Shortest Nonzero Path(群ラベル制約付き単一始点最短路) (graph/shortest-path/shortest-nonzero-path.hpp)

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• Last update: 2024-04-27 01:27:28+09:00
• Include: #include "graph/shortest-path/shortest-nonzero-path.hpp"

Verified with

• test/verify/yukicoder-1602.test.cpp

Code

/**
 * @brief Shortest Nonzero Path(群ラベル制約付き単一始点最短路)
 */
template <typename T, typename S, typename F>
struct ShortestNonzeroPath {
 private:
  constexpr static T INF = numeric_limits<T>::max();
  struct edge {
    int to;
    T cost;
    S label;
  };
  vector<vector<edge> > g;
  F f;
  vector<int> uf;

  int find_uf(int k) {
    if (uf[k] == -1) return k;
    return uf[k] = find_uf(uf[k]);
  }

  void unite_uf(int r, int c) { uf[c] = r; }

 public:
  explicit ShortestNonzeroPath(int n, const F &f) : g(n), f(f) {}

  void add_undirected_edge(int u, int v, const T &cost, const S &label) {
    add_directed_edge(u, v, cost, label);
    add_directed_edge(v, u, cost, label);
  }

  void add_directed_edge(int u, int v, const T &cost, const S &label) {
    g[u].emplace_back((edge){v, cost, label});
  }

  struct SP {
    vector<T> dist;
    vector<int> depth, parent;
    vector<S> label;
  };

  SP dijkstra(int s) {
    int n = (int)g.size();
    using pi = pair<T, int>;
    vector<T> dist(n, INF);
    vector<int> depth(n, -1), parent(n, -1);
    vector<S> label(n, S());
    priority_queue<pi, vector<pi>, greater<> > que;
    dist[s] = T(0);
    depth[s] = 0;
    que.emplace(0, s);
    while (not que.empty()) {
      T cost;
      int u;
      tie(cost, u) = que.top();
      que.pop();
      if (dist[u] < cost) {
        continue;
      }
      for (auto e : g[u]) {
        if (cost + e.cost < dist[e.to]) {
          dist[e.to] = cost + e.cost;
          depth[e.to] = depth[u] + 1;
          parent[e.to] = u;
          label[e.to] = f(label[u], e.label);
          que.emplace(dist[e.to], e.to);
        }
      }
    }
    return {dist, depth, parent, label};
  }

  vector<T> build(int s) {
    int n = (int)g.size();
    auto sp = dijkstra(s);

    uf.assign(n, -1);
    using pi = tuple<T, int, int>;
    priority_queue<pi, vector<pi>, greater<> > que;
    for (int u = 0; u < n; u++) {
      if (sp.dist[u] != INF) {
        for (int i = 0; i < (int)g[u].size(); i++) {
          auto &e = g[u][i];
          if (u < e.to and f(sp.label[u], e.label) != sp.label[e.to]) {
            que.emplace(sp.dist[u] + sp.dist[e.to] + e.cost, u, i);
          }
        }
      }
    }
    vector<T> dist(n, INF);
    vector<int> bs;
    while (not que.empty()) {
      T cost;
      int u0, i;
      tie(cost, u0, i) = que.top();
      que.pop();
      int v0 = g[u0][i].to;
      int u = find_uf(u0), v = find_uf(v0);
      while (u != v) {
        if (sp.depth[u] > sp.depth[v]) {
          bs.emplace_back(u);
          u = find_uf(sp.parent[u]);
        } else {
          bs.emplace_back(v);
          v = find_uf(sp.parent[v]);
        }
      }
      for (auto &x : bs) {
        unite_uf(u, x);
        dist[x] = cost - sp.dist[x];
        for (int j = 0; j < (int)g[x].size(); j++) {
          auto &e = g[x][j];
          if (f(sp.label[x], e.label) == sp.label[e.to]) {
            que.emplace(dist[x] + sp.dist[e.to] + e.cost, x, j);
          }
        }
      }
      bs.clear();
    }
    for (int i = 0; i < n; i++) {
      if (sp.label[i] != S() and sp.dist[i] < dist[i]) {
        dist[i] = sp.dist[i];
      }
    }
    return dist;
  }
};

template <typename T, typename S, typename F>
ShortestNonzeroPath<T, S, F> get_shortest_nonzero_path(int N, const F &f) {
  return ShortestNonzeroPath<T, S, F>{N, f};
}

