Luzhiled's Library

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:heavy_check_mark: test/verify/yosupo-directedmst.test.cpp

Depends on

Code

// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/directedmst
// clang-format on

#include <iostream>
#include <vector>

#include "../../graph/mst/directed-mst.hpp"

using namespace std;

int main() {
  int n, m, r;
  cin >> n >> m >> r;
  Edges<long long> edges;
  for (int i = 0; i < m; ++i) {
    int a, b;
    long long w;
    cin >> a >> b >> w;
    edges.emplace_back(a, b, w);
  }
  auto res = directed_mst(n, r, edges);
  cout << res.cost << "\n";
  vector<int> ans(n);
  ans[r] = r;
  for (auto& e : res.edges) {
    ans[e.to] = e.from;
  }
  for (int i = 0; i < n; i++) {
    if (i > 0) cout << " ";
    cout << ans[i];
  }
  cout << "\n";
}

#line 1 "test/verify/yosupo-directedmst.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/directedmst
// clang-format on

#include <iostream>
#include <vector>

#line 2 "graph/mst/directed-mst.hpp"

#line 4 "graph/mst/directed-mst.hpp"

#line 2 "structure/heap/skew-heap.hpp"

#include <cassert>
#include <utility>

/**
 * @brief Skew-Heap
 */
template <typename T, bool isMin = true>
struct SkewHeap {
  struct Node {
    T key, lazy;
    Node *l, *r;
    int idx;

    explicit Node(const T& key, int idx)
        : key(key), lazy(0), l(nullptr), r(nullptr), idx(idx) {}
  };

  SkewHeap() = default;

  Node* alloc(const T& key, int idx = -1) { return new Node(key, idx); }

  Node* propagate(Node* t) {
    if (t && t->lazy != 0) {
      if (t->l) t->l->lazy += t->lazy;
      if (t->r) t->r->lazy += t->lazy;
      t->key += t->lazy;
      t->lazy = 0;
    }
    return t;
  }

  Node* meld(Node* x, Node* y) {
    propagate(x), propagate(y);
    if (!x || !y) return x ? x : y;
    if ((x->key < y->key) ^ isMin) std::swap(x, y);
    x->r = meld(y, x->r);
    std::swap(x->l, x->r);
    return x;
  }

  Node* push(Node* t, const T& key, int idx = -1) {
    return meld(t, alloc(key, idx));
  }

  Node* pop(Node* t) {
    assert(t != nullptr);
    return meld(t->l, t->r);
  }

  Node* add(Node* t, const T& lazy) {
    if (t) {
      t->lazy += lazy;
      propagate(t);
    }
    return t;
  }

  Node* make_root() { return nullptr; }
};
#line 2 "graph/graph-template.hpp"

#include <cstddef>
#line 6 "graph/graph-template.hpp"

template <typename T = int>
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1)
      : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template <typename T = int>
struct Graph {
  std::vector<std::vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  std::size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false,
            bool directed = false) {
    for (int i = 0; i < M; i++) {
      int a, b;
      std::cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) std::cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline std::vector<Edge<T> >& operator[](const int& k) { return g[k]; }

  inline const std::vector<Edge<T> >& operator[](const int& k) const {
    return g[k];
  }
};

template <typename T = int>
using Edges = std::vector<Edge<T> >;
#line 7 "graph/mst/directed-mst.hpp"

/**
 * @brief Directed MST(最小有向全域木)
 *
 */
template <typename T>
struct MinimumSpanningTree {
  T cost;
  Edges<T> edges;
};

template <typename T>
MinimumSpanningTree<T> directed_mst(int V, int root, Edges<T> edges) {
  for (int i = 0; i < V; ++i) {
    if (i != root) edges.emplace_back(i, root, 0);
  }

  int x = 0;
  std::vector<int> par(2 * V, -1), vis(par), link(par);

  using Heap = SkewHeap<T, true>;
  using Node = typename Heap::Node;

