mincost_flow_example.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
  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 <vector>
#include <string>
#include <cstring>
#include <tpl_netcost.H>
#include <tpl_mincost.H>
 
using namespace std;
using namespace Aleph;
 
static void usage(const char* prog)
{
  cout << "Usage: " << prog << " [--compare] [--network <logistics|assignment|transportation|all>] [--help]\n";
  cout << "\nIf no flags are given, all demos are executed.\n";
}
 
static bool has_flag(int argc, char* argv[], const char* flag)
{
  for (int i = 1; i < argc; ++i)
    if (std::strcmp(argv[i], flag) == 0)
      return true;
  return false;
}
 
static const char* get_opt_value(int argc, char* argv[], const char* opt)
{
  for (int i = 1; i + 1 < argc; ++i)
    if (std::strcmp(argv[i], opt) == 0)
      return argv[i + 1];
  return nullptr;
}
 
// Type definitions
using Flow_Type = double;
using CostNet = Net_Cost_Graph<Net_Cost_Node<string>, Net_Cost_Arc<Empty_Class, Flow_Type>>;
using Node = CostNet::Node;
using Arc = CostNet::Arc;
 
CostNet build_simple_network()
{
  CostNet net;
  
  auto s = net.insert_node("Source");
  auto a = net.insert_node("A");
  auto b = net.insert_node("B");
  auto t = net.insert_node("Sink");
  
  // insert_arc(src, tgt, cap, cost)
  net.insert_arc(s, a, 10, 2.0);  // cap=10, cost=2
  net.insert_arc(s, b, 8, 3.0);   // cap=8, cost=3
  net.insert_arc(a, b, 5, 1.0);   // cap=5, cost=1
  net.insert_arc(a, t, 7, 4.0);   // cap=7, cost=4
  net.insert_arc(b, t, 10, 2.0);  // cap=10, cost=2
  
  return net;
}
 
static void demo_compare_algorithms_on_logistics()
{
  cout << "\n" << string(60, '=') << endl;
  cout << "Comparison: Cycle Canceling vs Network Simplex (Logistics Network)" << endl;
  cout << string(60, '=') << endl;
 
  {
    CostNet net = build_simple_network();
    auto r = max_flow_min_cost_by_cycle_canceling(net);
    auto flow = net.get_out_flow(net.get_source());
    auto cost = net.flow_cost();
    cout << "Cycle canceling:\n";
    cout << "  Max flow: " << flow << "\n";
    cout << "  Total cost: $" << fixed << setprecision(2) << cost << "\n";
    cout << "  Cycles cancelled: " << get<0>(r) << "\n";
  }
 
  {
    CostNet net = build_simple_network();
    size_t pivots = max_flow_min_cost_by_network_simplex(net);
    auto flow = net.get_out_flow(net.get_source());
    auto cost = net.flow_cost();
    cout << "Network simplex:\n";
    cout << "  Max flow: " << flow << "\n";
    cout << "  Total cost: $" << fixed << setprecision(2) << cost << "\n";
    cout << "  Pivots: " << pivots << "\n";
  }
}
 
void print_cost_network(CostNet& net, const string& title)
{
  cout << "\n=== " << title << " ===" << endl;
  cout << "Nodes: " << net.get_num_nodes() << ", Arcs: " << net.get_num_arcs() << endl;
  
  Flow_Type total_cost = 0;
  Flow_Type total_flow = 0;
  
  cout << "\nArc flows:" << endl;
  
  for (auto it = net.get_arc_it(); it.has_curr(); it.next())
  {
    auto* arc = it.get_curr();
    auto* src = net.get_src_node(arc);
    auto* tgt = net.get_tgt_node(arc);
    
    Flow_Type arc_cost = arc->flow * arc->cost;
    total_cost += arc_cost;
    
    if (net.is_source(src))
      total_flow += arc->flow;
    
    cout << "  " << setw(8) << left << src->get_info()
         << " -> " << setw(8) << left << tgt->get_info()
         << right << " : " << setw(4) << arc->flow 
         << " / " << setw(4) << arc->cap
         << " @ $" << arc->cost << endl;
  }
  
  cout << "\nTotal flow: " << total_flow << endl;
  cout << "Total cost: $" << fixed << setprecision(2) << total_cost << endl;
}
 
void demo_assignment_problem()
{
  cout << "\n" << string(60, '=') << endl;
  cout << "Example 2: Assignment Problem" << endl;
  cout << string(60, '=') << endl;
  
  cout << "\nProblem: Assign 3 workers to 3 jobs minimizing total cost." << endl;
  cout << "\nCost matrix:" << endl;
  cout << "          Job1  Job2  Job3" << endl;
  cout << "Worker1:   $9    $2    $7" << endl;
  cout << "Worker2:   $6    $4    $3" << endl;
  cout << "Worker3:   $5    $8    $1" << endl;
  
