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generalize Dijkstra's shortest paths to non-index adjacency lists #173

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6d8b771
generalize Dijkstra's shortest paths to non-index adjacency lists
akrzemi1 Jun 28, 2025
a00ea82
semantic requirements for record_for
akrzemi1 Jun 29, 2025
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2 changes: 2 additions & 0 deletions include/graph/algorithm/common_shortest_paths.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -158,6 +158,8 @@ class _null_range_type : public std::vector<size_t> {
_null_range_type(_null_range_type&& other) noexcept {}
_null_range_type(_null_range_type&& other, const Allocator& alloc) {}
_null_range_type(std::initializer_list<T> init, const Allocator& alloc = Allocator()) {}

size_t* vertex_record(_null_range_type& cont, size_t const& id) { return nullptr; }
};

inline static _null_range_type _null_predecessors;
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2 changes: 2 additions & 0 deletions include/graph/algorithm/dijkstra_clrs.hpp
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Expand Up @@ -45,6 +45,8 @@ class _null_range_type : public std::vector<size_t> {
_null_range_type(_null_range_type&& other) noexcept {}
_null_range_type(_null_range_type&& other, const Allocator& alloc) {}
_null_range_type(std::initializer_list<T> init, const Allocator& alloc = Allocator()) {}

size_t* vertex_record(_null_range_type&, size_t const&) { return nullptr; }
};

inline static _null_range_type null_predecessors;
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169 changes: 101 additions & 68 deletions include/graph/algorithm/dijkstra_shortest_paths.hpp
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Expand Up @@ -21,11 +21,62 @@
#include <ranges>
#include <format>


#ifndef GRAPH_DIJKSTRA_SHORTEST_PATHS_HPP
# define GRAPH_DIJKSTRA_SHORTEST_PATHS_HPP

namespace graph {

namespace detail {
// TODO: improve error messages by returning IDs.

template <adjacency_list G, record_for<G> Distances>
auto& validated_record(Distances& distances, vertex_id_t<G> const& uid)
{
auto* rec = vertex_record(distances, uid);
if (rec == nullptr)
[[unlikely]]
throw std::out_of_range(
"dijkstra_shortest_paths: distances do not have value for a vertex id");
return *rec;
}

template <adjacency_list G, record_for<G> Distances>
void validate_distances_record(G const& g, Distances& distances)
{
// TODO: change the secret `if constexpr` into another customization point
if constexpr (std::ranges::random_access_range<Distances>
&& std::ranges::sized_range<Distances>)
{
if (size(distances) < size(vertices(g))) {
throw std::out_of_range(
std::format("dijkstra_shortest_paths: size of distances of {} is less than the number of vertices {}",
size(distances), size(vertices(g))));
}
}
}
template <adjacency_list G, record_for<G> Predecessor>
void validate_predecessors_record(G const& g, Predecessor& predecessor)
{
if constexpr (std::ranges::random_access_range<Predecessor>
&& std::ranges::sized_range<Predecessor>)
{
if (size(predecessor) < size(vertices(g))) {
throw std::out_of_range(
std::format("dijkstra_shortest_paths: size of predecessor of {} is less than the number of vertices {}",
size(predecessor), size(vertices(g))));
}
}
}
template <adjacency_list G>
void validate_source(G const& g, vertex_id_t<G> const& uid)
{
auto it = find_vertex(g, uid);
if (it == std::ranges::end(vertices(g)))
throw std::out_of_range("dijkstra_shortest_paths: source vertex id is out of range");
}
}

/**
* @brief Dijkstra's single-source shortest paths algorithm with a visitor.
*
Expand Down Expand Up @@ -56,88 +107,75 @@ namespace graph {
* @tparam Compare Comparison function for Distance values. Defaults to less<distance_type>.
* @tparam Combine Combine function for Distance values. Defaults to plus<DistanctValue>.
*/
template <index_adjacency_list G,
template <adjacency_list G,
input_range Sources,
random_access_range Distances,
random_access_range Predecessors,
class WF = function<range_value_t<Distances>(edge_reference_t<G>)>,
record_for<G> Distances,
record_for<G> Predecessors,
class WF = function<record_t<Distances, G>(edge_reference_t<G>)>,
class Visitor = empty_visitor,
class Compare = less<range_value_t<Distances>>,
class Combine = plus<range_value_t<Distances>>>
class Compare = less<record_t<Distances, G>>,
class Combine = plus<record_t<Distances, G>>>
requires convertible_to<range_value_t<Sources>, vertex_id_t<G>> && //
is_arithmetic_v<range_value_t<Distances>> && //
sized_range<Distances> && //
sized_range<Predecessors> && //
convertible_to<vertex_id_t<G>, range_value_t<Predecessors>> &&
basic_edge_weight_function<G, WF, range_value_t<Distances>, Compare, Combine>