  Heap heap;
  std::vector<Node*> ins(2 * V, heap.make_root());

  for (int i = 0; i < (int)edges.size(); i++) {
    auto& e = edges[i];
    ins[e.to] = heap.push(ins[e.to], e.cost, i);
  }
  std::vector<int> st;
  auto go = [&](int x) {
    x = edges[ins[x]->idx].from;
    while (link[x] != -1) {
      st.emplace_back(x);
      x = link[x];
    }
    for (auto& p : st) {
      link[p] = x;
    }
    st.clear();
    return x;
  };
  for (int i = V; ins[x]; i++) {
    for (; vis[x] == -1; x = go(x)) vis[x] = 0;
    for (; x != i; x = go(x)) {
      auto w = ins[x]->key;
      auto v = heap.pop(ins[x]);
      v = heap.add(v, -w);
      ins[i] = heap.meld(ins[i], v);
      par[x] = i;
      link[x] = i;
    }
    for (; ins[x] && go(x) == x; ins[x] = heap.pop(ins[x]));
  }
  T cost = 0;
  Edges<T> ans;
  for (int i = root; i != -1; i = par[i]) {
    vis[i] = 1;
  }
  for (int i = x; i >= 0; i--) {
    if (vis[i] == 1) continue;
    cost += edges[ins[i]->idx].cost;
    ans.emplace_back(edges[ins[i]->idx]);
    for (int j = edges[ins[i]->idx].to; j != -1 && vis[j] == 0; j = par[j]) {
      vis[j] = 1;
    }
  }
  return {cost, ans};
}
#line 9 "test/verify/yosupo-directedmst.test.cpp"

using namespace std;

int main() {
  int n, m, r;
  cin >> n >> m >> r;
  Edges<long long> edges;
  for (int i = 0; i < m; ++i) {
    int a, b;
    long long w;
    cin >> a >> b >> w;
    edges.emplace_back(a, b, w);
  }
  auto res = directed_mst(n, r, edges);
  cout << res.cost << "\n";
  vector<int> ans(n);
  ans[r] = r;
  for (auto& e : res.edges) {
    ans[e.to] = e.from;
  }
  for (int i = 0; i < n; i++) {
    if (i > 0) cout << " ";
    cout << ans[i];
  }
  cout << "\n";
}

Test cases

Env Name Status Elapsed Memory
g++ example_00 :heavy_check_mark: AC 2 ms 4 MB
g++ example_01 :heavy_check_mark: AC 2 ms 4 MB
g++ max_random_00 :heavy_check_mark: AC 228 ms 55 MB
g++ max_random_01 :heavy_check_mark: AC 225 ms 55 MB
g++ max_random_02 :heavy_check_mark: AC 228 ms 56 MB
g++ max_random_03 :heavy_check_mark: AC 246 ms 55 MB
g++ max_random_04 :heavy_check_mark: AC 243 ms 55 MB
g++ random_00 :heavy_check_mark: AC 154 ms 38 MB
g++ random_01 :heavy_check_mark: AC 191 ms 48 MB
g++ random_02 :heavy_check_mark: AC 176 ms 29 MB
g++ random_03 :heavy_check_mark: AC 221 ms 51 MB
g++ random_04 :heavy_check_mark: AC 106 ms 18 MB
clang++ example_00 :heavy_check_mark: AC 2 ms 4 MB
clang++ example_01 :heavy_check_mark: AC 2 ms 4 MB
clang++ max_random_00 :heavy_check_mark: AC 231 ms 55 MB
clang++ max_random_01 :heavy_check_mark: AC 230 ms 55 MB
clang++ max_random_02 :heavy_check_mark: AC 240 ms 56 MB
clang++ max_random_03 :heavy_check_mark: AC 230 ms 55 MB
clang++ max_random_04 :heavy_check_mark: AC 235 ms 55 MB
clang++ random_00 :heavy_check_mark: AC 166 ms 38 MB
clang++ random_01 :heavy_check_mark: AC 195 ms 47 MB
clang++ random_02 :heavy_check_mark: AC 191 ms 30 MB
clang++ random_03 :heavy_check_mark: AC 230 ms 51 MB
clang++ random_04 :heavy_check_mark: AC 115 ms 18 MB
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