test/yosupo_directedmst.test.cpp

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• Last update: 2026-03-22 13:47:31+09:00
• Problem: https://judge.yosupo.jp/problem/directedmst

Depends on

• 最小全域有向木(Chu-Liu/Edmonds) (graph/chu_liu_edmonds.cpp)
• 高速入出力(Fast IO) (util/fastio.cpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/directedmst"

#include <vector>
using ll = long long;
using namespace std;

#include <cstdio>
#include <cstring>
#include <string>
#include <type_traits>

#include "../util/fastio.cpp"
#include "../graph/chu_liu_edmonds.cpp"

int main() {
    Scanner in;
    Printer out;
    int n, m, r;
    in.read(n, m, r);
    ChuLiuEdmonds<ll> dmst(n, r);
    for (int i = 0; i < m; ++i) {
        int a, b;
        ll c;
        in.read(a, b, c);
        dmst.add_edge(a, b, c);
    }
    auto res = dmst.solve();
    if (!res.exists) return 0;
    out.println(res.cost);
    for (int i = 0; i < n; ++i) {
        if (i) out.print(' ');
        out.print(res.parent[i]);
    }
    out.println();
    return 0;
}

#line 1 "test/yosupo_directedmst.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/directedmst"

#include <vector>
using ll = long long;
using namespace std;

#include <cstdio>
#include <cstring>
#include <string>
#include <type_traits>

#line 1 "util/fastio.cpp"
using namespace std;

extern "C" int fileno(FILE *);
extern "C" int isatty(int);

template<class T, class = void>
struct is_fastio_range : false_type {};

template<class T>
struct is_fastio_range<T, void_t<decltype(declval<T &>().begin()), decltype(declval<T &>().end())>> : true_type {};

template<class T, class = void>
struct has_fastio_value : false_type {};

template<class T>
struct has_fastio_value<T, void_t<decltype(declval<const T &>().value())>> : true_type {};

struct FastIoDigitTable {
    char num[40000];

    constexpr FastIoDigitTable() : num() {
        for (int i = 0; i < 10000; ++i) {
            int x = i;
            for (int j = 3; j >= 0; --j) {
                num[i * 4 + j] = char('0' + x % 10);
                x /= 10;
            }
        }
    }
};

struct Scanner {
    static constexpr int BUFSIZE = 1 << 17;
    static constexpr int OFFSET = 64;
    char buf[BUFSIZE + 1];
    int idx, size;
    bool interactive;

    Scanner() : idx(0), size(0), interactive(isatty(fileno(stdin))) {}

    inline void load() {
        int len = size - idx;
        memmove(buf, buf + idx, len);
        if (interactive) {
            if (fgets(buf + len, BUFSIZE + 1 - len, stdin)) size = len + (int)strlen(buf + len);
            else size = len;
        } else {
            size = len + (int)fread(buf + len, 1, BUFSIZE - len, stdin);
        }
        idx = 0;
        buf[size] = 0;
    }

    inline void ensure() {
        if (idx + OFFSET > size) load();
    }

    inline void ensure_interactive() {
        if (idx == size) load();
    }

    inline char skip() {
        if (interactive) {
            ensure_interactive();
            while (buf[idx] && buf[idx] <= ' ') {
                ++idx;
                ensure_interactive();
            }
            return buf[idx++];
        }
        ensure();
        while (buf[idx] && buf[idx] <= ' ') {
            ++idx;
            ensure();
        }
        return buf[idx++];
    }

    template<class T, typename enable_if<is_integral<T>::value, int>::type = 0>
    void read(T &x) {
        if (interactive) {
            char c = skip();
            bool neg = false;
            if constexpr (is_signed<T>::value) {
                if (c == '-') {
                    neg = true;
                    ensure_interactive();
                    c = buf[idx++];
                }
            }
            x = 0;
            while (c >= '0') {
                x = x * 10 + (c & 15);
                ensure_interactive();
                c = buf[idx++];
            }
            if constexpr (is_signed<T>::value) {
                if (neg) x = -x;
            }
            return;
        }
        char c = skip();
        bool neg = false;
        if constexpr (is_signed<T>::value) {
            if (c == '-') {
                neg = true;
                c = buf[idx++];
            }
        }
        x = 0;
        while (c >= '0') {
            x = x * 10 + (c & 15);
            c = buf[idx++];
        }
        if constexpr (is_signed<T>::value) {
            if (neg) x = -x;
        }
    }

    template<class T, typename enable_if<!is_integral<T>::value && !is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value && has_fastio_value<T>::value, int>::type = 0>
    void read(T &x) {
        long long v;
        read(v);
        x = T(v);
    }

    template<class Head, class Next, class... Tail>
    void read(Head &head, Next &next, Tail &...tail) {
        read(head);
        read(next, tail...);
    }

    template<class T, class U>
    void read(pair<T, U> &p) {
        read(p.first, p.second);
    }

    template<class T, typename enable_if<is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value, int>::type = 0>
    void read(T &a) {
        for (auto &x : a) read(x);
    }

