floyd.cc

Go to the documentation of this file.

 
/*
                          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
  copies or substantial portions of the Software.
 
  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
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
#include <gtest/gtest.h>
 
#include <tpl_graph_utils.H>
#include <Floyd_Warshall.H>
 
using namespace Aleph;
using namespace std;
 
// Graph type using proper node/arc wrappers
using Grafo = List_Digraph<Graph_Node<int>, Graph_Arc<int>>;
using GNode = Grafo::Node;
using GArc = Grafo::Arc;
 
namespace {
 
// Helper to insert arc between nodes by value
void insert_arc_by_value(Grafo& g, int src_val, int tgt_val, int weight)
{
  GNode* src = nullptr;
  GNode* tgt = nullptr;
  
  for (Grafo::Node_Iterator it(g); it.has_curr(); it.next_ne()) {
    auto n = it.get_curr();
    if (n->get_info() == src_val) src = n;
    if (n->get_info() == tgt_val) tgt = n;
  }
  
  if (src && tgt)
    g.insert_arc(src, tgt, weight);
}
 
} // namespace
 
// Test basic Floyd algorithm on a simple graph
TEST(FloydBasicGraph, computes_correct_distances)
{
  Grafo g;
  auto n0 = g.insert_node(0);
  auto n1 = g.insert_node(1);
  auto n2 = g.insert_node(2);
  
  // Create edges: 0->1 (weight 1), 1->2 (weight 2), 0->2 (weight 5)
  insert_arc_by_value(g, 0, 1, 1);
  insert_arc_by_value(g, 1, 2, 2);
  insert_arc_by_value(g, 0, 2, 5);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  EXPECT_FALSE(floyd.has_negative_cycle());
  
  const auto& dist = floyd.get_dist_mat();
 
  const long i0 = floyd.index_node(n0);
  const long i1 = floyd.index_node(n1);
  const long i2 = floyd.index_node(n2);
  
  // Distance from node to itself should be 0
  EXPECT_EQ(dist(i0, i0), 0);
  EXPECT_EQ(dist(i1, i1), 0);
  EXPECT_EQ(dist(i2, i2), 0);
  
  // Distance 0->1 should be 1 (direct edge)
  EXPECT_EQ(dist(i0, i1), 1);
  
  // Distance 0->2 should be 3 (0->1->2, not direct 0->2 with weight 5)
  EXPECT_EQ(dist(i0, i2), 3);
  
  // Distance 1->2 should be 2 (direct edge)
  EXPECT_EQ(dist(i1, i2), 2);
}
 
// Test handling of unreachable nodes
TEST(FloydBasicGraph, handles_unreachable_nodes)
{
  Grafo g;
  auto n0 = g.insert_node(0);
  auto n1 = g.insert_node(1);
  // No edges between nodes
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  const auto& dist = floyd.get_dist_mat();
  const int Inf = numeric_limits<int>::max();
 
  const long i0 = floyd.index_node(n0);
  const long i1 = floyd.index_node(n1);
  
  // Distances to unreachable nodes should be infinity
  EXPECT_EQ(dist(i0, i1), Inf);
  EXPECT_EQ(dist(i1, i0), Inf);
 
  // Unreachable paths should be reported as empty paths
  EXPECT_TRUE(floyd.get_min_path(i0, i1).is_empty());
  EXPECT_TRUE(floyd.get_min_path(i1, i0).is_empty());
}
 
// Test negative weights without negative cycles
TEST(FloydNegativeWeights, handles_negative_weights_without_cycles)
{
  Grafo g;
  auto n0 = g.insert_node(0);
  auto n1 = g.insert_node(1);
  auto n2 = g.insert_node(2);
  
  // 0->1 (weight -1), 1->2 (weight 2), 0->2 (weight 3)
  g.insert_arc(n0, n1, -1);
  g.insert_arc(n1, n2, 2);
  g.insert_arc(n0, n2, 3);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  EXPECT_FALSE(floyd.has_negative_cycle());
  
  // Get actual indices for nodes
  long i0 = floyd.index_node(n0);
  long i1 = floyd.index_node(n1);
  long i2 = floyd.index_node(n2);
  
  const auto& dist = floyd.get_dist_mat();
  
  // Distance 0->1 should be -1 (direct negative edge)
  EXPECT_EQ(dist(i0, i1), -1);
  
  // Distance 0->2 should be 1 (0->1->2: -1+2=1, better than direct 0->2: 3)
  EXPECT_EQ(dist(i0, i2), 1);
}
 
// Test negative cycle detection
TEST(FloydNegativeCycle, detects_negative_cycles)
{
  Grafo g;
  g.insert_node(0);
  g.insert_node(1);
  g.insert_node(2);
  
  // Create cycle: 0->1->2->0 with total weight -1
  insert_arc_by_value(g, 0, 1, 1);
  insert_arc_by_value(g, 1, 2, -1);
  insert_arc_by_value(g, 2, 0, -1);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  EXPECT_TRUE(floyd.has_negative_cycle());
}
 
// Test index_node method
TEST(FloydIndexNode, finds_correct_indices)
{
  Grafo g;
  g.insert_node(10);
  g.insert_node(20);
  g.insert_node(30);
  
  insert_arc_by_value(g, 10, 20, 1);
  insert_arc_by_value(g, 20, 30, 1);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  const auto nodes = floyd.get_nodes();
  
