spl

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:heavy_check_mark: graph/test/eulerian_trail_directed.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_directed"
#define FAST_IO
#include "../../graph/eulerian_trail.hpp"
#include "../../template/template.hpp"
#include "../../template/fastio.hpp"

void solve() {
    i32 n, m;
    rd.read(n, m);
    Graph<i32, 1> g(n);
    REP(i, m) {
        i32 u, v;
        rd.read(u, v);
        g.add_edge(u, v);
    }
    g.build();
    auto [vs, es] = eulerian_trail(g);
    if (vs.empty()) {
        wr.writeln("No");
    } else {
        wr.writeln("Yes");
        REP(i, m + 1) {
            wr.write(vs[i]);
            wr.write(" \n"[i == m]);
        }
        REP(i, m) {
            wr.write(es[i]);
            wr.write(" \n"[i == m - 1]);
        }
        if (m == 0) {
            wr.writeln();
        }
    }
}

int main() {
    i32 t;
    rd.read(t);
    while (t--) {
        solve();
    }
}
#line 1 "graph/test/eulerian_trail_directed.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_directed"
#define FAST_IO
#line 2 "graph/eulerian_trail.hpp"
#include <algorithm>
#include <utility>
#line 2 "graph/graph.hpp"
#include <iostream>
#include <cassert>
#include <vector>
template <typename T>
struct Edge {
    using W = T;
    int from, to, id;
    W weight;
    Edge<T> rev() const {
        return Edge<T>{to, from, id, weight};
    }
};
template <typename T>
void debug(const Edge<T> &e) {
    std::cerr << e.from << " -> " << e.to << " id = " << e.id << std::cerr << " weight = ";
    debug(e.weight);
}
template <typename T = int, bool DIR = false>
class Graph {
public:
    using E = Edge<T>;
    using W = T;
    static constexpr bool DIRECTED = DIR;
    struct Adjacency {
        using Iter = typename std::vector<E>::iterator;
        Iter be, en;
        Iter begin() const { return be; }
        Iter end() const { return en; }
        int size() const { return (int)std::distance(be, en); }
        E &operator[](int idx) const { return be[idx]; }
    };
    struct ConstAdjacency {
        using Iter = typename std::vector<E>::const_iterator;
        Iter be, en;
        Iter begin() const { return be; }
        Iter end() const { return en; }
        int size() const { return (int)std::distance(be, en); }
        const E &operator[](int idx) const { return be[idx]; }
    };

private:
    int n, m;
    std::vector<E> edges, csr;
    std::vector<int> sep;
    bool built;

public:
    Graph(int n) : n(n), m(0), built(false) {}
    int v() const { return n; }
    int e() const { return m; }
    int add_vertex() {
        return n++;
    }
    void add_edge(int from, int to, W weight = 1) {
        assert(0 <= from && from < n && 0 <= to && to < n);
        edges.emplace_back(E{from, to, m++, weight});
    }
    void build() {
        sep.assign(n + 1, 0);
        csr.resize(DIRECTED ? m : 2 * m);
        for (const E &e : edges) {
            ++sep[e.from + 1];
            if (!DIRECTED) {
                ++sep[e.to + 1];
            }
        }
        for (int i = 0; i < n; ++i) {
            sep[i + 1] += sep[i];
        }
        std::vector<int> c = sep;
        for (const E &e : edges) {
            csr[c[e.from]++] = e;
            if (!DIRECTED) {
                csr[c[e.to]++] = e.rev();
            }
        }
        built = true;
    }
    Adjacency operator[](int v) {
        assert(built && 0 <= v && v < n);
        return Adjacency{csr.begin() + sep[v], csr.begin() + sep[v + 1]};
    }
    ConstAdjacency operator[](int v) const {
        assert(built && 0 <= v && v < n);
        return ConstAdjacency{csr.begin() + sep[v], csr.begin() + sep[v + 1]};
    }
};
#line 5 "graph/eulerian_trail.hpp"

