net_apps.H

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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.
*/
 
#ifndef NET_APPS_H
#define NET_APPS_H
 
#include <array>
#include <vector>
#include <string>
#include <functional>
#include <tpl_net.H>
#include <tpl_maxflow.H>
#include <tpl_netcost.H>
#include <tpl_dynSetTree.H>
#include <tpl_dynListQueue.H>
 
namespace Aleph {
 
//==============================================================================
// CIRCULATION WITH DEMANDS
//==============================================================================
 
template <typename Flow_Type>
struct CirculationResult
{
  bool feasible{false};                
  Flow_Type excess_flow{0};            
  DynMapTree<void *, Flow_Type> flow;  
};
 
template <class Net, class GetDemand, class GetLower, template <class> class Maxflow = Dinic_Maximum_Flow>
CirculationResult<typename Net::Flow_Type> solve_circulation(Net &net, GetDemand get_demand,
                                                             GetLower get_lower)
{
  using Node = typename Net::Node;
  using Arc = typename Net::Arc;
  using Flow_Type = typename Net::Flow_Type;
 
  CirculationResult<Flow_Type> result;
 
  // Collect original nodes (before adding super nodes)
  DynList<Node *> original_nodes;
  for (Node_Iterator<Net> it(net); it.has_curr(); it.next_ne())
    original_nodes.append(it.get_curr());
 
  // Store original capacities to restore later
  DynMapTree<Arc *, Flow_Type> original_caps;
  for (Arc_Iterator<Net> it(net); it.has_curr(); it.next_ne())
    {
      Arc *arc = it.get_curr();
      original_caps[arc] = arc->cap;
    }
 
  // Create super-source and super-sink for the transformed network
  Node *super_source = net.insert_node();
  Node *super_sink = net.insert_node();
 
  // Track arcs we add so we can remove them later
  DynList<Arc *> added_arcs;
 
  // Calculate total positive ADJUSTED demand
  // (This must be computed from adjusted demands, not original demands)
  Flow_Type total_demand{0};
 
  // Add edges from super-source/to super-sink based on adjusted demands
  for (auto *v : original_nodes)
    {
      // Calculate adjusted demand: d'(v) = d(v) + l_out(v) - l_in(v)
      // This comes from the circulation reduction with lower bounds:
      // - For each arc (u,v) with lower bound l: the mandatory l units
      //   count as outflow from u and inflow to v.
      // - d'(u) = d(u) + l (gains "debt" from mandatory outflow)
      // - d'(v) = d(v) - l (satisfied by mandatory inflow)
      Flow_Type lower_in{0}, lower_out{0};
      for (typename Net::Node_Arc_Iterator ait(v); ait.has_curr(); ait.next_ne())
        {
          Arc *arc = ait.get_curr();
          Flow_Type lb = get_lower(arc);
          if (net.get_tgt_node(arc) == v)
            lower_in += lb;
          if (net.get_src_node(arc) == v)
            lower_out += lb;
        }
 
      Flow_Type adjusted_demand = get_demand(v) + lower_out - lower_in;
 
      if (adjusted_demand > 0)
        {
          total_demand += adjusted_demand;
          added_arcs.append(net.insert_arc(super_source, v, adjusted_demand));
        }
      else if (adjusted_demand < 0)
        added_arcs.append(net.insert_arc(v, super_sink, -adjusted_demand));
    }
 
  // Trivial case: no adjusted demands means circulation with lower bounds is feasible
  if (total_demand == Flow_Type{0})
    {
      result.feasible = true;
      // Set all flows to their lower bounds
      for (Arc_Iterator<Net> it(net); it.has_curr(); it.next_ne())
        {
          Arc *arc = it.get_curr();
          if (original_caps.contains(arc))
            result.flow[arc] = get_lower(arc);
        }
      // Cleanup: remove added arcs and nodes
      for (Arc *arc : added_arcs)
        net.remove_arc(arc);
      net.remove_node(super_source);
      net.remove_node(super_sink);
      return result;
    }
 