  // Test that we can find each node's index
  for (size_t i = 0; i < nodes.size(); ++i) {
    auto node = floyd.select_node(i);
    EXPECT_EQ(floyd.index_node(node), static_cast<long>(i));
  }
}
 
// Test null pointer handling
TEST(FloydIndexNode, throws_on_null_pointer)
{
  Grafo g;
  g.insert_node(0);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  EXPECT_THROW(floyd.index_node(nullptr), std::invalid_argument);
}
 
// Test path reconstruction with indices
TEST(FloydPathReconstruction, throws_on_invalid_indices)
{
  Grafo g;
  g.insert_node(0);
  g.insert_node(1);
  insert_arc_by_value(g, 0, 1, 1);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  const long n = g.get_num_nodes();
  
  EXPECT_THROW(floyd.get_min_path(-1L, 0L), std::out_of_range);
  EXPECT_THROW(floyd.get_min_path(0L, n), std::out_of_range);
  EXPECT_THROW(floyd.get_min_path(n, 0L), std::out_of_range);
}
 
// Test path reconstruction returns valid path
TEST(FloydPathReconstruction, returns_valid_path)
{
  Grafo g;
  auto n0 = g.insert_node(0);
  auto n1 = g.insert_node(1);
  auto n2 = g.insert_node(2);
  
  g.insert_arc(n0, n1, 1);
  g.insert_arc(n1, n2, 2);
  g.insert_arc(n0, n2, 5);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  // Get actual indices
  long i0 = floyd.index_node(n0);
  long i2 = floyd.index_node(n2);
  
  // Get shortest path from n0 to n2
  auto path = floyd.get_min_path(i0, i2);
  
  // Path should have at least 2 nodes (start and end)
  EXPECT_GE(path.size(), 2u);
  
  // First node should be n0, last should be n2
  EXPECT_EQ(path.get_first_node(), n0);
  EXPECT_EQ(path.get_last_node(), n2);
}
 
// Test self-path
TEST(FloydPathReconstruction, handles_self_paths)
{
  Grafo g;
  g.insert_node(0);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  auto path = floyd.get_min_path(0L, 0L);
  EXPECT_EQ(path.size(), 1u);
}
 
// Test entry formatting
TEST(FloydUtility, entry_formats_distances_correctly)
{
  Grafo g;
  g.insert_node(0);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  EXPECT_EQ(floyd.entry(42), "42");
  EXPECT_EQ(floyd.entry(numeric_limits<int>::max()), "Inf");
  EXPECT_EQ(floyd.entry(-5), "-5");
}
 
// Test path matrix structure
TEST(FloydMatrices, path_matrix_has_correct_structure)
{
  Grafo g;
  g.insert_node(0);
  g.insert_node(1);
  g.insert_node(2);
  
  insert_arc_by_value(g, 0, 1, 1);
  insert_arc_by_value(g, 1, 2, 1);
  insert_arc_by_value(g, 0, 2, 5);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  const auto& path_mat = floyd.get_path_mat();
  const auto& dist = floyd.get_dist_mat();
  const int Inf = numeric_limits<int>::max();
  const long n = g.get_num_nodes();
  
  EXPECT_EQ(path_mat.rows(), n);
  EXPECT_EQ(path_mat.cols(), n);
  
  // Path matrix entries should be valid node indices
  for (long i = 0; i < n; ++i) {
    for (long j = 0; j < n; ++j) {
      if (dist(i, j) == Inf) {
        EXPECT_EQ(path_mat(i, j), -1);
        continue;
      }
 
      // Reachable (including i == j): must be a valid index
      long k = path_mat(i, j);
      EXPECT_GE(k, 0);
      EXPECT_LT(k, n);
    }
  }
}
 
// Test complete graph
TEST(FloydLargeGraph, handles_complete_graph)
{
  const int N = 10;
  Grafo g;
  vector<GNode*> nodes;
  
  for (int i = 0; i < N; ++i)
    nodes.push_back(g.insert_node(i));
  
  // Create complete graph
  for (int i = 0; i < N; ++i)
    for (int j = 0; j < N; ++j)
      if (i != j)
        g.insert_arc(nodes[i], nodes[j], i + j + 1);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  EXPECT_FALSE(floyd.has_negative_cycle());
  
  const auto& dist = floyd.get_dist_mat();
  
  // All diagonal elements should be 0
  for (int i = 0; i < N; ++i)
    EXPECT_EQ(dist(i, i), 0);
  
  // All off-diagonal elements should be finite and positive
  for (int i = 0; i < N; ++i)
    for (int j = 0; j < N; ++j)
      if (i != j) {
        EXPECT_GT(dist(i, j), 0);
        EXPECT_LT(dist(i, j), numeric_limits<double>::max());
      }
}
 
// Test single node graph
TEST(FloydStress, handles_single_node_graph)
{
  Grafo g;
  g.insert_node(42);
  
  Floyd_All_Shortest_Paths<Grafo> floyd(g);
  
  EXPECT_FALSE(floyd.has_negative_cycle());
  
  const auto& dist = floyd.get_dist_mat();
  EXPECT_EQ(dist.rows(), 1);
  EXPECT_EQ(dist.cols(), 1);
  EXPECT_EQ(dist(0, 0), 0);
  
  // Test path reconstruction for single node
  auto path = floyd.get_min_path(0L, 0L);
  EXPECT_EQ(path.size(), 1u);
  EXPECT_EQ(path.get_first_node()->get_info(), 42);
}