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#include "graph/shortest-path/shortest-path-faster-algorithm.hpp"
#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;
}