test/verify/yosupo-k-shortest-walk.test.cpp

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• Last update: 2024-05-01 23:44:47+09:00
• Problem: https://judge.yosupo.jp/problem/k_shortest_walk

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)
• Dijkstra(単一始点最短路) (graph/shortest-path/dijkstra.hpp)
• K-Shortest-Walk (graph/shortest-path/k-shortest-walk.hpp)
• Leftist-Heap (structure/heap/leftist-heap.hpp)
• Persistent-Leftist-Heap (structure/heap/persistent-leftist-heap.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/k_shortest_walk

#include "../../template/template.hpp"

#include "../../graph/graph-template.hpp"
#include "../../graph/shortest-path/dijkstra.hpp"

#include "../../structure/heap/leftist-heap.hpp"
#include "../../structure/heap/persistent-leftist-heap.hpp"
#include "../../graph/shortest-path/k-shortest-walk.hpp"

int main() {
  int N, M, S, T, K;
  cin >> N >> M >> S >> T >> K;
  Graph< int64 > g(N);
  g.read(M, 0, true, true);
  auto ret = k_shortest_walk(g, S, T, K);
  for(int i = 0; i < K; i++) {
    if(i >= (int)ret.size()) cout << -1 << "\n";
    else cout << ret[i] << "\n";
  }
}

#line 1 "test/verify/yosupo-k-shortest-walk.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/k_shortest_walk

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-k-shortest-walk.test.cpp"

#line 2 "graph/graph-template.hpp"

/**
 * @brief Graph Template(グラフテンプレート)
 */
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 {
  vector<vector<Edge<T> > > g;
  int es;

  Graph() = default;

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

  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;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

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

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

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 2 "graph/shortest-path/dijkstra.hpp"

#line 4 "graph/shortest-path/dijkstra.hpp"

/**
 * @brief Dijkstra(単一始点最短路)
 *
 */
template <typename T>
struct ShortestPath {
  vector<T> dist;
  vector<int> from, id;
};

template <typename T>
ShortestPath<T> dijkstra(const Graph<T> &g, int s) {
  const auto INF = numeric_limits<T>::max();
  vector<T> dist(g.size(), INF);
  vector<int> from(g.size(), -1), id(g.size(), -1);
  using Pi = pair<T, int>;
  priority_queue<Pi, vector<Pi>, greater<> > que;
  dist[s] = 0;
  que.emplace(dist[s], s);
  while (!que.empty()) {
    T cost;
    int idx;
    tie(cost, idx) = que.top();
    que.pop();
    if (dist[idx] < cost) continue;
    for (auto &e : g[idx]) {
      auto next_cost = cost + e.cost;
      if (dist[e.to] <= next_cost) continue;
      dist[e.to] = next_cost;
      from[e.to] = idx;
      id[e.to] = e.idx;
      que.emplace(dist[e.to], e.to);
    }
  }
  return {dist, from, id};
}
#line 7 "test/verify/yosupo-k-shortest-walk.test.cpp"

#line 1 "structure/heap/leftist-heap.hpp"
/**
 * @brief Leftist-Heap
 */
template <typename T, bool isMin = true>
struct LeftistHeap {
  struct Node {
    Node *l, *r;
    int s;
    T key;
    int idx;

    explicit Node(const T &key, int idx)
        : key(key), s(1), l(nullptr), r(nullptr), idx(idx) {}
  };

  LeftistHeap() = default;

  virtual Node *clone(Node *t) { return t; }

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

  Node *meld(Node *a, Node *b) {
    if (!a || !b) return a ? a : b;
    if ((a->key < b->key) ^ isMin) swap(a, b);
    a = clone(a);
    a->r = meld(a->r, b);
    if (!a->l || a->l->s < a->r->s) swap(a->l, a->r);
    a->s = (a->r ? a->r->s : 0) + 1;
    return a;
  }

  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 *make_root() { return nullptr; }
};
#line 1 "structure/heap/persistent-leftist-heap.hpp"
/**
 * @brief Persistent-Leftist-Heap
 */
template <typename T, bool isMin = true>
struct PersistentLeftistHeap : LeftistHeap<T, isMin> {
  using Node = typename LeftistHeap<T, isMin>::Node;

  Node *clone(Node *t) override { return new Node(*t); }
};
#line 2 "graph/shortest-path/k-shortest-walk.hpp"

#line 4 "graph/shortest-path/k-shortest-walk.hpp"