  // Adjust arc capacities: cap' = cap - lower_bound
  for (Arc_Iterator<Net> it(net); it.has_curr(); it.next_ne())
    {
      Arc *arc = it.get_curr();
      Node *src = net.get_src_node(arc);
      Node *tgt = net.get_tgt_node(arc);
 
      // Skip super-source/sink arcs (they don't have lower bounds)
      if (src == super_source or tgt == super_sink)
        continue;
 
      Flow_Type lb = get_lower(arc);
      arc->cap -= lb;
    }
 
  // Ensure super_source is the ONLY source and super_sink is the ONLY sink.
  // For the max-flow to correctly compute feasibility, we need paths from s* to t*.
  //
  // For original sinks (nodes with no outgoing arcs), flow arriving at them has
  // nowhere to go. We add arcs to super_sink. The capacity should be the incoming
  // capacity from ORIGINAL arcs only (not demand arcs), since we're measuring
  // how much flow can reach this sink through the original network.
  //
  // For original sources (nodes with no incoming arcs), we add zero-capacity
  // arcs just to make them non-sources in the network topology.
  for (auto *v : original_nodes)
    {
      // Check if v is still a source (no incoming arcs)
      if (net.get_in_degree(v) == 0)
        added_arcs.append(net.insert_arc(super_source, v, Flow_Type{0}));
 
      // Check if v is still a sink (no outgoing arcs): add arc to super_sink
      // Compute incoming capacity from ORIGINAL arcs only
      if (net.get_out_degree(v) == 0)
        {
          Flow_Type in_cap_orig{0};
          for (typename Net::Node_Arc_Iterator ait(v); ait.has_curr(); ait.next_ne())
            if (Arc *arc = ait.get_curr(); net.get_tgt_node(arc) == v and original_caps.contains(arc))
              in_cap_orig += arc->cap;  // Use modified cap (original - lower)
          added_arcs.append(net.insert_arc(v, super_sink, in_cap_orig));
        }
    }
 
  // Solve max-flow on the transformed network
  Flow_Type max_flow = Maxflow<Net>()(net);
 
  result.feasible = (max_flow == total_demand);
  result.excess_flow = max_flow;
 
  // Compute actual circulation flow on original arcs.
  // The max-flow determines feasibility but may route through auxiliary arcs.
  // We need to compute flows on original arcs using flow conservation equations.
  //
  // For each original arc, start with lower bound and adjust based on demands.
  // First, initialize flows to lower bounds.
  for (Arc_Iterator<Net> it(net); it.has_curr(); it.next_ne())
    {
      Arc *arc = it.get_curr();
      if (original_caps.contains(arc))
        result.flow[arc] = get_lower(arc);
    }
 
  // If feasible, compute the actual circulation flows.
  // For each node, we need: inflow - outflow = demand
  // Use an iterative approach: repeatedly process nodes until all balances are satisfied.
  if (result.feasible)
    {
      // Iterate until all nodes have correct flow balance
      bool changed = true;
      int max_iterations = original_nodes.size() * 2;  // Safety limit
      while (changed and max_iterations-- > 0)
        {
          changed = false;
          for (auto *v : original_nodes)
            {
              // Compute current balance at v
              Flow_Type current_in{0}, current_out{0};
              for (typename Net::Node_Arc_Iterator ait(v); ait.has_curr(); ait.next_ne())
                {
                  Arc *arc = ait.get_curr();
                  if (not original_caps.contains(arc))
                    continue;
                  if (net.get_tgt_node(arc) == v)
                    current_in += result.flow[arc];
                  if (net.get_src_node(arc) == v)
                    current_out += result.flow[arc];
                }
 
              // imbalance = (current_in - current_out) - demand
              Flow_Type imbalance = (current_in - current_out) - get_demand(v);
 
              if (imbalance < Flow_Type{0})
                {
                  // Node needs more inflow - increase flow on incoming arcs
                  Flow_Type deficit = -imbalance;
                  for (typename Net::Node_Arc_Iterator ait(v); ait.has_curr(); ait.next_ne())
                    {
                      Arc *arc = ait.get_curr();
                      if (not original_caps.contains(arc))
                        continue;
                      if (net.get_tgt_node(arc) != v)
                        continue;
 
