Yen's algorithm
(Mylib/Graph/ShortestPath/yen_algorithm.cpp)

• View this file on GitHub
• Last update: 2021-04-23 23:44:44+09:00
• Link: View error logs on GitHub Actions

Operations

Requirements

Notes

Problems

References

• https://qiita.com/nariaki3551/items/821dc6ffdc552d3d5f22#%E7%AC%AC1%E6%9C%80%E7%9F%AD%E8%B7%AF

Depends on

• Basic graph (Mylib/Graph/Template/graph.cpp)

Verified with

• test/yukicoder/1069/main.test.cpp

Code

#pragma once
#include <functional>
#include <optional>
#include <queue>
#include <utility>
#include <vector>
#include "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  namespace yen_algorithm_impl {
    template <typename T>
    auto shortest_path(
        const graph<T> &g,
        int from,
        int t,
        const std::vector<bool> &usable,
        const std::vector<std::vector<bool>> &valid) {
      using Path = std::pair<T, std::vector<int>>;
      using P    = std::pair<T, int>;

      const int N = g.size();
      std::vector<bool> visited(N, false);
      std::vector<std::optional<T>> dist(N);
      std::vector<std::pair<int, int>> restore(N);

      std::priority_queue<P, std::vector<P>, std::greater<P>> pq;

      dist[from] = 0;
      pq.emplace(0, from);

      while (not pq.empty()) {
        auto [d, i] = pq.top();
        pq.pop();

        if (visited[i]) continue;
        visited[i] = true;

        for (int k = 0; k < (int) g[i].size(); ++k) {
          if (not valid[i][k] or not usable[g[i][k].to]) continue;
          auto &e = g[i][k];

          if (not dist[e.to] or *dist[e.to] > d + e.cost) {
            dist[e.to]    = d + e.cost;
            restore[e.to] = std::make_pair(i, k);
            if (not visited[e.to]) pq.emplace(*dist[e.to], e.to);
          }
        }
      }

      std::optional<Path> ret;

      if (dist[t]) {
        std::vector<int> p;

        int cur = t;
        while (cur != from) {
          auto [i, j] = restore[cur];
          p.push_back(j);
          cur = i;
        }

        std::reverse(p.begin(), p.end());

        ret = std::make_pair(*dist[t], p);
      }

      return ret;
    }
  }  // namespace yen_algorithm_impl

  template <typename T>
  auto yen_algorithm(const graph<T> &g, int s, int t, int K) {
    using Path = std::pair<T, std::vector<int>>;

    const int N = g.size();

    std::vector<std::vector<bool>> valid(N);
    std::vector<std::optional<Path>> result(K);
    std::priority_queue<Path, std::vector<Path>, std::greater<Path>> stock;

    for (int i = 0; i < N; ++i) {
      valid[i].assign(g[i].size(), true);
    }

    for (int i = 0; i < K; ++i) {
      if (i == 0) {
        std::vector<bool> usable(N, true);
        if (auto res = yen_algorithm_impl::shortest_path(g, s, t, usable, valid); res) stock.push(*res);
      } else {
        std::vector<int> prev_path;

        {
          int cur = s;
          for (auto u : result[i - 1]->second) {
            prev_path.push_back(cur);
            cur = g[cur][u].to;
          }
          prev_path.push_back(t);
        }

        std::vector<bool> check(i, true);
        std::vector<bool> usable(N, true);

        for (int k = 0; k < (int) prev_path.size() - 1; ++k) {
          const int u = prev_path[k];

          for (int j = 0; j < i; ++j) {
            if (check[j]) {
              valid[prev_path[k]][result[j]->second[k]] = false;
            }
          }

          if (auto res = yen_algorithm_impl::shortest_path(g, u, t, usable, valid); res) {
            auto [c, p] = *res;

            std::vector<int> temp;
            for (int j = 0; j < k; ++j) {
              int v = result[i - 1]->second[j];

              c += g[prev_path[j]][v].cost;
              temp.push_back(v);
            }

            temp.insert(temp.end(), p.begin(), p.end());
            stock.emplace(c, temp);
          }

          usable[u] = false;

          for (int j = 0; j < i; ++j) {
            if (check[j]) {
              valid[prev_path[k]][result[j]->second[k]] = true;
            }
          }

          for (int j = 0; j < i; ++j) {
            if (check[j]) {
              if (prev_path[k + 1] != g[prev_path[k]][result[j]->second[k]].to) {
                check[j] = false;
              }
            }
          }
        }
      }

      if (stock.empty()) break;

      result[i] = stock.top();
      stock.pop();

      while (not stock.empty() and stock.top() == result[i]) {
        stock.pop();
      }
    }

    return result;
  }
}  // namespace haar_lib

#line 2 "Mylib/Graph/ShortestPath/yen_algorithm.cpp"
#include <functional>
#include <optional>
#include <queue>
#include <utility>
#include <vector>
#line 2 "Mylib/Graph/Template/graph.cpp"
#include <iostream>
#line 4 "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  template <typename T>
  struct edge {
    int from, to;
    T cost;
    int index = -1;
    edge() {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
    edge(int from, int to, T cost, int index) : from(from), to(to), cost(cost), index(index) {}
  };

  template <typename T>
  struct graph {
    using weight_type = T;
    using edge_type   = edge<T>;