    void read(char &c) {
        c = skip();
    }

    void read(string &s) {
        s.clear();
        if (interactive) {
            ensure_interactive();
            while (buf[idx] && buf[idx] <= ' ') {
                ++idx;
                ensure_interactive();
            }
            while (true) {
                int start = idx;
                while (idx < size && buf[idx] > ' ') ++idx;
                s.append(buf + start, idx - start);
                if (idx < size) break;
                load();
                if (size == 0) break;
            }
            if (idx < size) ++idx;
            return;
        }
        ensure();
        while (buf[idx] && buf[idx] <= ' ') {
            ++idx;
            ensure();
        }
        while (true) {
            int start = idx;
            while (idx < size && buf[idx] > ' ') ++idx;
            s.append(buf + start, idx - start);
            if (idx < size) break;
            load();
        }
        if (idx < size) ++idx;
    }
};

struct Printer {
    static constexpr int BUFSIZE = 1 << 17;
    static constexpr int OFFSET = 64;
    char buf[BUFSIZE];
    int idx;
    bool interactive;
    inline static constexpr FastIoDigitTable table{};

    Printer() : idx(0), interactive(isatty(fileno(stdout))) {}
    ~Printer() { flush(); }

    inline void flush() {
        if (idx) {
            fwrite(buf, 1, idx, stdout);
            idx = 0;
        }
    }

    inline void pc(char c) {
        if (idx > BUFSIZE - OFFSET) flush();
        buf[idx++] = c;
        if (interactive && c == '\n') flush();
    }

    inline void print_range(const char *s, size_t n) {
        size_t pos = 0;
        while (pos < n) {
            if (idx == BUFSIZE) flush();
            size_t chunk = min(n - pos, (size_t)(BUFSIZE - idx));
            memcpy(buf + idx, s + pos, chunk);
            idx += (int)chunk;
            pos += chunk;
        }
    }

    void print(const char *s) {
        print_range(s, strlen(s));
    }

    void print(const string &s) {
        print_range(s.data(), s.size());
    }

    void print(char c) {
        pc(c);
    }

    void print(bool b) {
        pc(char('0' + (b ? 1 : 0)));
    }

    template<class T, typename enable_if<is_integral<T>::value && !is_same<T, bool>::value, int>::type = 0>
    void print(T x) {
        if (idx > BUFSIZE - 100) flush();
        using U = typename make_unsigned<T>::type;
        U y;
        if constexpr (is_signed<T>::value) {
            if (x < 0) {
                buf[idx++] = '-';
                y = U(0) - static_cast<U>(x);
            } else {
                y = static_cast<U>(x);
            }
        } else {
            y = x;
        }
        if (y == 0) {
            buf[idx++] = '0';
            return;
        }
        static constexpr int TMP_SIZE = sizeof(U) * 10 / 4;
        char tmp[TMP_SIZE];
        int pos = TMP_SIZE;
        while (y >= 10000) {
            pos -= 4;
            memcpy(tmp + pos, table.num + (y % 10000) * 4, 4);
            y /= 10000;
        }
        if (y >= 1000) {
            memcpy(buf + idx, table.num + (y << 2), 4);
            idx += 4;
        } else if (y >= 100) {
            memcpy(buf + idx, table.num + (y << 2) + 1, 3);
            idx += 3;
        } else if (y >= 10) {
            unsigned q = (unsigned(y) * 205) >> 11;
            buf[idx] = char('0' + q);
            buf[idx + 1] = char('0' + (unsigned(y) - q * 10));
            idx += 2;
        } else {
            buf[idx++] = char('0' + y);
        }
        memcpy(buf + idx, tmp + pos, TMP_SIZE - pos);
        idx += TMP_SIZE - pos;
    }

    template<class T, typename enable_if<!is_integral<T>::value && !is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value && has_fastio_value<T>::value, int>::type = 0>
    void print(const T &x) {
        print(x.value());
    }

    template<class T, typename enable_if<is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value, int>::type = 0>
    void print(const T &a) {
        bool first = true;
        for (auto &&x : a) {
            if (!first) pc(' ');
            first = false;
            print(x);
        }
    }

    template<class T>
    void println(const T &x) {
        print(x);
        pc('\n');
    }

    template<class Head, class... Tail>
    void println(const Head &head, const Tail &...tail) {
        print(head);
        ((pc(' '), print(tail)), ...);
        pc('\n');
    }

    void println() {
        pc('\n');
    }
};

template<class T>
Scanner &operator>>(Scanner &in, T &x) {
    in.read(x);
    return in;
}

template<class T>
Printer &operator<<(Printer &out, const T &x) {
    out.print(x);
    return out;
}

/**
 * @brief 高速入出力(Fast IO)
 */
#line 1 "graph/chu_liu_edmonds.cpp"
template<class T>
struct ChuLiuEdmonds {
    struct Edge {
        int from, to;
        T cost;
    };

    struct Result {
        bool exists;
        T cost;
        vector<int> parent;
        vector<int> edge_id;
    };

    struct UnionFind {
        vector<int> p;

        explicit UnionFind(int n) : p(n, -1) {}

        int root(int x) {
            if (p[x] < 0) return x;
            return p[x] = root(p[x]);
        }

        bool unite(int a, int b) {
            a = root(a);
            b = root(b);
            if (a == b) return false;
            if (p[a] > p[b]) swap(a, b);
            p[a] += p[b];
            p[b] = a;
            return true;
        }
    };

    struct SkewHeapNode {
        T key, lazy;
        int idx;
        SkewHeapNode *l, *r;