#line 1 "graph/shortest-path/shortest-nonzero-path.hpp"
/**
 * @brief Shortest Nonzero Path(群ラベル制約付き単一始点最短路)
 */
template <typename T, typename S, typename F>
struct ShortestNonzeroPath {
 private:
  constexpr static T INF = numeric_limits<T>::max();
  struct edge {
    int to;
    T cost;
    S label;
  };
  vector<vector<edge> > g;
  F f;
  vector<int> uf;

  int find_uf(int k) {
    if (uf[k] == -1) return k;
    return uf[k] = find_uf(uf[k]);
  }

  void unite_uf(int r, int c) { uf[c] = r; }

 public:
  explicit ShortestNonzeroPath(int n, const F &f) : g(n), f(f) {}

  void add_undirected_edge(int u, int v, const T &cost, const S &label) {
    add_directed_edge(u, v, cost, label);
    add_directed_edge(v, u, cost, label);
  }

  void add_directed_edge(int u, int v, const T &cost, const S &label) {
    g[u].emplace_back((edge){v, cost, label});
  }

  struct SP {
    vector<T> dist;
    vector<int> depth, parent;
    vector<S> label;
  };

  SP dijkstra(int s) {
    int n = (int)g.size();
    using pi = pair<T, int>;
    vector<T> dist(n, INF);
    vector<int> depth(n, -1), parent(n, -1);
    vector<S> label(n, S());
    priority_queue<pi, vector<pi>, greater<> > que;
    dist[s] = T(0);
    depth[s] = 0;
    que.emplace(0, s);
    while (not que.empty()) {
      T cost;
      int u;
      tie(cost, u) = que.top();
      que.pop();
      if (dist[u] < cost) {
        continue;
      }
      for (auto e : g[u]) {
        if (cost + e.cost < dist[e.to]) {
          dist[e.to] = cost + e.cost;
          depth[e.to] = depth[u] + 1;
          parent[e.to] = u;
          label[e.to] = f(label[u], e.label);
          que.emplace(dist[e.to], e.to);
        }
      }
    }
    return {dist, depth, parent, label};
  }

  vector<T> build(int s) {
    int n = (int)g.size();
    auto sp = dijkstra(s);

    uf.assign(n, -1);
    using pi = tuple<T, int, int>;
    priority_queue<pi, vector<pi>, greater<> > que;
    for (int u = 0; u < n; u++) {
      if (sp.dist[u] != INF) {
        for (int i = 0; i < (int)g[u].size(); i++) {
          auto &e = g[u][i];
          if (u < e.to and f(sp.label[u], e.label) != sp.label[e.to]) {
            que.emplace(sp.dist[u] + sp.dist[e.to] + e.cost, u, i);
          }
        }
      }
    }
    vector<T> dist(n, INF);
    vector<int> bs;
    while (not que.empty()) {
      T cost;
      int u0, i;
      tie(cost, u0, i) = que.top();
      que.pop();
      int v0 = g[u0][i].to;
      int u = find_uf(u0), v = find_uf(v0);
      while (u != v) {
        if (sp.depth[u] > sp.depth[v]) {
          bs.emplace_back(u);
          u = find_uf(sp.parent[u]);
        } else {
          bs.emplace_back(v);
          v = find_uf(sp.parent[v]);
        }
      }
      for (auto &x : bs) {
        unite_uf(u, x);
        dist[x] = cost - sp.dist[x];
        for (int j = 0; j < (int)g[x].size(); j++) {
          auto &e = g[x][j];
          if (f(sp.label[x], e.label) == sp.label[e.to]) {
            que.emplace(dist[x] + sp.dist[e.to] + e.cost, x, j);
          }
        }
      }
      bs.clear();
    }
    for (int i = 0; i < n; i++) {
      if (sp.label[i] != S() and sp.dist[i] < dist[i]) {
        dist[i] = sp.dist[i];
      }
    }
    return dist;
  }
};

template <typename T, typename S, typename F>
ShortestNonzeroPath<T, S, F> get_shortest_nonzero_path(int N, const F &f) {
  return ShortestNonzeroPath<T, S, F>{N, f};
}

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