    std::vector<std::vector<edge<T>>> data;

    auto& operator[](size_t i) { return data[i]; }
    const auto& operator[](size_t i) const { return data[i]; }

    auto begin() const { return data.begin(); }
    auto end() const { return data.end(); }

    graph() {}
    graph(int N) : data(N) {}

    bool empty() const { return data.empty(); }
    int size() const { return data.size(); }

    void add_edge(int i, int j, T w, int index = -1) {
      data[i].emplace_back(i, j, w, index);
    }

    void add_undirected(int i, int j, T w, int index = -1) {
      add_edge(i, j, w, index);
      add_edge(j, i, w, index);
    }

    template <size_t I, bool DIRECTED = true, bool WEIGHTED = true>
    void read(int M) {
      for (int i = 0; i < M; ++i) {
        int u, v;
        std::cin >> u >> v;
        u -= I;
        v -= I;
        T w = 1;
        if (WEIGHTED) std::cin >> w;
        if (DIRECTED)
          add_edge(u, v, w, i);
        else
          add_undirected(u, v, w, i);
      }
    }
  };

  template <typename T>
  using tree = graph<T>;
}  // namespace haar_lib
#line 8 "Mylib/Graph/ShortestPath/yen_algorithm.cpp"

namespace haar_lib {
  namespace yen_algorithm_impl {
    template <typename T>
    auto shortest_path(
        const graph<T> &g,
        int from,
        int t,
        const std::vector<bool> &usable,
        const std::vector<std::vector<bool>> &valid) {
      using Path = std::pair<T, std::vector<int>>;
      using P    = std::pair<T, int>;

      const int N = g.size();
      std::vector<bool> visited(N, false);
      std::vector<std::optional<T>> dist(N);
      std::vector<std::pair<int, int>> restore(N);

      std::priority_queue<P, std::vector<P>, std::greater<P>> pq;

      dist[from] = 0;
      pq.emplace(0, from);

      while (not pq.empty()) {
        auto [d, i] = pq.top();
        pq.pop();

        if (visited[i]) continue;
        visited[i] = true;

        for (int k = 0; k < (int) g[i].size(); ++k) {
          if (not valid[i][k] or not usable[g[i][k].to]) continue;
          auto &e = g[i][k];

          if (not dist[e.to] or *dist[e.to] > d + e.cost) {
            dist[e.to]    = d + e.cost;
            restore[e.to] = std::make_pair(i, k);
            if (not visited[e.to]) pq.emplace(*dist[e.to], e.to);
          }
        }
      }

      std::optional<Path> ret;

      if (dist[t]) {
        std::vector<int> p;

        int cur = t;
        while (cur != from) {
          auto [i, j] = restore[cur];
          p.push_back(j);
          cur = i;
        }

        std::reverse(p.begin(), p.end());

        ret = std::make_pair(*dist[t], p);
      }

      return ret;
    }
  }  // namespace yen_algorithm_impl

  template <typename T>
  auto yen_algorithm(const graph<T> &g, int s, int t, int K) {
    using Path = std::pair<T, std::vector<int>>;

    const int N = g.size();

    std::vector<std::vector<bool>> valid(N);
    std::vector<std::optional<Path>> result(K);
    std::priority_queue<Path, std::vector<Path>, std::greater<Path>> stock;

    for (int i = 0; i < N; ++i) {
      valid[i].assign(g[i].size(), true);
    }

    for (int i = 0; i < K; ++i) {
      if (i == 0) {
        std::vector<bool> usable(N, true);
        if (auto res = yen_algorithm_impl::shortest_path(g, s, t, usable, valid); res) stock.push(*res);
      } else {
        std::vector<int> prev_path;

        {
          int cur = s;
          for (auto u : result[i - 1]->second) {
            prev_path.push_back(cur);
            cur = g[cur][u].to;
          }
          prev_path.push_back(t);
        }

        std::vector<bool> check(i, true);
        std::vector<bool> usable(N, true);

        for (int k = 0; k < (int) prev_path.size() - 1; ++k) {
          const int u = prev_path[k];

          for (int j = 0; j < i; ++j) {
            if (check[j]) {
              valid[prev_path[k]][result[j]->second[k]] = false;
            }
          }

          if (auto res = yen_algorithm_impl::shortest_path(g, u, t, usable, valid); res) {
            auto [c, p] = *res;

            std::vector<int> temp;
            for (int j = 0; j < k; ++j) {
              int v = result[i - 1]->second[j];

              c += g[prev_path[j]][v].cost;
              temp.push_back(v);
            }

            temp.insert(temp.end(), p.begin(), p.end());
            stock.emplace(c, temp);
          }

          usable[u] = false;

          for (int j = 0; j < i; ++j) {
            if (check[j]) {
              valid[prev_path[k]][result[j]->second[k]] = true;
            }
          }

          for (int j = 0; j < i; ++j) {
            if (check[j]) {
              if (prev_path[k + 1] != g[prev_path[k]][result[j]->second[k]].to) {
                check[j] = false;
              }
            }
          }
        }
      }

      if (stock.empty()) break;

      result[i] = stock.top();
      stock.pop();

      while (not stock.empty() and stock.top() == result[i]) {
        stock.pop();
      }
    }

    return result;
  }
}  // namespace haar_lib

Back to top page