Bellman

include/graph/algorithm/bellman_ford_shortest_paths.hpp

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+/**
+ * @file bellman_ford_shortest_paths.hpp
+ * 
+ * @brief Single-Source Shortest paths and shortest distances algorithms using Bellman-Ford's algorithm.
+ * 
+ * @copyright Copyright (c) 2024
+ * 
+ * SPDX-License-Identifier: BSL-1.0
+ *
+ * @authors
+ *   Andrew Lumsdaine
+ *   Phil Ratzloff
+ */
+
+#include "graph/graph.hpp"
+#include "graph/views/incidence.hpp"
+#include "graph/views/edgelist.hpp"
+#include "graph/algorithm/common_shortest_paths.hpp"
+
+#include <ranges>
+#include <fmt/format.h>
+
+#ifndef GRAPH_BELLMAN_SHORTEST_PATHS_HPP
+#  define GRAPH_BELLMAN_SHORTEST_PATHS_HPP
+
+//#  define ENABLE_EVAL_NEG_WEIGHT_CYCLE 1  // for debugging
+
+namespace std::graph {
+
+template <adjacency_list G>
+class bellman_visitor_base {
+  // Types
+public:
+  using graph_type             = G;
+  using vertex_desc_type       = vertex_descriptor<vertex_id_t<G>, vertex_reference_t<G>, void>;
+  using sourced_edge_desc_type = edge_descriptor<vertex_id_t<G>, true, edge_reference_t<G>, void>;
+
+  // Visitor Functions
+public:
+  // vertex visitor functions
+  //constexpr void on_initialize_vertex(vertex_desc_type&& vdesc) {}
+  //constexpr void on_discover_vertex(vertex_desc_type&& vdesc) {}
+  //constexpr void on_examine_vertex(vertex_desc_type&& vdesc) {}
+  //constexpr void on_finish_vertex(vertex_desc_type&& vdesc) {}
+
+  // edge visitor functions
+  constexpr void on_examine_edge(sourced_edge_desc_type&& edesc) {}
+  constexpr void on_edge_relaxed(sourced_edge_desc_type&& edesc) {}
+  constexpr void on_edge_not_relaxed(sourced_edge_desc_type&& edesc) {}
+  constexpr void on_edge_minimized(sourced_edge_desc_type&& edesc) {}
+  constexpr void on_edge_not_minimized(sourced_edge_desc_type&& edesc) {}
+};
+
+template <class G, class Visitor>
+concept bellman_visitor = //is_arithmetic<typename Visitor::distance_type> &&
+      requires(Visitor& v, Visitor::vertex_desc_type& vdesc, Visitor::sourced_edge_desc_type& edesc) {
+        //typename Visitor::distance_type;
+
+        //{ v.on_initialize_vertex(vdesc) };
+        //{ v.on_discover_vertex(vdesc) };
+        //{ v.on_examine_vertex(vdesc) };
+        //{ v.on_finish_vertex(vdesc) };
+
+        { v.on_examine_edge(edesc) };
+        { v.on_edge_relaxed(edesc) };
+        { v.on_edge_not_relaxed(edesc) };
+        { v.on_edge_minimized(edesc) };
+        { v.on_edge_not_minimized(edesc) };
+      };
+
+/**
+ * @brief Bellman-Ford's single-source shortest paths algorithm with a visitor.
+ * 
+ * The implementation was taken from boost::graph bellman_ford_shortest_paths.
+ * 
+ * Complexity: O(V * E)
+ * 
+ * Pre-conditions:
+ *  - 0 <= source < num_vertices(g)
+ *  - predecessors has been initialized with init_shortest_paths().
+ *  - distances has been initialized with init_shortest_paths().
+ *  - The weight function must return a value that can be compared (e.g. <) with the Distance 
+ *    type and combined (e.g. +) with the Distance type.
+ *  - The visitor must implement the bellman_visitor concept and is typically derived from
+ *    bellman_visitor_base.
+ * 
+ * Throws:
+ *  - out_of_range if the source vertex is out of range.
