Bellman-Ford algorithm
(Mylib/Graph/ShortestPath/bellman_ford.cpp)
Operations
Requirements
Notes
Problems
References
Depends on
Verified with
Code
#pragma once
#include <algorithm>
#include <cassert>
#include <vector>
#include "Mylib/Graph/Template/graph.cpp"
#include "Mylib/Math/unbounded.cpp"
namespace haar_lib {
template <typename T>
auto bellman_ford(const graph<T> &g, int src) {
using type = unbounded<T>;
const int n = g.size();
std::vector<type> dist(n, type::positive_inf());
dist[src] = 0;
for (int i = 0; i < n; ++i) {
for (int s = 0; s < n; ++s) {
for (auto &e : g[s]) {
int t = e.to;
T d = e.cost;
if (dist[s].is_finite() and
dist[t].is_finite() and
dist[s].value() + d < dist[t].value() and i == n - 1) {
dist[t] = type::negative_inf();
} else {
if (dist[s].is_finite()) {
if (dist[t].is_positive_inf()) {
dist[t] = dist[s].value() + d;
} else if (dist[t].is_finite()) {
dist[t] = std::min(dist[t].value(), dist[s].value() + d);
}
}
}
}
}
}
for (int i = 0; i < n; ++i) {
for (int s = 0; s < n; ++s) {
for (auto &e : g[s]) {
if (dist[s].is_negative_inf()) {
dist[e.to] = type::negative_inf();
}
}
}
}
return dist;
}
} // namespace haar_lib
#line 2 "Mylib/Graph/ShortestPath/bellman_ford.cpp"
#include <algorithm>
#include <cassert>
#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 3 "Mylib/Math/unbounded.cpp"
template <typename T>
struct unbounded {
private:
enum class tag_t { POSITIVE_INFINITY,
NEGATIVE_INFINITY,
FINITE } tag_;
T value_;
unbounded(tag_t tag_) : tag_(tag_) {}
public:
using value_type = T;
unbounded() : tag_(tag_t::FINITE), value_(T()) {}
unbounded(T value_) : tag_(tag_t::FINITE), value_(value_) {}
unbounded(const unbounded<T>& that) : tag_(that.tag_), value_(that.value_) {}
bool is_positive_inf() const { return tag_ == tag_t::POSITIVE_INFINITY; }
bool is_negative_inf() const { return tag_ == tag_t::NEGATIVE_INFINITY; }
bool is_finite() const { return tag_ == tag_t::FINITE; }
T value() const { return value_; }
T& value() { return value_; }
static auto positive_inf() {
return unbounded(tag_t::POSITIVE_INFINITY);
}
static auto negative_inf() {
return unbounded(tag_t::NEGATIVE_INFINITY);
}
friend std::ostream& operator<<(std::ostream& s, const unbounded& a) {
switch (a.tag_) {
case tag_t::POSITIVE_INFINITY: s << "∞"; break;
case tag_t::NEGATIVE_INFINITY: s << "-∞"; break;
case tag_t::FINITE: s << a.value_;
}
return s;
}
unbounded operator-() const {
if (is_finite())
return -value_;
else if (is_positive_inf())
return unbounded::negative_inf();
return unbounded::positive_inf();
}
auto& operator+=(unbounded that) {
if (is_finite()) {
if (that.is_finite())
value_ += that.value_;
else
tag_ = that.tag_;
}
return *this;
}
auto operator+(unbounded that) const {
return unbounded(*this) += that;
}
auto& operator-=(unbounded that) {
return (*this) += (-that);
}
auto operator-(unbounded that) const {
return unbounded(*this) -= that;
}
int compare(unbounded that) const {
if (is_positive_inf()) {
if (that.is_positive_inf())
return 0;
else
return 1;
} else if (is_negative_inf()) {
if (that.is_negative_inf())
return 0;
else
return -1;
} else {
if (that.is_positive_inf())
return -1;
else if (that.is_negative_inf())
return 1;
else
return (value_ > that.value_) - (value_ < that.value_);
}
}
bool operator==(unbounded that) const { return compare(that) == 0; }
bool operator!=(unbounded that) const { return compare(that) != 0; }
bool operator<(unbounded that) const { return compare(that) < 0; }
bool operator<=(unbounded that) const { return compare(that) <= 0; }
bool operator>(unbounded that) const { return compare(that) > 0; }
bool operator>=(unbounded that) const { return compare(that) >= 0; }
};
#line 7 "Mylib/Graph/ShortestPath/bellman_ford.cpp"
namespace haar_lib {
template <typename T>
auto bellman_ford(const graph<T> &g, int src) {
using type = unbounded<T>;
const int n = g.size();
std::vector<type> dist(n, type::positive_inf());
dist[src] = 0;
for (int i = 0; i < n; ++i) {
for (int s = 0; s < n; ++s) {
for (auto &e : g[s]) {
int t = e.to;
T d = e.cost;
if (dist[s].is_finite() and
dist[t].is_finite() and
dist[s].value() + d < dist[t].value() and i == n - 1) {
dist[t] = type::negative_inf();
} else {
if (dist[s].is_finite()) {
if (dist[t].is_positive_inf()) {
dist[t] = dist[s].value() + d;
} else if (dist[t].is_finite()) {
dist[t] = std::min(dist[t].value(), dist[s].value() + d);
}
}
}
}
}
}
for (int i = 0; i < n; ++i) {
for (int s = 0; s < n; ++s) {
for (auto &e : g[s]) {
if (dist[s].is_negative_inf()) {
dist[e.to] = type::negative_inf();
}
}
}
}
return dist;
}
} // namespace haar_lib
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Basic graph
(Mylib/Graph/Template/graph.cpp)