convertible_to<vertex_id_t<G>, record_t<Predecessors, G>> &&
basic_edge_weight_function<G, WF, record_t<Distances, G>, Compare, Combine>
constexpr void dijkstra_shortest_paths(
G&& g,
const Sources& sources,
Distances& distances,
Predecessors& predecessor,
WF&& weight = [](edge_reference_t<G> uv) { return range_value_t<Distances>(1); }, // default weight(uv) -> 1
WF&& weight = [](edge_reference_t<G> uv) { return record_t<Distances, G>(1); }, // default weight(uv) -> 1
Visitor&& visitor = empty_visitor(),
Compare&& compare = less<range_value_t<Distances>>(),
Combine&& combine = plus<range_value_t<Distances>>()) {
Compare&& compare = less<record_t<Distances, G>>(),
Combine&& combine = plus<record_t<Distances, G>>()) {
using id_type = vertex_id_t<G>;
using distance_type = range_value_t<Distances>;
using distance_type = record_t<Distances, G>;
using weight_type = invoke_result_t<WF, edge_reference_t<G>>;

// relxing the target is the function of reducing the distance from the source to the target
auto relax_target = [&g, &predecessor, &distances, &compare, &combine] //
(edge_reference_t<G> e, vertex_id_t<G> uid, const weight_type& w_e) -> bool {
const id_type vid = target_id(g, e);
const distance_type d_u = distances[static_cast<size_t>(uid)];
const distance_type d_v = distances[static_cast<size_t>(vid)];
const distance_type d_u = detail::validated_record<G>(distances, uid);
const distance_type d_v = detail::validated_record<G>(distances, vid);

if (compare(combine(d_u, w_e), d_v)) {
distances[static_cast<size_t>(vid)] = combine(d_u, w_e);
detail::validated_record<G>(distances, vid) = combine(d_u, w_e);
if constexpr (!is_same_v<Predecessors, _null_range_type>) {
predecessor[static_cast<size_t>(vid)] = uid;
detail::validated_record<G>(predecessor, vid) = uid;
}
return true;
}
return false;
};

if (size(distances) < size(vertices(g))) {
throw std::out_of_range(
std::format("dijkstra_shortest_paths: size of distances of {} is less than the number of vertices {}",
size(distances), size(vertices(g))));
}
if constexpr (!is_same_v<Predecessors, _null_range_type>) {
if (size(predecessor) < size(vertices(g))) {
throw std::out_of_range(
std::format("dijkstra_shortest_paths: size of predecessor of {} is less than the number of vertices {}",
size(predecessor), size(vertices(g))));
}
}
detail::validate_distances_record(g, distances);
if constexpr (!is_same_v<Predecessors, _null_range_type>)
detail::validate_predecessors_record(g, predecessor);

constexpr auto zero = shortest_path_zero<distance_type>();
constexpr auto infinite = shortest_path_infinite_distance<distance_type>();

const id_type N = static_cast<id_type>(num_vertices(g));

auto qcompare = [&distances](id_type a, id_type b) {
return distances[static_cast<size_t>(a)] > distances[static_cast<size_t>(b)];
auto dist_a = detail::validated_record<G>(distances, a);
auto dist_b = detail::validated_record<G>(distances, b);
return dist_a > dist_b;
};
using Queue = std::priority_queue<id_type, std::vector<id_type>, decltype(qcompare)>;
Queue queue(qcompare);

// (The optimizer removes this loop if on_initialize_vertex() is empty.)
if constexpr (has_on_initialize_vertex<G, Visitor>) {
for (id_type uid = 0; uid < N; ++uid) {
visitor.on_initialize_vertex({uid, *find_vertex(g, uid)});
}
auto&& vtcs = vertices(g);
for (auto it = std::ranges::begin(vtcs), end = std::ranges::end(vtcs); it != end; ++it)
visitor.on_initialize_vertex({vertex_id(g, it), *it});
}

// Seed the queue with the initial vertice(s)
for (auto&& source : sources) {
if (source >= N || source < 0) {
throw std::out_of_range(std::format("dijkstra_shortest_paths: source vertex id '{}' is out of range", source));
}
detail::validate_source(g, source);
queue.push(source);
distances[static_cast<size_t>(source)] = zero; // mark source as discovered
detail::validated_record<G>(distances, source) = zero; // mark source as discovered
if constexpr (has_on_discover_vertex<G, Visitor>) {
visitor.on_discover_vertex({source, *find_vertex(g, source)});
}
Expand Down Expand Up @@ -165,7 +203,7 @@ constexpr void dijkstra_shortest_paths(
}
}

const bool is_neighbor_undiscovered = (distances[static_cast<size_t>(vid)] == infinite);
const bool is_neighbor_undiscovered = (detail::validated_record<G>(distances, vid) == infinite);
const bool was_edge_relaxed = relax_target(uv, uid, w);

if (is_neighbor_undiscovered) {
Expand Down Expand Up @@ -207,27 +245,25 @@ constexpr void dijkstra_shortest_paths(
} // while(!queue.empty())
}

