edge_type>(n, buff);
        buff.clear();
        prepared = true;
    }

    int size() const {
        return n;
    }

    int node_number() const {
        return n;
    }

    int edge_number() const {
        return m;
    }

    edge_type get_edge(int i) const {
        return edges[i];
    }

    std::vector<edge_type> get_edges() const {
        return edges;
    }

    const auto operator[](int i) const {
        return csr[i];
    }
    auto operator[](int i) {
        return csr[i];
    }

  private:
    int n, m = 0;

    std::vector<std::pair<int,edge_type>> buff;

    std::vector<edge_type> edges;
    simple_csr<edge_type> csr;
    bool prepared = false;
};

}  // namespace ebi
#line 11 "graph/euler_trail.hpp"

namespace ebi {

template <class T>
std::optional<std::pair<std::vector<int>, std::vector<int>>>
euler_trail_undirected(const Graph<T> &g, bool circuit = false) {
    int n = g.node_number();
    int m = g.edge_number();
    int s = -1, t = -1;
    for (int v : std::views::iota(0, n)) {
        if (g[v].size() & 1) {
            if (s < 0)
                s = v;
            else if (t < 0)
                t = v;
            else
                return std::nullopt;
        }
    }
    if (circuit && s != -1) return std::nullopt;
    if (!circuit && (s != -1 && t == -1)) return std::nullopt;
    if (m == 0) return std::pair<std::vector<int>, std::vector<int>>({0}, {});
    if (s < 0) s = g.get_edge(0).from;
    std::vector<int> ids(n, 0);
    std::vector<bool> used(m, false);
    std::vector<int> vs, es;
    auto dfs = [&](auto &&self, int v) -> void {
        while (ids[v] < (int)g[v].size()) {
            auto e = g[v][ids[v]++];
            if (used[e.id]) continue;
            used[e.id] = true;
            self(self, e.to);
            es.emplace_back(e.id);
        }
        vs.emplace_back(v);
    };
    dfs(dfs, s);
    if ((int)es.size() != m) return std::nullopt;
    return std::pair<std::vector<int>, std::vector<int>>(vs, es);
}

template <class T>
std::optional<std::pair<std::vector<int>, std::vector<int>>>
euler_trail_directed(const Graph<T> &g, bool circuit = false) {
    int n = g.node_number();
    int m = g.edge_number();
    std::vector<int> in(n, 0), out(n, 0);
    for (auto e : g.get_edges()) {
        in[e.to]++;
        out[e.from]++;
    }
    int s = -1, t = -1;
    for (auto v : std::views::iota(0, n)) {
        if (in[v] + 1 == out[v]) {
            if (s != -1) return std::nullopt;
            s = v;
        } else if (in[v] == out[v] + 1) {
            if (t != -1) return std::nullopt;
            t = v;
        } else if (in[v] == out[v])
            continue;
        else
            return std::nullopt;
    }
    if (circuit && (s != -1 || t != -1)) return std::nullopt;
    if (!circuit && ((s == -1 && t != -1) || (s != -1 && t == -1)))
        return std::nullopt;
    if (m == 0) return std::pair<std::vector<int>, std::vector<int>>({0}, {});
    if (s == -1) s = g.get_edge(0).from;
    std::vector<int> vs, es;
    std::vector<int> ids(n, 0);
    auto dfs = [&](auto &&self, int v) -> void {
        while (ids[v] < (int)g[v].size()) {
            auto e = g[v][ids[v]++];
            self(self, e.to);
            es.emplace_back(e.id);
        }
        vs.emplace_back(v);
    };
    dfs(dfs, s);
    if ((int)es.size() != m) return std::nullopt;
    std::reverse(vs.begin(), vs.end());
    std::reverse(es.begin(), es.end());
    return std::pair<std::vector<int>, std::vector<int>>(vs, es);
}

}  // namespace ebi

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