graph_scenarios_test.cc

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
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  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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  SOFTWARE.
*/
 
 
#include <gtest/gtest.h>
 
#include <Bellman_Ford.H>
#include <Dijkstra.H>
#include <Tarjan.H>
#include <random_graph.H>
#include <tpl_graph.H>
 
#include <cstdlib>
#include <limits>
#include <random>
#include <vector>
 
using namespace Aleph;
 
namespace
{
using DGraph = List_Digraph<Graph_Node<int>, Graph_Arc<int>>;
using DNode = DGraph::Node;
 
template <class GT, class SA>
class Out_Iterator_Ne : public Out_Iterator<GT, SA>
{
public:
  using Base = Out_Iterator<GT, SA>;
  using Base::Base;
 
  typename GT::Arc * get_current_arc_ne() const noexcept
  {
    return const_cast<Out_Iterator_Ne *>(this)->get_current_arc();
  }
};
 
struct BinHeapTag
{
  template <class G, class D, class A>
  using Heap = ArcHeap<G, D, A>;
};
 
using DijkstraInt =
  Dijkstra_Min_Paths<DGraph, Dft_Dist<DGraph>, Node_Arc_Iterator,
                     Dft_Show_Arc<DGraph>, BinHeapTag::template Heap>;
 
using DijkstraIntAllArcs =
  Dijkstra_Min_Paths<DGraph, Dft_Dist<DGraph>, Out_Iterator_Ne,
                     Dft_Show_Arc<DGraph>, BinHeapTag::template Heap>;
 
struct InitNodeNoop
{
  void operator()(DGraph &, DNode *) const noexcept {}
};
 
struct InitArcRandNonNegative
{
  std::mt19937 rng;
  std::uniform_int_distribution<int> dist;
 
  explicit InitArcRandNonNegative(uint32_t seed, int max_w)
    : rng(seed), dist(0, max_w)
  {
  }
 
  void operator()(DGraph &, DGraph::Arc *a)
  {
    a->get_info() = dist(rng);
  }
};
 
struct InitArcRandAllowNegative
{
  std::mt19937 rng;
  std::uniform_int_distribution<int> dist;
 
  explicit InitArcRandAllowNegative(uint32_t seed, int min_w, int max_w)
    : rng(seed), dist(min_w, max_w)
  {
  }
 
  void operator()(DGraph &, DGraph::Arc *a)
  {
    a->get_info() = dist(rng);
  }
};
 
static DNode * pick_node_by_index(DGraph & g, size_t idx)
{
  size_t i = 0;
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne(), ++i)
    if (i == idx)
      return it.get_curr();
  return nullptr;
}
 
static std::pair<DNode *, DNode *> pick_two_distinct_nodes(DGraph & g,
                                                          uint32_t seed)
{
  std::mt19937 rng(seed);
  std::uniform_int_distribution<size_t> dist(0, g.get_num_nodes() - 1);
 
  const size_t i = dist(rng);
  size_t j = dist(rng);
  while (j == i)
    j = dist(rng);
 
  auto *s = pick_node_by_index(g, i);
  auto *t = pick_node_by_index(g, j);
  return {s, t};
}
 
void expect_dijkstra_matches_bellman_ford(DGraph & g, DNode *s, DNode *t)
{
  ASSERT_NE(s, nullptr);
  ASSERT_NE(t, nullptr);
 
  // Dijkstra
  DijkstraInt dij;
  Path<DGraph> dij_path(g);
  const int dij_dist = dij(g, s, t, dij_path);
 
  // Bellman-Ford (no negative weights/cycles in this test)
  Bellman_Ford<DGraph> bf(g);
  const bool neg = bf.paint_spanning_tree(s);
  ASSERT_FALSE(neg);
 
  Path<DGraph> bf_path(g);
  const int bf_dist = bf.get_min_path(t, bf_path);
 
  // Both implementations use max() as INF on unreachable.
  EXPECT_EQ(dij_dist, bf_dist);
 
  // If reachable, paths must be non-empty and end at t.
  if (bf_dist != std::numeric_limits<int>::max())
    {
      EXPECT_FALSE(dij_path.is_empty());
      EXPECT_FALSE(bf_path.is_empty());
 
      EXPECT_EQ(dij_path.get_last_node(), t);
      EXPECT_EQ(bf_path.get_last_node(), t);
    }
  else
    {
      EXPECT_TRUE(dij_path.is_empty());
      EXPECT_TRUE(bf_path.is_empty());
    }
}
} // namespace
 