+ * 
+ * @tparam G            The graph type,
+ * @tparam Distances    The distance random access range.
+ * @tparam Predecessors The predecessor random access range.
+ * @tparam WF           Edge weight function. Defaults to a function that returns 1.
+ * @tparam Visitor      Visitor type with functions called for different events in the algorithm.
+ *                      Function calls are removed by the optimizer if not uesd.
+ * @tparam Compare      Comparison function for Distance values. Defaults to less<DistanceValue>.
+ * @tparam Combine      Combine function for Distance values. Defaults to plus<DistanctValue>.
+ * 
+ * @return true if all edges were minimized, false if a negative weight cycle was found. If an edge
+ *         was not minimized, the on_edge_not_minimized event is called.
+ */
+template <index_adjacency_list        G,
+          ranges::random_access_range Distances,
+          ranges::random_access_range Predecessors,
+          class WF      = std::function<ranges::range_value_t<Distances>(edge_reference_t<G>)>,
+          class Visitor = bellman_visitor_base<G>,
+          class Compare = less<ranges::range_value_t<Distances>>,
+          class Combine = plus<ranges::range_value_t<Distances>>>
+requires is_arithmetic_v<ranges::range_value_t<Distances>> && //
+         convertible_to<vertex_id_t<G>, ranges::range_value_t<Predecessors>> &&
+         basic_edge_weight_function<G, WF, ranges::range_value_t<Distances>, Compare, Combine>
+// && bellman_visitor<G, Visitor>
+bool bellman_ford_shortest_paths(
+      G&                   g,
+      const vertex_id_t<G> source,
+      Distances&           distances,
+      Predecessors&        predecessor,
+      WF&&                 weight =
+            [](edge_reference_t<G> uv) { return ranges::range_value_t<Distances>(1); }, // default weight(uv) -> 1
+      Visitor&& visitor = bellman_visitor_base<G>(),
+      Compare&& compare = less<ranges::range_value_t<Distances>>(),
+      Combine&& combine = plus<ranges::range_value_t<Distances>>()) {
+  using id_type       = vertex_id_t<G>;
+  using DistanceValue = ranges::range_value_t<Distances>;
+  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 {
+    id_type             vid = target_id(g, e);
+    const DistanceValue d_u = distances[static_cast<size_t>(uid)];
+    const DistanceValue d_v = distances[static_cast<size_t>(vid)];
+
+    if (compare(combine(d_u, w_e), d_v)) {
+      distances[static_cast<size_t>(vid)] = combine(d_u, w_e);
+      if constexpr (!is_same_v<Predecessors, _null_range_type>) {
+        predecessor[static_cast<size_t>(vid)] = uid;
+      }
+      return true;
+    }
+    return false;
+  };
+
+  constexpr auto zero     = shortest_path_zero<DistanceValue>();
+  constexpr auto infinite = shortest_path_invalid_distance<DistanceValue>();
+
+  const id_type N = static_cast<id_type>(num_vertices(g));
+
+  distances[source] = zero;
+  if (source >= N || source < 0) {
+    throw out_of_range(fmt::format("bellman_fored_shortest_paths: source vertex id of '{}' is out of range", source));
+  }
+
+  for (id_type k = 0; k < N; ++k) {
+    bool at_least_one_edge_relaxed = false;
+    for (auto&& [uid, vid, uv, w] : views::edgelist(g, weight)) {
+      visitor.on_examine_edge({uid, vid, uv});
+      if (relax_target(uv, uid, w)) {
+        at_least_one_edge_relaxed = true;
+        visitor.on_edge_relaxed({uid, vid, uv});
+      } else
+        visitor.on_edge_not_relaxed({uid, vid, uv});
+    }
+    if (!at_least_one_edge_relaxed)
+      break;
+  }
+
+  // Check for negative weight cycles
+  for (auto&& [uid, vid, uv, w] : views::edgelist(g, weight)) {
+    if (compare(combine(distances[uid], w), distances[vid])) {
+      visitor.on_edge_not_minimized({uid, vid, uv});
+
+#  if ENABLE_EVAL_NEG_WEIGHT_CYCLE // for debugging
+      // A negative cycle exists; find a vertex on the cycle
+      // (Thanks to Wikipedia's Bellman-Ford article for this code)
+      predecessor[vid] = uid;
+      vector<bool> visited(num_vertices(g), false);
+      visited[vid] = true;
+      while (!visited[uid]) {
+        visited[uid] = true;
+        uid          = predecessor[uid];
+      }
+      // uid is a vertex in a negative cycle, fill ncycle with the vertices in the cycle
+      vector<id_type> ncycle;
+      ncycle.push_back(uid);
+      vid = predecessor[uid];
+      while (vid != uid) {
+        ncycle.push_back(vid);
+        vid = predecessor[vid]
+      }
+#  endif
+      return false;
+    } else {
+      visitor.on_edge_minimized({uid, vid, uv});
+    }
+  }
+
+  return true;
+}
+
+/**
+ * @brief Shortest distnaces from a single source using Bellman-Ford's single-source shortest paths 
+ *        algorithm with a visitor.