template <index_adjacency_list G,
random_access_range Distances,
random_access_range Predecessors,
template <adjacency_list G,
record_for<G> Distances,
record_for<G> Predecessors,
class WF = function<range_value_t<Distances>(edge_reference_t<G>)>,
class Visitor = empty_visitor,
class Compare = less<range_value_t<Distances>>,
class Combine = plus<range_value_t<Distances>>>
requires is_arithmetic_v<range_value_t<Distances>> && //
sized_range<Distances> && //
sized_range<Predecessors> && //
convertible_to<vertex_id_t<G>, range_value_t<Predecessors>> &&
basic_edge_weight_function<G, WF, range_value_t<Distances>, Compare, Combine>
class Compare = less<record_t<Distances, G>>,
class Combine = plus<record_t<Distances, G>>>
requires
convertible_to<vertex_id_t<G>, record_t<Predecessors, G>> &&
basic_edge_weight_function<G, WF, record_t<Distances, G>, Compare, Combine>
constexpr void dijkstra_shortest_paths(
G&& g,
vertex_id_t<G> source,
Distances& distances,
Predecessors& predecessor,
WF&& weight = [](edge_reference_t<G> uv) { return range_value_t<Distances>(1); }, // default weight(uv) -> 1
Visitor&& visitor = empty_visitor(),
Compare&& compare = less<range_value_t<Distances>>(),
Combine&& combine = plus<range_value_t<Distances>>()) {
Compare&& compare = less<record_t<Distances, G>>(),
Combine&& combine = plus<record_t<Distances, G>>()) {
dijkstra_shortest_paths(g, subrange(&source, (&source + 1)), distances, predecessor, weight,
forward<Visitor>(visitor), forward<Compare>(compare), forward<Combine>(combine));
}
Expand Down Expand Up @@ -260,44 +296,41 @@ constexpr void dijkstra_shortest_paths(
*/
template <index_adjacency_list G,
input_range Sources,
random_access_range Distances,
record_for<G> Distances,
class WF = function<range_value_t<Distances>(edge_reference_t<G>)>,
class Visitor = empty_visitor,
class Compare = less<range_value_t<Distances>>,
class Combine = plus<range_value_t<Distances>>>
requires convertible_to<range_value_t<Sources>, vertex_id_t<G>> && //
sized_range<Distances> && //
is_arithmetic_v<range_value_t<Distances>> && //
basic_edge_weight_function<G, WF, range_value_t<Distances>, Compare, Combine>
basic_edge_weight_function<G, WF, record_t<Distances, G>, Compare, Combine>
constexpr void dijkstra_shortest_distances(
G&& g,
const Sources& sources,
Distances& distances,
WF&& weight = [](edge_reference_t<G> uv) { return range_value_t<Distances>(1); }, // default weight(uv) -> 1
Visitor&& visitor = empty_visitor(),
Compare&& compare = less<range_value_t<Distances>>(),
Combine&& combine = plus<range_value_t<Distances>>()) {
Compare&& compare = less<record_t<Distances, G>>(),
Combine&& combine = plus<record_t<Distances, G>>()) {
dijkstra_shortest_paths(g, sources, distances, _null_predecessors, forward<WF>(weight), forward<Visitor>(visitor),
forward<Compare>(compare), forward<Combine>(combine));
}

template <index_adjacency_list G,
random_access_range Distances,
class WF = function<range_value_t<Distances>(edge_reference_t<G>)>,
record_for<G> Distances,
class WF = function<record_t<Distances, G>(edge_reference_t<G>)>,
class Visitor = empty_visitor,
class Compare = less<range_value_t<Distances>>,
class Combine = plus<range_value_t<Distances>>>
class Compare = less<record_t<Distances, G>>,
class Combine = plus<record_t<Distances, G>>>
requires is_arithmetic_v<range_value_t<Distances>> && //
sized_range<Distances> && //
basic_edge_weight_function<G, WF, range_value_t<Distances>, Compare, Combine>
basic_edge_weight_function<G, WF, record_t<Distances, G>, Compare, Combine>
constexpr void dijkstra_shortest_distances(
G&& g,
vertex_id_t<G> source,
Distances& distances,
WF&& weight = [](edge_reference_t<G> uv) { return range_value_t<Distances>(1); }, // default weight(uv) -> 1
Visitor&& visitor = empty_visitor(),
Compare&& compare = less<range_value_t<Distances>>(),
Combine&& combine = plus<range_value_t<Distances>>()) {
Compare&& compare = less<record_t<Distances, G>>(),
Combine&& combine = plus<record_t<Distances, G>>()) {
dijkstra_shortest_paths(g, subrange(&source, (&source + 1)), distances, _null_predecessors, forward<WF>(weight),
forward<Visitor>(visitor), forward<Compare>(compare), forward<Combine>(combine));
}
Expand Down
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