/**
 * @brief K-Shortest-Walk
 *
 * @see https://qiita.com/hotman78/items/42534a01c4bd05ed5e1e
 */
template <typename T>
vector<T> k_shortest_walk(const Graph<T> &g, int s, int t, int k) {
  int N = (int)g.size();
  Graph<T> rg(N);
  for (int i = 0; i < N; i++) {
    for (auto &e : g[i]) rg.add_directed_edge(e.to, i, e.cost);
  }
  auto dist = dijkstra(rg, t);
  if (dist.from[s] == -1) return {};
  auto &p = dist.dist;
  vector<vector<int> > ch(N);
  for (int i = 0; i < N; i++) {
    if (dist.from[i] >= 0) ch[dist.from[i]].emplace_back(i);
  }
  using PHeap = PersistentLeftistHeap<T>;
  using Node = typename PHeap::Node;
  PHeap heap;
  vector<Node *> h(N, heap.make_root());
  {
    queue<int> que;
    que.emplace(t);
    while (!que.empty()) {
      int idx = que.front();
      que.pop();
      if (dist.from[idx] >= 0) {
        h[idx] = heap.meld(h[idx], h[dist.from[idx]]);
      }
      bool used = true;
      for (auto &e : g[idx]) {
        if (e.to != t && dist.from[e.to] == -1) continue;
        if (used && dist.from[idx] == e.to && p[e.to] + e.cost == p[idx]) {
          used = false;
          continue;
        }
        h[idx] = heap.push(h[idx], e.cost - p[idx] + p[e.to], e.to);
      }
      for (auto &to : ch[idx]) que.emplace(to);
    }
  }
  using pi = pair<T, Node *>;
  auto comp = [](const pi &x, const pi &y) { return x.first > y.first; };
  priority_queue<pi, vector<pi>, decltype(comp)> que(comp);
  Node *root = heap.make_root();
  root = heap.push(root, p[s], s);
  que.emplace(p[s], root);
  vector<T> ans;
  while (!que.empty()) {
    T cost;
    Node *cur;
    tie(cost, cur) = que.top();
    que.pop();
    ans.emplace_back(cost);
    if ((int)ans.size() == k) break;
    if (cur->l) que.emplace(cost + cur->l->key - cur->key, cur->l);
    if (cur->r) que.emplace(cost + cur->r->key - cur->key, cur->r);
    if (h[cur->idx]) que.emplace(cost + h[cur->idx]->key, h[cur->idx]);
  }
  return ans;
}
#line 11 "test/verify/yosupo-k-shortest-walk.test.cpp"

int main() {
  int N, M, S, T, K;
  cin >> N >> M >> S >> T >> K;
  Graph< int64 > g(N);
  g.read(M, 0, true, true);
  auto ret = k_shortest_walk(g, S, T, K);
  for(int i = 0; i < K; i++) {
    if(i >= (int)ret.size()) cout << -1 << "\n";
    else cout << ret[i] << "\n";
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	almost_path_00	AC	127 ms	39 MB
g++	almost_path_01	AC	101 ms	30 MB
g++	almost_path_02	AC	35 ms	13 MB
g++	dense_00	AC	224 ms	141 MB
g++	dense_01	AC	223 ms	140 MB
g++	example_00	AC	7 ms	4 MB
g++	loop_00	AC	265 ms	67 MB
g++	max_random_00	AC	163 ms	46 MB
g++	max_random_01	AC	167 ms	46 MB
g++	max_random_02	AC	162 ms	46 MB
g++	max_random_03	AC	154 ms	46 MB
g++	max_random_04	AC	155 ms	46 MB
g++	path_00	AC	238 ms	51 MB
g++	random_00	AC	141 ms	41 MB
g++	random_01	AC	159 ms	43 MB
g++	random_02	AC	36 ms	14 MB
g++	random_03	AC	99 ms	37 MB
g++	random_04	AC	61 ms	31 MB
g++	small_random_00	AC	7 ms	4 MB
g++	small_random_01	AC	6 ms	4 MB
g++	small_random_02	AC	6 ms	4 MB
g++	smallest_random_00	AC	6 ms	4 MB
g++	smallest_random_01	AC	6 ms	4 MB
g++	smallest_random_02	AC	6 ms	4 MB
g++	sparse_00	AC	27 ms	27 MB
g++	sparse_01	AC	28 ms	27 MB
clang++	almost_path_00	AC	124 ms	39 MB
clang++	almost_path_01	AC	99 ms	30 MB
clang++	almost_path_02	AC	34 ms	13 MB
clang++	dense_00	AC	228 ms	142 MB
clang++	dense_01	AC	224 ms	141 MB
clang++	example_00	AC	7 ms	4 MB
clang++	loop_00	AC	241 ms	66 MB
clang++	max_random_00	AC	152 ms	46 MB
clang++	max_random_01	AC	148 ms	46 MB
clang++	max_random_02	AC	151 ms	46 MB
clang++	max_random_03	AC	165 ms	46 MB
clang++	max_random_04	AC	149 ms	46 MB
clang++	path_00	AC	191 ms	51 MB
clang++	random_00	AC	131 ms	41 MB
clang++	random_01	AC	146 ms	43 MB
clang++	random_02	AC	36 ms	14 MB
clang++	random_03	AC	98 ms	37 MB
clang++	random_04	AC	61 ms	31 MB
clang++	small_random_00	AC	7 ms	4 MB
clang++	small_random_01	AC	6 ms	4 MB
clang++	small_random_02	AC	6 ms	4 MB
clang++	smallest_random_00	AC	6 ms	4 MB
clang++	smallest_random_01	AC	6 ms	4 MB
clang++	smallest_random_02	AC	6 ms	4 MB
clang++	sparse_00	AC	27 ms	27 MB
clang++	sparse_01	AC	27 ms	27 MB

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