+ * 
+ * This is identical to bellman_ford_shortest_paths() except that it does not require a predecessors range.
+ * 
+ * Complexity: O(V * E)
+ * 
+ * Pre-conditions:
+ *  - distances has been initialized with init_shortest_paths().
+ *  - The weight function must return a value that can be compared (e.g. <) with the Distance 
+ *    type and combined (e.g. +) with the Distance type.
+ *  - The visitor must implement the bellman_visitor concept and is typically derived from
+ *    bellman_visitor_base.
+ * 
+ * Throws:
+ *  - out_of_range if the source vertex is out of range.
+ * 
+ * @tparam G            The graph type,
+ * @tparam Distances    The distance random access range.
+ * @tparam WF           Edge weight function. Defaults to a function that returns 1.
+ * @tparam Visitor      Visitor type with functions called for different events in the algorithm.
+ *                      Function calls are removed by the optimizer if not uesd.
+ * @tparam Compare      Comparison function for Distance values. Defaults to less<DistanceValue>.
+ * @tparam Combine      Combine function for Distance values. Defaults to plus<DistanctValue>.
+ * 
+ * @return true if all edges were minimized, false if a negative weight cycle was found. If an edge
+ *         was not minimized, the on_edge_not_minimized event is called.
+ */
+template <index_adjacency_list        G,
+          ranges::random_access_range Distances,
+          class WF      = std::function<ranges::range_value_t<Distances>(edge_reference_t<G>)>,
+          class Visitor = bellman_visitor_base<G>,
+          class Compare = less<ranges::range_value_t<Distances>>,
+          class Combine = plus<ranges::range_value_t<Distances>>>
+requires is_arithmetic_v<ranges::range_value_t<Distances>> && //
+         basic_edge_weight_function<G, WF, ranges::range_value_t<Distances>, Compare, Combine>
+//&& bellman_visitor<G, Visitor>
+bool bellman_ford_shortest_distances(
+      G&                   g,
+      const vertex_id_t<G> source,
+      Distances&           distances,
+      WF&&                 weight =
+            [](edge_reference_t<G> uv) { return ranges::range_value_t<Distances>(1); }, // default weight(uv) -> 1
+      Visitor&& visitor = bellman_visitor_base<G>(),
+      Compare&& compare = less<ranges::range_value_t<Distances>>(),
+      Combine&& combine = plus<ranges::range_value_t<Distances>>()) {
+  return bellman_ford_shortest_paths(g, source, distances, _null_predecessors, forward<WF>(weight),
+                                     std::forward<Visitor>(visitor), std::forward<Compare>(compare),
+                                     std::forward<Combine>(combine));
+}
+
+} // namespace std::graph
+
+#endif // GRAPH_BELLMAN_SHORTEST_PATHS_HPP

include/graph/algorithm/common_shortest_paths.hpp

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+#pragma once
+
+#include <algorithm>
+
+#ifndef GRAPH_COMMON_SHORTEST_PATHS_HPP
+#  define GRAPH_COMMON_SHORTEST_PATHS_HPP
+
+namespace std::graph {
+template <class G, class WF, class DistanceValue, class Compare, class Combine> // For exposition only
+concept basic_edge_weight_function =                                            // e.g. weight(uv)
+      is_arithmetic_v<DistanceValue> && strict_weak_order<Compare, DistanceValue, DistanceValue> &&
+      assignable_from<add_lvalue_reference_t<DistanceValue>,
+                      invoke_result_t<Combine, DistanceValue, invoke_result_t<WF, edge_reference_t<G>>>>;
+
+template <class G, class WF, class DistanceValue> // For exposition only
+concept edge_weight_function =                    // e.g. weight(uv)
+      is_arithmetic_v<invoke_result_t<WF, edge_reference_t<G>>> &&
+      basic_edge_weight_function<G, WF, DistanceValue, less<DistanceValue>, plus<DistanceValue>>;
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Returns a value to define an invalid distance used to initialize distance values
+ * in the distance range before one of the shorts paths functions.