template <typename T>
std::pair<std::vector<int>, std::vector<int>> eulerian_trail_directed(
    const Graph<T, true> &g) {
    assert(g.v() >= 1);
    std::vector<int> vs, es;
    std::vector<int> itr(g.v(), 0);
    auto dfs = [&](auto dfs, int v) -> void {
        while (itr[v] < g[v].size()) {
            const Edge<T> &e = g[v][itr[v]++];
            dfs(dfs, e.to);
            vs.push_back(e.to);
            es.push_back(e.id);
        }
    };

    std::vector<int> flux(g.v(), 0);
    for (int i = 0; i < g.v(); ++i) {
        flux[i] += g[i].size();
        for (auto e : g[i]) {
            --flux[e.to];
        }
    }
    int st = -1;
    for (int i = 0; i < g.v(); ++i) {
        if (flux[i] == 1) {
            if (st != -1) {
                // no eulerian trail
                return std::make_pair(vs, es);
            }
            st = i;
        }
        if (flux[i] >= 2) {
            // no eulerian trail
            return std::make_pair(vs, es);
        }
    }
    if (st == -1) {
        for (int i = 0; i < g.v(); ++i) {
            if (g[i].size() > 0) {
                st = i;
            }
        }
    }
    if (st == -1) {
        // no edge
        vs.push_back(0);
        return std::make_pair(vs, es);
    }

    vs.reserve(g.e() + 1);
    es.reserve(g.e());
    dfs(dfs, st);
    if ((int)es.size() != g.e()) {
        return std::make_pair(std::vector<int>(), std::vector<int>());
    }
    vs.push_back(st);
    std::reverse(vs.begin(), vs.end());
    std::reverse(es.begin(), es.end());
    return std::make_pair(vs, es);
}

template <typename T>
std::pair<std::vector<int>, std::vector<int>> eulerian_trail_undirected(
    const Graph<T, false> &g) {
    assert(g.v() >= 1);
    std::vector<int> vs, es;

    int st = -1;
    int cnt = 0;
    for (int i = 0; i < g.v(); ++i) {
        int deg = g[i].size();
        if (deg % 2 == 1) {
            ++cnt;
            st = i;
        }
    }
    if (cnt >= 3) {
        // no eulerian trail
        return std::make_pair(std::vector<int>(), std::vector<int>());
    }
    if (st == -1) {
        for (int i = 0; i < g.v(); ++i) {
            if (g[i].size() > 0) {
                st = i;
            }
        }
    }
    if (st == -1) {
        // no edge
        vs.push_back(0);
        return std::make_pair(vs, es);
    }

    std::vector<int> itr(g.v(), 0), used(g.e(), 0);
    auto dfs = [&](auto dfs, int v) -> void {
        while (itr[v] < g[v].size()) {
            const Edge<T> &e = g[v][itr[v]++];
            if (std::exchange(used[e.id], 1)) {
                continue;
            }
            dfs(dfs, e.to);
            vs.push_back(e.to);
            es.push_back(e.id);
        }
    };

    vs.reserve(g.e() + 1);
    es.reserve(g.e());
    dfs(dfs, st);
    if ((int)es.size() != g.e()) {
        return std::make_pair(std::vector<int>(), std::vector<int>());
    }
    vs.push_back(st);
    std::reverse(vs.begin(), vs.end());
    std::reverse(es.begin(), es.end());
    return std::make_pair(vs, es);
}

// (vs, es)
template <typename T, bool DIR>
std::pair<std::vector<int>, std::vector<int>> eulerian_trail(
    const Graph<T, DIR> &g) {
    if constexpr (DIR) {
        return eulerian_trail_directed(g);
    } else {
        return eulerian_trail_undirected(g);
    }
}
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
    return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
    return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
    V<i32> ret(arr.size());
    iota(ALL(ret), 0);
    sort(ALL(ret), [&](i32 i, i32 j) -> bool {
        if (arr[i] == arr[j]) {
            return i < j;
        } else {
            return arr[i] < arr[j];
        }
    });
    return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
    for (T &ele : x) {
        scan(ele);
    }
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
    scan(head);
    read(tail...);
}
#define CHAR(...)     \
    char __VA_ARGS__; \
    read(__VA_ARGS__);
#define U32(...)     \
    u32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define U64(...)     \
    u64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I32(...)     \
    i32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I64(...)     \
    i64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define F64(...)     \
    f64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define STR(...)        \
    string __VA_ARGS__; \
    read(__VA_ARGS__);
#define VEC(type, name, size) \
    V<type> name(size);       \
    read(name);
#define VVEC(type, name, size1, size2)    \
    VV<type> name(size1, V<type>(size2)); \
    read(name);
#line 4 "template/fastio.hpp"
#include <type_traits>
#line 6 "template/fastio.hpp"