TEST(GraphScenarios, DisconnectedGraph_UnreachablePath)
{
  DGraph g;
  auto *a = g.insert_node(1);
  auto *b = g.insert_node(2);
  auto *c = g.insert_node(3);
  auto *d = g.insert_node(4);
 
  // Component 1: a -> b
  g.insert_arc(a, b, 5);
 
  // Component 2: c -> d
  g.insert_arc(c, d, 7);
 
  DijkstraInt dij;
  Path<DGraph> path(g);
  const int dist = dij(g, a, d, path);
 
  EXPECT_EQ(dist, std::numeric_limits<int>::max());
  EXPECT_TRUE(path.is_empty());
}
 
TEST(GraphScenarios, Multigraph_ParallelArcs_DijkstraChoosesMin)
{
  DGraph g;
  auto *s = g.insert_node(0);
  auto *t = g.insert_node(1);
 
  const auto arcs_before = g.get_num_arcs();
 
  g.insert_arc(s, t, 10);
  g.insert_arc(s, t, 3);
  g.insert_arc(s, t, 7);
 
  // Some graph types in Aleph-w behave as simple graphs and may collapse
  // parallel arcs. If so, skip this multigraph-specific expectation.
  if (const auto arcs_after = g.get_num_arcs(); arcs_after - arcs_before < 3)
    GTEST_SKIP() << "Graph type does not appear to support parallel arcs (multigraph).";
 
  // Important: for multigraphs, use an iterator that visits all arcs.
  // Some iterators may collapse parallel arcs by target node.
  DijkstraIntAllArcs dij;
  Path<DGraph> path(g);
  const int dist = dij(g, s, t, path);
 
  EXPECT_EQ(dist, 3);
  EXPECT_FALSE(path.is_empty());
}
 
TEST(GraphScenarios, BellmanFord_NegativeWeights_NoNegativeCycle)
{
  DGraph g;
  auto *n0 = g.insert_node(0);
  auto *n1 = g.insert_node(1);
  auto *n2 = g.insert_node(2);
  auto *n3 = g.insert_node(3);
 
  // No negative cycle: best path 0->1->2->3 = -2 + 3 + -1 = 0
  g.insert_arc(n0, n1, -2);
  g.insert_arc(n1, n2, 3);
  g.insert_arc(n2, n3, -1);
  g.insert_arc(n0, n3, 5);
 
  Bellman_Ford<DGraph> bf(g);
  const bool neg = bf.paint_spanning_tree(n0);
  EXPECT_FALSE(neg);
 
  Path<DGraph> path(g);
  const int dist = bf.get_min_path(n3, path);
  EXPECT_EQ(dist, 0);
  EXPECT_FALSE(path.is_empty());
}
 
TEST(GraphScenarios, SparseVsDense_DijkstraMatchesBellmanFord)
{
  // Keep these sizes modest; this is a correctness test, not a perf test.
  const size_t N = 200;
 
  // Sparse: ~4N arcs
  {
    InitNodeNoop init_node;
    InitArcRandNonNegative init_arc(1234, 20);
 
    Random_Digraph<DGraph, InitNodeNoop, InitArcRandNonNegative> gen(
        777, init_node, init_arc);
 
    auto g = gen(N, size_t(4 * N), false /* strongly connected? */);
 
    auto [s, t] = pick_two_distinct_nodes(g, 999);
    expect_dijkstra_matches_bellman_ford(g, s, t);
  }
 
  // Dense: probability p.
  {
    InitNodeNoop init_node;
    InitArcRandNonNegative init_arc(4321, 20);
 
    Random_Digraph<DGraph, InitNodeNoop, InitArcRandNonNegative> gen(
        888, init_node, init_arc);
 
    auto g = gen(N, 0.08, false /* strongly connected? */);
 
    auto [s, t] = pick_two_distinct_nodes(g, 1001);
    expect_dijkstra_matches_bellman_ford(g, s, t);
  }
}
 
TEST(GraphScenarios, MultiGraph_TarjanCycleDetection)
{
  DGraph g;
  auto *a = g.insert_node(1);
  auto *b = g.insert_node(2);
 
  // Parallel arcs alone do not create a cycle.
  g.insert_arc(a, b, 1);
  g.insert_arc(a, b, 2);
 
  Tarjan_Connected_Components<DGraph> tarjan;
  EXPECT_FALSE(tarjan.has_cycle(g));
 
  // Add one back edge: now there is a cycle.
  g.insert_arc(b, a, 0);
  Tarjan_Connected_Components<DGraph> tarjan2;
  EXPECT_TRUE(tarjan2.has_cycle(g));
}