+ * 
+ * @tparam DistanceValue The type of the distance.
+ * 
+ * @return A unique sentinal value to indicate that a value is invalid, or undefined.
+*/
+template <class DistanceValue>
+constexpr auto shortest_path_invalid_distance() {
+  return numeric_limits<DistanceValue>::max();
+}
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Returns a distance value of zero.
+ * 
+ * @tparam DistanceValue The type of the distance.
+ * 
+ * @return A value of zero distance.
+*/
+template <class DistanceValue>
+constexpr auto shortest_path_zero() {
+  return DistanceValue();
+}
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Intializes the distance values to shortest_path_invalid_distance().
+ * 
+ * @tparam Distances The range type of the distances.
+ * 
+ * @param distances The range of distance values to initialize.
+*/
+template <class Distances>
+constexpr void init_shortest_paths(Distances& distances) {
+  ranges::fill(distances, shortest_path_invalid_distance<ranges::range_value_t<Distances>>());
+}
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Intializes the distance and predecessor values for shortest paths algorithms.
+ * 
+ * @tparam Distances The range type of the distances.
+ * @tparam Predecessors The range type of the predecessors.
+ * 
+ * @param distances The range of distance values to initialize.
+ * @param predecessors The range of predecessors to initialize.
+*/
+template <class Distances, class Predecessors>
+constexpr void init_shortest_paths(Distances& distances, Predecessors& predecessors) {
+  init_shortest_paths(distances);
+
+  using pred_t = ranges::range_value_t<Predecessors>;
+  pred_t i     = pred_t();
+  for (auto& pred : predecessors)
+    pred = i++;
+}
+
+/**
+ * @brief An always-empty random_access_range.
+ * 
+ * A unique range type that can be used at compile time to determine if predecessors need to
+ * be evaluated.
+ * 
+ * This is not in the P1709 proposal. It's a quick hack to allow us to implement quickly.
+*/
+class _null_range_type : public std::vector<size_t> {
+  using T         = size_t;
+  using Allocator = std::allocator<T>;
+  using Base      = std::vector<T, Allocator>;
+
+public:
+  _null_range_type() noexcept(noexcept(Allocator())) = default;
+  explicit _null_range_type(const Allocator& alloc) noexcept {}
+  _null_range_type(Base::size_type count, const T& value, const Allocator& alloc = Allocator()) {}
+  explicit _null_range_type(Base::size_type count, const Allocator& alloc = Allocator()) {}
+  template <class InputIt>
+  _null_range_type(InputIt first, InputIt last, const Allocator& alloc = Allocator()) {}
+  _null_range_type(const _null_range_type& other) : Base() {}
+  _null_range_type(const _null_range_type& other, const Allocator& alloc) {}
+  _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()) {}
+};
+
+inline static _null_range_type _null_predecessors;
+
+} // namespace std::graph
+
+#endif // GRAPH_COMMON_SHORTEST_PATHS_HPP