// unable to read INT_MIN (int), LLONG_MIN (long long)
class Reader {
    FILE *fp;
    static constexpr int BUF = 1 << 18;
    char buf[BUF];
    char *pl, *pr;

    void reread() {
        int wd = pr - pl;
        std::memcpy(buf, pl, wd);
        pl = buf;
        pr = buf + wd;
        pr += std::fread(pr, 1, BUF - wd, fp);
    }

    char skip() {
        char ch = *pl++;
        while (ch <= ' ') {
            ch = *pl++;
        }
        return ch;
    }

    template <typename T>
    void read_unsigned(T &x) {
        if (pr - pl < 64) {
            reread();
        }
        x = 0;
        char ch = skip();
        while ('0' <= ch) {
            x = 10 * x + (0xf & ch);
            ch = *pl++;
        }
    }
    template <typename T>
    void read_signed(T &x) {
        if (pr - pl < 64) {
            reread();
        }
        x = 0;
        bool neg = false;
        char ch = skip();
        if (ch == '-') {
            ch = *pl++;
            neg = true;
        }
        while ('0' <= ch) {
            x = 10 * x + (0xf & ch);
            ch = *pl++;
        }
        if (neg) {
            x = -x;
        }
    }

    void read_single(int &x) { read_signed(x); }
    void read_single(unsigned &x) { read_unsigned(x); }
    void read_single(long &x) { read_signed(x); }
    void read_single(unsigned long &x) { read_signed(x); }
    void read_single(long long &x) { read_signed(x); }
    void read_single(unsigned long long &x) { read_unsigned(x); }

public:
    Reader(FILE *fp) : fp(fp), pl(buf), pr(buf) { reread(); }

    void read() {}
    template <typename Head, typename... Tail>
    void read(Head &head, Tail &...tail) {
        read_single(head);
        read(tail...);
    }
};

struct NumberToString {
    char buf[10000][4];
    constexpr NumberToString() : buf() {
        for (int i = 0; i < 10000; ++i) {
            int n = i;
            for (int j = 3; j >= 0; --j) {
                buf[i][j] = '0' + n % 10;
                n /= 10;
            }
        }
    }
} constexpr number_to_string_precalc;

class Writer {
    FILE *fp;
    static constexpr int BUF = 1 << 18;
    char buf[BUF];
    char *ptr;

    void write_u32(unsigned x) {
        if ((buf + BUF - ptr) < 32) {
            flush();
        }
        static char sml[12];
        int t = 8;
        while (x >= 10000) {
            unsigned n = x % 10000;
            x /= 10000;
            std::memcpy(sml + t, number_to_string_precalc.buf[n], 4);
            t -= 4;
        }
        if (x >= 1000) {
            std::memcpy(ptr, number_to_string_precalc.buf[x], 4);
            ptr += 4;
        } else if (x >= 100) {
            std::memcpy(ptr, number_to_string_precalc.buf[x] + 1, 3);
            ptr += 3;
        } else if (x >= 10) {
            unsigned q = (x * 103) >> 10;
            *ptr++ = q | '0';
            *ptr++ = (x - 10 * q) | '0';
        } else {
            *ptr++ = '0' | x;
        }
        std::memcpy(ptr, sml + (t + 4), 8 - t);
        ptr += 8 - t;
    }

