Shortest-Path-Faster-Algorithm(単一始点最短路)
(graph/shortest-path/shortest-path-faster-algorithm.hpp)

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• Last update: 2022-09-11 00:53:50+09:00
• Include: #include "graph/shortest-path/shortest-path-faster-algorithm.hpp"

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)

Verified with

• test/verify/aoj-grl-1-b-2.test.cpp

Code

#pragma once

#include "../graph-template.hpp"

/**
 * @brief Shortest-Path-Faster-Algorithm(単一始点最短路)
 */
template< typename T >
vector< T > shortest_path_faster_algorithm(const Graph< T > &g, int s) {
  const auto INF = numeric_limits< T >::max();
  vector< T > dist(g.size(), INF);
  vector< int > pending(g.size(), 0), times(g.size(), 0);
  queue< int > que;

  que.emplace(s);
  pending[s] = true;
  ++times[s];
  dist[s] = 0;

  while(!que.empty()) {
    int p = que.front();
    que.pop();
    pending[p] = false;
    for(auto &e : g[p]) {
      T next_cost = dist[p] + e.cost;
      if(next_cost >= dist[e.to]) continue;
      dist[e.to] = next_cost;
      if(!pending[e.to]) {
        if(++times[e.to] >= (int)g.size()) return vector< T >();
        pending[e.to] = true;
        que.emplace(e.to);
      }
    }
  }
  return dist;
}

#line 2 "graph/shortest-path/shortest-path-faster-algorithm.hpp"

#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 4 "graph/shortest-path/shortest-path-faster-algorithm.hpp"

/**
 * @brief Shortest-Path-Faster-Algorithm(単一始点最短路)
 */
template< typename T >
vector< T > shortest_path_faster_algorithm(const Graph< T > &g, int s) {
  const auto INF = numeric_limits< T >::max();
  vector< T > dist(g.size(), INF);
  vector< int > pending(g.size(), 0), times(g.size(), 0);
  queue< int > que;

  que.emplace(s);
  pending[s] = true;
  ++times[s];
  dist[s] = 0;

  while(!que.empty()) {
    int p = que.front();
    que.pop();
    pending[p] = false;
    for(auto &e : g[p]) {
      T next_cost = dist[p] + e.cost;
      if(next_cost >= dist[e.to]) continue;
      dist[e.to] = next_cost;
      if(!pending[e.to]) {
        if(++times[e.to] >= (int)g.size()) return vector< T >();
        pending[e.to] = true;
        que.emplace(e.to);
      }
    }
  }
  return dist;
}

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