        SkewHeapNode(T key, int idx) : key(key), lazy(0), idx(idx), l(nullptr), r(nullptr) {}
    };

    int n, root;
    vector<Edge> edges;

    explicit ChuLiuEdmonds(int n, int root) : n(n), root(root) {}

    int add_edge(int from, int to, T cost) {
        edges.push_back({from, to, cost});
        return (int)edges.size() - 1;
    }

    static void push(SkewHeapNode *node) {
        if (node == nullptr || node->lazy == T(0)) return;
        if (node->l != nullptr) {
            node->l->key += node->lazy;
            node->l->lazy += node->lazy;
        }
        if (node->r != nullptr) {
            node->r->key += node->lazy;
            node->r->lazy += node->lazy;
        }
        node->lazy = T(0);
    }

    static SkewHeapNode* meld(SkewHeapNode *a, SkewHeapNode *b) {
        if (a == nullptr) return b;
        if (b == nullptr) return a;
        if (b->key < a->key) swap(a, b);
        push(a);
        a->r = meld(a->r, b);
        swap(a->l, a->r);
        return a;
    }

    static SkewHeapNode* pop(SkewHeapNode *a) {
        push(a);
        return meld(a->l, a->r);
    }

    Result solve() const {
        vector<SkewHeapNode> nodes;
        nodes.reserve(edges.size());
        vector<SkewHeapNode*> come(n, nullptr);
        for (int i = 0; i < (int)edges.size(); ++i) {
            nodes.emplace_back(edges[i].cost, i);
            come[edges[i].to] = meld(come[edges[i].to], &nodes.back());
        }

        UnionFind uf(n);
        vector<int> used(n, -1), from(n, -1), stem(n, -1);
        vector<T> from_cost(n, T(0));
        vector<int> parent_edge(edges.size(), -1), order;
        used[root] = root;
        T total = T(0);

        for (int start = 0; start < n; ++start) {
            if (used[start] != -1) continue;
            int cur = start;
            vector<int> child_edges;
            int cycle = 0;
            while (used[cur] == -1 || used[cur] == start) {
                used[cur] = start;
                while (come[cur] != nullptr && uf.root(edges[come[cur]->idx].from) == cur) {
                    come[cur] = pop(come[cur]);
                }
                if (come[cur] == nullptr) return {false, T(0), {}, {}};
                int idx = come[cur]->idx;
                int src = uf.root(edges[idx].from);
                T cost = come[cur]->key;
                come[cur] = pop(come[cur]);

                from[cur] = src;
                from_cost[cur] = cost;
                if (stem[cur] == -1) stem[cur] = idx;
                total += cost;
                order.push_back(idx);
                while (cycle) {
                    parent_edge[child_edges.back()] = idx;
                    child_edges.pop_back();
                    --cycle;
                }
                child_edges.push_back(idx);

                if (used[src] == start) {
                    int p = cur;
                    do {
                        if (come[p] != nullptr) {
                            come[p]->key -= from_cost[p];
                            come[p]->lazy -= from_cost[p];
                        }
                        if (p != cur) {
                            int pv = p;
                            int cv = cur;
                            uf.unite(pv, cv);
                            cur = uf.root(cv);
                            come[cur] = meld(come[pv], come[cv]);
                        }
                        p = uf.root(from[p]);
                        ++cycle;
                    } while (p != cur);
                } else {
                    cur = src;
                }
            }
        }

        vector<int> used_edge(edges.size(), 0), edge_id(n, -1), parent(n, -1);
        parent[root] = root;
        for (int i = (int)order.size() - 1; i >= 0; --i) {
            int idx = order[i];
            if (used_edge[idx]) continue;
            int v = edges[idx].to;
            edge_id[v] = idx;
            parent[v] = edges[idx].from;
            int x = stem[v];
            while (x != idx) {
                used_edge[x] = 1;
                x = parent_edge[x];
            }
        }
        return {true, total, parent, edge_id};
    }
};

/**
 * @brief 最小全域有向木(Chu-Liu/Edmonds)
 */
#line 14 "test/yosupo_directedmst.test.cpp"

int main() {
    Scanner in;
    Printer out;
    int n, m, r;
    in.read(n, m, r);
    ChuLiuEdmonds<ll> dmst(n, r);
    for (int i = 0; i < m; ++i) {
        int a, b;
        ll c;
        in.read(a, b, c);
        dmst.add_edge(a, b, c);
    }
    auto res = dmst.solve();
    if (!res.exists) return 0;
    out.println(res.cost);
    for (int i = 0; i < n; ++i) {
        if (i) out.print(' ');
        out.print(res.parent[i]);
    }
    out.println();
    return 0;
}

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