    void write_u64(unsigned long long x) {
        if ((buf + BUF - ptr) < 32) {
            flush();
        }
        if (x >= 10000000000000000) {
            unsigned long long z = x % 100000000;
            x /= 100000000;
            unsigned long long y = x % 100000000;
            x /= 100000000;
            if (x >= 1000) {
                std::memcpy(ptr, number_to_string_precalc.buf[x], 4);
                ptr += 4;
            } else if (x >= 100) {
                std::memcpy(ptr, number_to_string_precalc.buf[x] + 1, 3);
                ptr += 3;
            } else if (x >= 10) {
                unsigned q = (x * 103) >> 10;
                *ptr++ = q | '0';
                *ptr++ = (x - 10 * q) | '0';
            } else {
                *ptr++ = '0' | x;
            }
            std::memcpy(ptr, number_to_string_precalc.buf[y / 10000], 4);
            std::memcpy(ptr + 4, number_to_string_precalc.buf[y % 10000], 4);
            std::memcpy(ptr + 8, number_to_string_precalc.buf[z / 10000], 4);
            std::memcpy(ptr + 12, number_to_string_precalc.buf[z % 10000], 4);
            ptr += 16;
        } else {
            static char sml[12];
            int t = 8;
            while (x >= 10000) {
                unsigned long long n = x % 10000;
                x /= 10000;
                std::memcpy(sml + t, number_to_string_precalc.buf[n], 4);
                t -= 4;
            }
            if (x >= 1000) {
                std::memcpy(ptr, number_to_string_precalc.buf[x], 4);
                ptr += 4;
            } else if (x >= 100) {
                std::memcpy(ptr, number_to_string_precalc.buf[x] + 1, 3);
                ptr += 3;
            } else if (x >= 10) {
                unsigned q = (x * 103) >> 10;
                *ptr++ = q | '0';
                *ptr++ = (x - 10 * q) | '0';
            } else {
                *ptr++ = '0' | x;
            }
            std::memcpy(ptr, sml + (t + 4), 8 - t);
            ptr += 8 - t;
        }
    }

    void write_char(char c) {
        if (ptr == buf + BUF) {
            flush();
        }
        *ptr++ = c;
    }

    template <typename T>
    void write_unsigned(T x) {
        if constexpr (std::is_same_v<T, unsigned long long> ||
                      std::is_same_v<T, unsigned long>) {
            write_u64(x);
        } else {
            write_u32(x);
        }
    }

    template <typename T>
    void write_signed(T x) {
        std::make_unsigned_t<T> y = x;
        if (x < 0) {
            write_char('-');
            y = -y;
        }
        write_unsigned(y);
    }
    
    void write_string(const std::string &s) {
        for (char c : s) {
            write_char(c);
        }
    }

    void write_single(int x) { write_signed(x); }
    void write_single(unsigned x) { write_unsigned(x); }
    void write_single(long x) { write_signed(x); }
    void write_single(unsigned long x) { write_unsigned(x); }
    void write_single(long long x) { write_signed(x); }
    void write_single(unsigned long long x) { write_unsigned(x); }
    void write_single(char c) { write_char(c); }
    void write_single(const std::string &s) { write_string(s); }

public:
    Writer(FILE *fp) : fp(fp), ptr(buf) {}
    ~Writer() { flush(); }

    void flush() {
        std::fwrite(buf, 1, ptr - buf, fp);
        ptr = buf;
    }

    void write() {}
    template <typename Head, typename... Tail>
    void write(Head &&head, Tail &&...tail) {
        write_single(head);
        if (sizeof...(Tail)) {
            write_char(' ');
        }
        write(std::forward<Tail>(tail)...);
    }

    template <typename... T>
    void writeln(T &&...t) {
        write(std::forward<T>(t)...);
        write_char('\n');
    }
};

Reader rd(stdin);
Writer wr(stdout);
#line 6 "graph/test/eulerian_trail_directed.test.cpp"

void solve() {
    i32 n, m;
    rd.read(n, m);
    Graph<i32, 1> g(n);
    REP(i, m) {
        i32 u, v;
        rd.read(u, v);
        g.add_edge(u, v);
    }
    g.build();
    auto [vs, es] = eulerian_trail(g);
    if (vs.empty()) {
        wr.writeln("No");
    } else {
        wr.writeln("Yes");
        REP(i, m + 1) {
            wr.write(vs[i]);
            wr.write(" \n"[i == m]);
        }
        REP(i, m) {
            wr.write(es[i]);
            wr.write(" \n"[i == m - 1]);
        }
        if (m == 0) {
            wr.writeln();
        }
    }
}

int main() {
    i32 t;
    rd.read(t);
    while (t--) {
        solve();
    }
}
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