                      Flow_Type slack = original_caps[arc] - result.flow[arc];
                      Flow_Type increase = (slack < deficit) ? slack : deficit;
                      if (increase > Flow_Type{0})
                        {
                          result.flow[arc] += increase;
                          deficit -= increase;
                          changed = true;
                        }
                      if (deficit <= Flow_Type{0})
                        break;
                    }
                }
              else if (imbalance > Flow_Type{0})
                {
                  // Node has excess inflow - increase flow on outgoing arcs
                  Flow_Type excess = imbalance;
                  for (typename Net::Node_Arc_Iterator ait(v); ait.has_curr(); ait.next_ne())
                    {
                      Arc *arc = ait.get_curr();
                      if (not original_caps.contains(arc))
                        continue;
                      if (net.get_src_node(arc) != v)
                        continue;
 
                      Flow_Type slack = original_caps[arc] - result.flow[arc];
                      Flow_Type increase = (slack < excess) ? slack : excess;
                      if (increase > Flow_Type{0})
                        {
                          result.flow[arc] += increase;
                          excess -= increase;
                          changed = true;
                        }
                      if (excess <= Flow_Type{0})
                        break;
                    }
                }
            }
        }
    }
 
  // Cleanup: restore original capacities and reset flows
  for (Arc_Iterator<Net> it(net); it.has_curr(); it.next_ne())
    {
      Arc *arc = it.get_curr();
      if (original_caps.contains(arc))
        {
          arc->cap = original_caps[arc];
          arc->flow = Flow_Type{0};  // Reset flow
        }
    }
 
  // Cleanup: remove added arcs (must be done before removing nodes)
  for (Arc *arc : added_arcs)
    net.remove_arc(arc);
 
  // Cleanup: remove super nodes we created
  net.remove_node(super_source);
  net.remove_node(super_sink);
 
  return result;
}
 
//==============================================================================
// PROJECT SELECTION (MAX PROFIT / CLOSURE)
//==============================================================================
 
template <typename Value_Type>
struct Project
{
  size_t id;                          
  Value_Type profit;                  
  std::vector<size_t> prerequisites;  
  std::string name;                   
 
  Project(size_t id_, Value_Type profit_, const std::vector<size_t> &prereqs = {},
          const std::string &name_ = "")
    : id(id_), profit(profit_), prerequisites(prereqs), name(name_)
  {}
};
 
template <typename Value_Type>
struct ProjectSelectionResult
{
  Value_Type max_profit{0};      
  std::vector<size_t> selected;  
  Value_Type total_revenue{0};   
  Value_Type total_cost{0};      
};
 
template <typename Value_Type>
ProjectSelectionResult<Value_Type> solve_project_selection(const std::vector<Project<Value_Type>> &projects)
{
  using Net = Net_Graph<Net_Node<Empty_Class>, Net_Arc<Empty_Class, Value_Type>>;
  using Node = typename Net::Node;
 
  ProjectSelectionResult<Value_Type> result;
 
  if (projects.empty())
    return result;
 
  Net net;
  const Value_Type INF = std::numeric_limits<Value_Type>::max() / 2;
 
  // Create source and sink
  Node *source = net.insert_node();
  Node *sink = net.insert_node();
 
  // Create project nodes
  std::vector<Node *> project_nodes(projects.size());
  for (size_t i = 0; i < projects.size(); ++i)
    project_nodes[i] = net.insert_node();
 
  // Connect based on profits
  Value_Type sum_positive{0};
 
  for (size_t i = 0; i < projects.size(); ++i)
    {
      Value_Type p = projects[i].profit;
 
      // Source to all projects (capacity = profit if positive, 0 otherwise)
      // This ensures all project nodes are not sources
      Value_Type source_cap = (p > 0) ? p : Value_Type{0};
      net.insert_arc(source, project_nodes[i], source_cap);
      if (p > 0)
        sum_positive += p;
 
      // All projects connect to sink (cost projects with capacity = -profit,
      // others with capacity 0 to ensure proper network structure)
      Value_Type sink_cap = (p < 0) ? -p : Value_Type{0};
      net.insert_arc(project_nodes[i], sink, sink_cap);
 