  vector<vector<double>> costs = {
    {9, 2, 7},  // Worker 1
    {6, 4, 3},  // Worker 2
    {5, 8, 1}   // Worker 3
  };
  
  auto result = solve_assignment<double>(costs);
  
  cout << "\nOptimal assignment:" << endl;
  
  if (result.feasible)
  {
    for (auto it = result.assignments.get_it(); it.has_curr(); it.next())
    {
      auto [w, j] = it.get_curr();
      cout << "  Worker" << (w+1) << " -> Job" << (j+1)
           << " (cost = $" << costs[w][j] << ")" << endl;
    }
    cout << "\nMinimum total cost: $" << result.total_cost << endl;
  }
  else
  {
    cout << "No feasible assignment found." << endl;
  }
}
 
void demo_transportation_problem()
{
  cout << "\n" << string(60, '=') << endl;
  cout << "Example 3: Transportation Problem" << endl;
  cout << string(60, '=') << endl;
  
  cout << "\nProblem: Ship goods from 2 warehouses to 3 stores." << endl;
  
  vector<double> supply = {30, 20};
  vector<double> demand = {15, 20, 15};
  vector<vector<double>> costs = {
    {4, 8, 8},  // Warehouse 1 to stores
    {6, 2, 4}   // Warehouse 2 to stores
  };
  
  auto result = solve_transportation<double>(supply, demand, costs);
  
  if (result.feasible)
  {
    cout << "\nOptimal shipments:" << endl;
    for (size_t i = 0; i < result.shipments.size(); ++i)
    {
      cout << "  Warehouse" << (i+1) << ": ";
      for (size_t j = 0; j < result.shipments[i].size(); ++j)
        cout << setw(6) << result.shipments[i][j] << " ";
      cout << endl;
    }
    cout << "\nMinimum cost: $" << result.total_cost << endl;
  }
  else
  {
    cout << "No feasible solution found." << endl;
  }
}
 
void demo_mincost_maxflow()
{
  cout << "\n" << string(60, '=') << endl;
  cout << "Example 1: Min-Cost Max-Flow" << endl;
  cout << string(60, '=') << endl;
  
  CostNet net = build_simple_network();
  
  print_cost_network(net, "Initial Network");
  
  cout << "\n--- Computing Min-Cost Max-Flow ---" << endl;
  
  // Using cycle canceling
  auto result = max_flow_min_cost_by_cycle_canceling(net);
  auto flow = net.get_out_flow(net.get_source());
  auto cost = net.flow_cost();
  
  print_cost_network(net, "After Optimization");
  
  cout << "\n*** Results ***" << endl;
  cout << "Maximum flow: " << flow << endl;
  cout << "Minimum cost: $" << fixed << setprecision(2) << cost << endl;
  cout << "Cycles cancelled: " << get<0>(result) << endl;
}
 
int main(int argc, char* argv[])
{
  cout << "=== Minimum Cost Maximum Flow ===" << endl;
  cout << "Optimize flow networks with costs per unit\n" << endl;
 
  if (has_flag(argc, argv, "--help"))
    {
      usage(argv[0]);
      return 0;
    }
 
  const bool compare = has_flag(argc, argv, "--compare");
  const char* network = get_opt_value(argc, argv, "--network");
  const string sel = network ? string(network) : string("all");
 
  if (compare)
    {
      demo_compare_algorithms_on_logistics();
      return 0;
    }
 
  if (argc == 1 || sel == "all" || sel == "logistics")
    demo_mincost_maxflow();
  if (argc == 1 || sel == "all" || sel == "assignment")
    demo_assignment_problem();
  if (argc == 1 || sel == "all" || sel == "transportation")
    demo_transportation_problem();
 
  if (!(argc == 1 || sel == "all" || sel == "logistics" || sel == "assignment" || sel == "transportation"))
    {
      cout << "Unknown --network value: " << sel << "\n";
      usage(argv[0]);
      return 1;
    }
  
  cout << "\n" << string(60, '=') << endl;
  cout << "Summary" << endl;
  cout << string(60, '=') << endl;
  
  cout << R"(
Min-Cost Max-Flow Problem:
  
  Given: Network with capacities and per-unit costs
  Find: Flow maximizing total flow at minimum cost
  
Algorithms:
  - Cycle Canceling: Simple, cancel negative-cost cycles
  - Network Simplex: Efficient, maintains spanning tree
  
Applications:
  - Transportation: Ship goods at minimum cost
  - Assignment: Match entities minimizing total cost
  - Supply Chain: Optimize logistics networks
)" << endl;
  
  return 0;
}