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#
ifndef
CPP_ALGORITHM_DIJKSTRA_H
#
define
CPP_ALGORITHM_DIJKSTRA_H
#
include
<
map
>
#
include
<
queue
>
#
include
<
set
>
#
include
<
vector
>
/*
*
* @brief Dijkstra algorithm
* @details Dijkstra algorithm is a single source shortest path algorithm that handle non-negative edge weights.
* @note
* - class representation: @ref Dijkstra::Graph, @ref Dijkstra::Vertex, @ref Dijkstra::MinComparator
*/
namespace
Dijkstra
{
/*
*
* \brief Vertex of Dijkstra algorithm.
* \details Each vertex has a unique id, a set of neighbors, a predecessor and a distance.
*/
struct
Vertex
{
explicit
Vertex
(
const
char
id)
: id(id), neighbors(std::set<Vertex*>()), predecessor(
nullptr
), distance(std::numeric_limits<
int
>::max())
{
}
char
id;
std::set<Vertex*> neighbors;
Vertex* predecessor;
int
distance;
};
/*
*
* \brief Comparator for priority queue.
*/
class
MinComparator
{
public:
bool
operator
()(
const
Vertex* l,
const
Vertex* r)
const
{
return
(l->
distance
> r->
distance
); }
};
/*
*
* \brief Graph of Dijkstra algorithm.
*/
class
Graph
{
public:
/*
*
* \brief Dijkstra algorithm.
* \details A single source shortest path algorithm that handle non-negative edge weights.
* It find the shortest path between two vertices in a graph.
* Relaxation is the process of updating the distance of a vertex, when a shorter path is found.
* \param source source vertex
*/
void
DijkstraAlgorithm
(Vertex& source);
/*
*
* \brief Reordering elements of the queue.
* \param min_queue minimum priority queue
*/
void
ReorderQueue
(std::priority_queue<Vertex*, std::vector<Vertex*>, MinComparator>& min_queue);
void
AddVertex
(Vertex& v);
void
AddEdge
(Vertex& u, Vertex& v,
int
weight);
private:
std::vector<Vertex*> vertices;
std::vector<std::tuple<Vertex*, Vertex*>> adjacency_list;
std::map<std::pair<
char
,
char
>,
int
> weight_list;
};
}
//
----------------------------------------------------------------------------
inline
void
Dijkstra::Graph::DijkstraAlgorithm
(Vertex& source)
{
std::priority_queue<Vertex*, std::vector<Vertex*>, MinComparator> min_queue;
for
(
auto
v : vertices)
{
min_queue.
push
(v);
}
while
(!min_queue.
empty
())
{
const
auto
u = min_queue.
top
();
min_queue.
pop
();
for
(
const
auto
v : u->
neighbors
)
{
//
Relaxation
const
auto
weight_uv = weight_list.
at
(
std::make_pair
(u->
id
, v->
id
));
if
(v->
distance
> (u->
distance
+ weight_uv))
{
v->
distance
= u->
distance
+ weight_uv;
v->
predecessor
= u;
}
ReorderQueue
(min_queue);
}
}
}
//
----------------------------------------------------------------------------
inline
void
Dijkstra::Graph::ReorderQueue
(std::priority_queue<Vertex*, std::vector<Vertex*>, MinComparator>& min_queue)
{
auto
queue = std::priority_queue<Vertex*, std::vector<Vertex*>, MinComparator>{};
const
int
min_queue_size =
static_cast
<
int
>(min_queue.
size
());
for
(
int
i =
0
; i < min_queue_size; ++i)
{
queue.
push
(min_queue.
top
());
min_queue.
pop
();
}
min_queue =
std::move
(queue);
}
//
----------------------------------------------------------------------------
inline
void
Dijkstra::Graph::AddVertex
(Vertex& v)
{
vertices.
push_back
(&v);
}
//
----------------------------------------------------------------------------
inline
void
Dijkstra::Graph::AddEdge
(Vertex& u, Vertex& v,
int
weight)
{
adjacency_list.
emplace_back
(&u, &v);
weight_list.
insert
(
std::make_pair
(
std::make_pair
(u.
id
, v.
id
), weight));
u.
neighbors
.
insert
(&v);
}
#
endif
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