mst_example.C

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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
  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 <iostream>
#include <iomanip>
#include <string>
#include <chrono>
#include <random>
#include <tpl_graph.H>
#include <Kruskal.H>
#include <Prim.H>
#include <tclap/CmdLine.h>
 
using namespace std;
using namespace Aleph;
 
// Node: location name
using LocationNode = Graph_Node<string>;
 
// Arc: cable length (cost)
using CableArc = Graph_Arc<double>;
 
// Undirected graph for network design
using NetworkGraph = List_Graph<LocationNode, CableArc>;
 
// Distance accessor
struct CableLength
{
  using Distance_Type = double;
  static constexpr double Max_Distance = numeric_limits<double>::infinity();
  static constexpr double Zero_Distance = 0.0;
  
  double operator()(NetworkGraph::Arc* arc) const
  {
    return arc->get_info();
  }
};
 
NetworkGraph build_campus_network()
{
  NetworkGraph g;
  
  // Buildings
  auto library   = g.insert_node("Library");
  auto admin     = g.insert_node("AdminBldg");
  auto gym       = g.insert_node("Gym");
  auto scilab    = g.insert_node("SciLab");
  auto mainhall  = g.insert_node("MainHall");
  auto dorm      = g.insert_node("Dorm");
  auto artstudio = g.insert_node("ArtStudio");
  auto cafeteria = g.insert_node("Cafeteria");
  auto theater   = g.insert_node("Theater");
  
  // Potential cable routes (with lengths in meters)
  g.insert_arc(library, admin, 15);
  g.insert_arc(admin, gym, 20);
  g.insert_arc(library, scilab, 12);
  g.insert_arc(admin, mainhall, 8);
  g.insert_arc(gym, dorm, 25);
  g.insert_arc(scilab, mainhall, 10);
  g.insert_arc(mainhall, dorm, 18);
  g.insert_arc(scilab, artstudio, 22);
  g.insert_arc(mainhall, cafeteria, 14);
  g.insert_arc(dorm, theater, 16);
  g.insert_arc(artstudio, cafeteria, 9);
  g.insert_arc(cafeteria, theater, 11);
  
  // Additional cross-connections for more interesting MST
  g.insert_arc(library, mainhall, 17);
  g.insert_arc(scilab, cafeteria, 19);
  g.insert_arc(admin, dorm, 30);
  
  return g;
}
 
NetworkGraph generate_random_graph(size_t num_nodes, size_t num_edges, 
                                   unsigned seed)
{
  NetworkGraph g;
  if (num_nodes == 0)
    return g;
 
  if (num_edges < num_nodes - 1)
    num_edges = num_nodes - 1;
 
  mt19937 rng(seed);
  uniform_real_distribution<double> weight_dist(1.0, 100.0);
  
  // Create nodes
  vector<NetworkGraph::Node*> nodes;
  for (size_t i = 0; i < num_nodes; i++)
    nodes.push_back(g.insert_node("N" + to_string(i)));
 
  if (num_nodes == 1)
    return g;
  
  // First, create a spanning tree to ensure connectivity
  for (size_t i = 1; i < num_nodes; i++)
  {
    uniform_int_distribution<size_t> parent_dist(0, i - 1);
    size_t parent = parent_dist(rng);
    g.insert_arc(nodes[parent], nodes[i], weight_dist(rng));
  }
  
  // Add remaining edges
  size_t edges_to_add = num_edges - (num_nodes - 1);
  uniform_int_distribution<size_t> node_dist(0, num_nodes - 1);
  
  for (size_t i = 0; i < edges_to_add; i++)
  {
    size_t a = node_dist(rng);
    size_t b = node_dist(rng);
    if (a != b)
      g.insert_arc(nodes[a], nodes[b], weight_dist(rng));
  }
  
  return g;
}
 
void print_mst(NetworkGraph& tree, const string& algorithm)
{
  double total_weight = 0;
  
  cout << "\n" << algorithm << " MST Edges:" << endl;
  for (auto ait = tree.get_arc_it(); ait.has_curr(); ait.next())
  {
    auto* arc = ait.get_curr();
    auto* src = tree.get_src_node(arc);
    auto* tgt = tree.get_tgt_node(arc);
    double weight = arc->get_info();
    total_weight += weight;
    
    cout << "  " << setw(12) << left << src->get_info() 
         << " --- " << setw(5) << right << weight 
         << " --- " << tgt->get_info() << endl;
  }
  
  cout << "Total weight: " << total_weight << endl;
  cout << "Edges in MST: " << tree.get_num_arcs() << endl;
}
 
double run_kruskal(NetworkGraph& g, NetworkGraph& tree, bool verbose)
{
  auto start = chrono::high_resolution_clock::now();
  
  Kruskal_Min_Spanning_Tree<NetworkGraph, CableLength> kruskal;
  kruskal(g, tree);
  
  auto end = chrono::high_resolution_clock::now();
  double ms = chrono::duration<double, milli>(end - start).count();
  
  if (verbose)
    print_mst(tree, "Kruskal's");
  
  return ms;
}
 
double run_prim(NetworkGraph& g, NetworkGraph& tree, bool verbose)
{
  auto start = chrono::high_resolution_clock::now();
  