      // Add prerequisite edges (infinite capacity)
      for (size_t prereq : projects[i].prerequisites)
        if (prereq < projects.size())
          net.insert_arc(project_nodes[i], project_nodes[prereq], INF);
    }
 
  // Solve min-cut (via max-flow)
  Value_Type min_cut = dinic_maximum_flow(net);
 
  result.max_profit = sum_positive - min_cut;
 
  // Find selected projects (reachable from source in residual graph)
  DynSetTree<Node *> reachable;
 
  // BFS from source in residual graph
  DynListQueue<Node *> queue;
  queue.put(source);
  reachable.insert(source);
 
  while (not queue.is_empty())
    {
      Node *u = queue.front();
      queue.get();
 
      for (typename Net::Node_Arc_Iterator it(u); it.has_curr(); it.next_ne())
        {
          auto arc = it.get_curr();
          auto v = net.get_connected_node(arc, u);
 
          if (reachable.contains(v))
            continue;
 
          // Check residual capacity
          Value_Type residual;
          if (net.get_src_node(arc) == u)
            residual = arc->cap - arc->flow;
          else
            residual = arc->flow;
 
          if (residual > Value_Type{0})
            {
              reachable.insert(v);
              queue.put(v);
            }
        }
    }
 
  // Projects reachable from source are selected
  for (size_t i = 0; i < projects.size(); ++i)
    if (reachable.contains(project_nodes[i]))
      {
        result.selected.push_back(i);
        if (projects[i].profit > 0)
          result.total_revenue += projects[i].profit;
        else
          result.total_cost += -projects[i].profit;
      }
 
  return result;
}
 
//==============================================================================
// BASEBALL ELIMINATION
//==============================================================================
 
struct Team
{
  std::string name;
  int wins;
  int losses;
  int remaining;             
  std::vector<int> against;  
 
  Team(const std::string &n = "", int w = 0, int l = 0, int r = 0)
    : name(n), wins(w), losses(l), remaining(r)
  {}
};
 
struct BaseballEliminationResult
{
  bool eliminated{false};           
  std::vector<size_t> certificate;  
  int max_possible_wins{0};         
};
 
inline BaseballEliminationResult check_baseball_elimination(const std::vector<Team> &teams,
                                                            size_t team_idx)
{
  using Net = Net_Graph<Net_Node<Empty_Class>, Net_Arc<Empty_Class, int>>;
  using Node = Net::Node;
 
  BaseballEliminationResult result;
 
  if (team_idx >= teams.size())
    return result;
 
  const Team &x = teams[team_idx];
  result.max_possible_wins = x.wins + x.remaining;
 
  // Trivial elimination check
  for (size_t i = 0; i < teams.size(); ++i)
    if (i != team_idx and teams[i].wins > result.max_possible_wins)
      {
        result.eliminated = true;
        result.certificate.push_back(i);
        return result;
      }
 
  Net net;
 
  Node *source = net.insert_node();
  Node *sink = net.insert_node();
 
  // Create team nodes (excluding team x)
  std::vector<Node *> team_nodes(teams.size(), nullptr);
  for (size_t i = 0; i < teams.size(); ++i)
    if (i != team_idx)
      {
        team_nodes[i] = net.insert_node();
 
        // Team to sink: capacity = max wins x can have - current wins of i
        if (int cap = result.max_possible_wins - teams[i].wins; cap > 0)
          net.insert_arc(team_nodes[i], sink, cap);
      }
 
  // Create game nodes
  int total_games = 0;
  for (size_t i = 0; i < teams.size(); ++i)
    {
      if (i == team_idx)
        continue;
 
      for (size_t j = i + 1; j < teams.size(); ++j)
        {
          if (j == team_idx)
            continue;
 
          int games = teams[i].against[j];
          if (games > 0)
            {
              constexpr int INF = 1000000;
              total_games += games;
 
              Node *game_node = net.insert_node();
              net.insert_arc(source, game_node, games);
              net.insert_arc(game_node, team_nodes[i], INF);
              net.insert_arc(game_node, team_nodes[j], INF);
            }
        }
    }
 
  // Ensure network has single source and sink
  net.make_super_source();
  net.make_super_sink();
 
  const int max_flow = dinic_maximum_flow(net);
 
  result.eliminated = (max_flow < total_games);
 
  // If eliminated, find certificate (teams in source side of min-cut)
  if (result.eliminated)
    {
      // BFS from source in residual graph
      DynSetTree<Node *> reachable;
      DynListQueue<Node *> queue;
      queue.put(source);
      reachable.insert(source);
 
      while (not queue.is_empty())
        {
          Node *u = queue.front();
          queue.get();
 
          for (Net::Node_Arc_Iterator it(u); it.has_curr(); it.next_ne())
            {
              const auto arc = it.get_curr();
              auto v = net.get_connected_node(arc, u);
 
              if (reachable.contains(v))
                continue;
 
              if (const int residual =
                    (net.get_src_node(arc) == u) ? (arc->cap - arc->flow) : arc->flow;
                  residual > 0)
                {
                  reachable.insert(v);
                  queue.put(v);
                }
            }
        }
 
      for (size_t i = 0; i < teams.size(); ++i)
        if (i != team_idx and team_nodes[i] != nullptr and reachable.contains(team_nodes[i]))
          result.certificate.push_back(i);
    }
 
  return result;
}
 
//==============================================================================
// IMAGE SEGMENTATION (BINARY LABELING)
//==============================================================================
 
struct SegmentationResult
{
  std::vector<std::vector<int>> labels;  
  double energy{0};                      
};
 
template <typename Value_Type>
SegmentationResult segment_image(size_t rows, size_t cols,
                                 const std::vector<std::vector<std::array<Value_Type, 2>>> &data_cost,
                                 Value_Type smoothness)
{
  using Net = Net_Graph<Net_Node<Empty_Class>, Net_Arc<Empty_Class, Value_Type>>;
  using Node = typename Net::Node;
 
  SegmentationResult result;
  result.labels.resize(rows, std::vector<int>(cols, 0));
 
  if (rows == 0 or cols == 0)
    return result;
 
  Net net;
 
  // Create source (label 0) and sink (label 1)
  Node *source = net.insert_node();
  Node *sink = net.insert_node();
 
  // Create pixel nodes
  std::vector<std::vector<Node *>> pixels(rows, std::vector<Node *>(cols));
  for (size_t i = 0; i < rows; ++i)
    for (size_t j = 0; j < cols; ++j)
      pixels[i][j] = net.insert_node();
 
  // Add data term edges (standard graph cut model for binary labeling)
  // See: Boykov, Kolmogorov "An Experimental Comparison of Min-Cut/Max-Flow Algorithms"
  for (size_t i = 0; i < rows; ++i)
    for (size_t j = 0; j < cols; ++j)
      {
        // Source to pixel: capacity = cost of background (label 0)
        // If this arc is cut, pixel goes to sink side = background
        net.insert_arc(source, pixels[i][j], data_cost[i][j][0]);
 
        // Pixel to sink: capacity = cost of foreground (label 1)
        // If this arc is cut, pixel stays on source side = foreground
        net.insert_arc(pixels[i][j], sink, data_cost[i][j][1]);
      }
 
  // Add smoothness term edges (4-connected)
  for (size_t i = 0; i < rows; ++i)
    for (size_t j = 0; j < cols; ++j)
      {
        // Right neighbor
        if (j + 1 < cols)
          {
            net.insert_arc(pixels[i][j], pixels[i][j + 1], smoothness);
            net.insert_arc(pixels[i][j + 1], pixels[i][j], smoothness);
          }
 
        // Bottom neighbor
        if (i + 1 < rows)
          {
            net.insert_arc(pixels[i][j], pixels[i + 1][j], smoothness);
            net.insert_arc(pixels[i + 1][j], pixels[i][j], smoothness);
          }
      }
 
  // Ensure network has single source and sink
  net.make_super_source();
  net.make_super_sink();
 
  // Compute min-cut
  Value_Type min_cut = dinic_maximum_flow(net);
  result.energy = static_cast<double>(min_cut);
 
  // Extract labels (BFS from source in residual graph)
  DynSetTree<Node *> foreground;  // Reachable = foreground (label 1)
 