  Prim_Min_Spanning_Tree<NetworkGraph, CableLength> prim;
  prim(g, tree);
  
  auto end = chrono::high_resolution_clock::now();
  double ms = chrono::duration<double, milli>(end - start).count();
  
  if (verbose)
    print_mst(tree, "Prim's");
  
  return ms;
}
 
double mst_total_weight(NetworkGraph& tree)
{
  double total = 0;
  for (auto ait = tree.get_arc_it(); ait.has_curr(); ait.next())
    total += ait.get_curr()->get_info();
  return total;
}
 
int main(int argc, char* argv[])
{
  try
  {
    TCLAP::CmdLine cmd("Minimum Spanning Tree Example", ' ', "1.0");
    
    TCLAP::SwitchArg benchArg("b", "benchmark",
      "Run performance benchmark", false);
    TCLAP::ValueArg<size_t> nodesArg("n", "nodes",
      "Number of nodes for benchmark", false, 1000, "size_t");
    TCLAP::ValueArg<size_t> edgesArg("e", "edges",
      "Number of edges for benchmark", false, 5000, "size_t");
    TCLAP::ValueArg<unsigned> seedArg("s", "seed",
      "Random seed", false, 42, "unsigned");
    TCLAP::SwitchArg verboseArg("v", "verbose",
      "Show detailed output", false);
    
    cmd.add(benchArg);
    cmd.add(nodesArg);
    cmd.add(edgesArg);
    cmd.add(seedArg);
    cmd.add(verboseArg);
    
    cmd.parse(argc, argv);
    
    bool benchmark = benchArg.getValue();
    size_t num_nodes = nodesArg.getValue();
    size_t num_edges = edgesArg.getValue();
    unsigned seed = seedArg.getValue();
    bool verbose = verboseArg.getValue();
    
    cout << "=== Minimum Spanning Tree Algorithms ===" << endl;
    
    if (!benchmark)
    {
      // Demo with small graph
      cout << "\nBuilding campus network..." << endl;
      NetworkGraph g = build_campus_network();
      
      cout << "Network has " << g.get_num_nodes() << " buildings and "
           << g.get_num_arcs() << " potential cable routes." << endl;
      
      // Run Kruskal
      cout << "\n--- Kruskal's Algorithm ---" << endl;
      cout << "Strategy: Sort edges, add if no cycle (uses Union-Find)" << endl;
      
      NetworkGraph kruskal_tree;
      double kruskal_time = run_kruskal(g, kruskal_tree, true);
      cout << "Time: " << fixed << setprecision(3) << kruskal_time << " ms" << endl;
      
      // Run Prim
      cout << "\n--- Prim's Algorithm ---" << endl;
      cout << "Strategy: Grow tree from start, always add cheapest edge" << endl;
      
      NetworkGraph prim_tree;
      double prim_time = run_prim(g, prim_tree, true);
      cout << "Time: " << fixed << setprecision(3) << prim_time << " ms" << endl;
      
      // Verify both give same total weight
      double kruskal_weight = mst_total_weight(kruskal_tree);
      double prim_weight = mst_total_weight(prim_tree);
      
      cout << "\n--- Verification ---" << endl;
      cout << "Kruskal MST weight: " << kruskal_weight << endl;
      cout << "Prim MST weight:    " << prim_weight << endl;
      
      if (abs(kruskal_weight - prim_weight) < 1e-9)
        cout << "Both algorithms found optimal MST!" << endl;
      else
        cout << "Warning: Weights differ (may have multiple optimal MSTs)" << endl;
    }
    else
    {
      // Performance benchmark
      cout << "\nGenerating random graph with " << num_nodes << " nodes and "
           << num_edges << " edges..." << endl;
      
      NetworkGraph g = generate_random_graph(num_nodes, num_edges, seed);
      cout << "Graph created: " << g.get_num_nodes() << " nodes, "
           << g.get_num_arcs() << " edges" << endl;
      
      // Benchmark Kruskal
      NetworkGraph kruskal_tree;
      double kruskal_time = run_kruskal(g, kruskal_tree, verbose);
      
      // Benchmark Prim
      NetworkGraph prim_tree;
      double prim_time = run_prim(g, prim_tree, verbose);
      
      cout << "\n--- Performance Results ---" << endl;
      cout << setw(15) << "Algorithm" << setw(15) << "Time (ms)" 
           << setw(15) << "MST Weight" << endl;
      cout << string(45, '-') << endl;
      cout << setw(15) << "Kruskal" 
           << setw(15) << fixed << setprecision(3) << kruskal_time
           << setw(15) << setprecision(2) << mst_total_weight(kruskal_tree) << endl;
      cout << setw(15) << "Prim"
           << setw(15) << fixed << setprecision(3) << prim_time
           << setw(15) << setprecision(2) << mst_total_weight(prim_tree) << endl;
      
      cout << "\n--- Complexity Analysis ---" << endl;
      cout << "V = " << num_nodes << ", E = " << num_edges << endl;
      cout << "E/V ratio: " << fixed << setprecision(2) 
           << (double)num_edges / num_nodes << " (";
      
      double ratio = (double)num_edges / num_nodes;
      if (ratio < 2)
        cout << "sparse graph -> Kruskal recommended";
      else if (ratio > 10)
        cout << "dense graph -> Prim recommended";
      else
        cout << "medium density -> similar performance";
      cout << ")" << endl;
    }
    
    cout << "\n=== Algorithm Summary ===" << endl;
    cout << "Kruskal: O(E log E), best for sparse graphs" << endl;
    cout << "Prim:    O(E log V), best for dense graphs" << endl;
    
    return 0;
  }
  catch (TCLAP::ArgException& e)
  {
    cerr << "Error: " << e.error() << " for arg " << e.argId() << endl;
    return 1;
  }
}