  DynListQueue<Node *> queue;
  queue.put(source);
  foreground.insert(source);
 
  while (not queue.is_empty())
    {
      Node *u = queue.front();
      queue.get();
 
      for (typename Net::Node_Arc_Iterator it(u); it.has_curr(); it.next_ne())
        {
          auto arc = it.get_curr();
          auto v = net.get_connected_node(arc, u);
 
          if (foreground.contains(v))
            continue;
 
          Value_Type residual = (net.get_src_node(arc) == u) ? (arc->cap - arc->flow) : arc->flow;
 
          if (residual > Value_Type{0})
            {
              foreground.insert(v);
              queue.put(v);
            }
        }
    }
 
  // Set labels
  for (size_t i = 0; i < rows; ++i)
    for (size_t j = 0; j < cols; ++j)
      result.labels[i][j] = foreground.contains(pixels[i][j]) ? 1 : 0;
 
  return result;
}
 
//==============================================================================
// SURVEY DESIGN
//==============================================================================
 
struct SurveyQuestion
{
  size_t id;
  int min_responses;  
  int max_responses;  
};
 
struct SurveyRespondent
{
  size_t id;
  int min_questions;                       
  int max_questions;                       
  std::vector<size_t> eligible_questions;  
};
 
struct SurveyDesignResult
{
  bool feasible{false};
  std::vector<std::pair<size_t, size_t>> assignments;  
};
 
inline SurveyDesignResult design_survey(const std::vector<SurveyQuestion> &questions,
                                        const std::vector<SurveyRespondent> &respondents)
{
  using Net = Net_Graph<Net_Node<Empty_Class>, Net_Arc<Empty_Class, int>>;
  using Node = Net::Node;
 
  SurveyDesignResult result;
 
  if (questions.empty() or respondents.empty())
    return result;
 
  Net net;
 
  Node *source = net.insert_node();
  Node *sink = net.insert_node();
 
  // Create question nodes
  std::vector<Node *> question_nodes(questions.size());
  for (size_t i = 0; i < questions.size(); ++i)
    {
      question_nodes[i] = net.insert_node();
 
      // Question to sink: [min, max] responses
      // For feasibility check, use max capacity
      net.insert_arc(question_nodes[i], sink, questions[i].max_responses);
    }
 
  // Create respondent nodes
  std::vector<Node *> respondent_nodes(respondents.size());
  for (size_t i = 0; i < respondents.size(); ++i)
    {
      respondent_nodes[i] = net.insert_node();
 
      // Source to respondent: [min, max] questions
      net.insert_arc(source, respondent_nodes[i], respondents[i].max_questions);
 
      // Respondent to eligible questions
      for (size_t q : respondents[i].eligible_questions)
        if (q < questions.size())
          net.insert_arc(respondent_nodes[i], question_nodes[q], 1);
    }
 
  // Ensure network has single source and sink
  net.make_super_source();
  net.make_super_sink();
 
  // Compute max flow
  dinic_maximum_flow(net);
 
  // Check if minimum constraints are satisfied
  result.feasible = true;
 
  for (size_t i = 0; i < questions.size(); ++i)
    {
      int responses = 0;
      for (Net::Node_Arc_Iterator it(question_nodes[i]); it.has_curr(); it.next_ne())
        if (const auto arc = it.get_curr(); net.get_tgt_node(arc) == sink)
          responses = arc->flow;
 
      if (responses < questions[i].min_responses)
        {
          result.feasible = false;
          break;
        }
    }
 
  // Extract assignments
  if (result.feasible)
    for (size_t r = 0; r < respondents.size(); ++r)
      for (Net::Node_Arc_Iterator it(respondent_nodes[r]); it.has_curr(); it.next_ne())
        if (const auto arc = it.get_curr(); arc->flow > 0)
          {
            // Find which question this is
            const auto tgt = net.get_tgt_node(arc);
            for (size_t q = 0; q < questions.size(); ++q)
              if (question_nodes[q] == tgt)
                {
                  result.assignments.push_back({r, q});
                  break;
                }
          }
 
  return result;
}
 
}  // namespace Aleph
 
#endif  // NET_APPS_H