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Push-relabel in C++

In a course on discrete maths I took in my second year, we had to implement the push-relabel algorithm in C++. This is a modified solution that has a worse theoretical, but better practical running time.

#include <iostream>
#include <vector>
#include <fstream>
#include <algorithm>
#include <map>

using std::vector;
using node = int;
using edge = int;
using capacity = int;
using flow = int;

struct Edge {
  node from;   // from < 2^31
  node to;     // to   < 2^31
  capacity u;  // capacity < 2^31 
  flow f;      // flow <= capacity
};

// In an EdgeCollection we store both edges and their inverses. 
// A edge is represented by an integer [0,edges.size) and its inverse edge 
// by the negative minus one [-edges.size, 0).
class EdgeCollection {
public:
  EdgeCollection(vector<Edge>& es): edges{es} {}
  edge inverse(edge e) {
    return -e-1;
  }
  node from(edge e) {
    return e >= 0 ? edges[e].from : edges[inverse(e)].to;
  }
  node to(edge e) {
    return e >= 0 ? edges[e].to : edges[inverse(e)].from;
  }
  node capacity_left(edge e) {
    return e >= 0 ? edges[e].u - edges[e].f : get_flow(inverse(e));
  }
  flow get_flow(edge e) {
    return e >= 0 ? edges[e].f : capacity_left(inverse(e));
  }
  void augment(edge e, flow f) {
    if(e >= 0)    edges[e].f += f;
    else edges[inverse(e)].f -= f;
  }
  std::size_t size() {
    return edges.size();
  }
private:
  vector<Edge> edges;
};

// GoldbergTarjan contains the main push_relabel algorithm.
// We maintain the following invariants:
//  - incident[v] contains a list of edges starting in v,
//    inverse or otherwise, without duplicates.
//  - ex[v] stores the excess at v.
//  - phi[v] stores the distance phi(v).
//  - L[i] stores the active nodes v with phi[v] == i
//    without duplicates.
//  - A[v] stores a vector of allowed edges starting in v,
//    inverse or otherwise, without duplicates.
//    We may keep edges that were allowed once but aren't anymore.
class GoldbergTarjan {
public:
    GoldbergTarjan(int num_nodes, EdgeCollection ec, node source, node t_node)
      :phi(num_nodes,0), s{source}, t{t_node}, incoming(num_nodes), 
      outgoing(num_nodes), A(num_nodes), edges{ec}, ex(num_nodes, 0) {
      for(std::size_t i = 0; i < edges.size(); ++i) {
        if(edges.from(i) == s) {
          edges.augment(i, edges.capacity_left(i));
          if(edges.to(i) != t and edges.get_flow(i) > 0) 
            L.insert({0, edges.to(i)});
          ex[edges.to(i)] += edges.get_flow(i);
          ex[s] -= edges.get_flow(i);
        }
        outgoing[edges.from(i)].push_back(i);
        incoming[edges.to(i)].push_back(edges.inverse(i));
      }
      phi[s] = num_nodes; // phi[v] == 0 else (see initialization)
    }

    EdgeCollection push_relabel() {
      node v = get_maximum_active_node();
      bool still_active = false;
      while(v != -1) {
        if(A[v].size() != 0) {
          still_active = push(A[v].back());
        } else {
          relabel(v);
          // v is active and since it was the maximum active node before
          // it will be now (phi[v] never decreases).
          still_active = true;
        }
        v = still_active ? v : get_maximum_active_node();
      }
      return edges;
    }

    flow value() {
      return -ex[s];
    }
private:
    vector<unsigned> phi;
    node s,t;
    vector<vector<edge>> incoming;
    vector<vector<edge>> outgoing;
    std::multimap<int, node> L;
    vector<vector<edge>> A;
    EdgeCollection edges;
    vector<int> ex;

    bool push(edge e) { // returns true iff ex[v] remains > 0
      node v = edges.from(e); 
      node w = edges.to(e);
      if(phi[v] != phi[w] + 1) {
        A[v].pop_back(); // We remove not-any-more-allowed edges
        return true;
      }
      bool still_active = true;
      flow gamma = std::min(ex[v], edges.capacity_left(e));
      edges.augment(e, gamma);
      ex[v] -= gamma;
      ex[w] += gamma;
      if(ex[v] == 0) {
        L.erase(--L.end());
        still_active = false;
      }
      if(edges.capacity_left(e) == 0)          A[v].pop_back();
      if(ex[w] == gamma and w != s and w != t) L.insert({phi[w], w});
      return still_active;
    }

    void relabel(node v) {
      unsigned m = 2*phi.size();
      L.erase(--L.end());
      // Splitting outgoing and incoming is better for branch-prediction.
      std::vector<vector<edge>*> incident({&(outgoing[v]), &(incoming[v])});
      for(auto* vec : incident)
        for(auto e : *vec)
          if(edges.capacity_left(e) > 0)
            m = std::min(m, phi[edges.to(e)] + 1);
      phi[v] = m;
      L.insert({phi[v],v});
      for(auto* vec : incident)
        for(auto e : *vec)
          if(phi[v] == phi[edges.to(e)] + 1 and edges.capacity_left(e) > 0)
            A[v].push_back(e);
    }
    node get_maximum_active_node() {
      if(L.size() != 0) return L.rbegin()->second;
      return -1;
    }
};

int main(int argc, char *argv[]) {
  if(argc != 2) {
    // We expect exactly one argument...
    std::cout << "Aufruf: " << argv[0] << " <filename>" << std::endl;
  } else {
    // which should be a filename...
    std::ifstream file(argv[1]);
    unsigned int n = 0;
    vector<Edge> edges(0);
    if(!file.is_open()) {
      // of a non-busy file.
      std::cout << "Konnte Datei nicht öffnen." << std::endl;
    } else {
      file >> n; // First we read the number of nodes...
      node a, b; capacity c;
      while(file >> a >> b >> c) {
        // and then the edges...
        edges.push_back(Edge {a,b,c});
      }
    } 
    GoldbergTarjan gt(n, EdgeCollection(edges), 0, 1);
    EdgeCollection result = gt.push_relabel();
    std::cout << gt.value() << std::endl;
    for(std::size_t i = 0; i < result.size(); ++i) {
      if(result.get_flow(i) > 0) {
        std::cout << i << " " << result.get_flow(i) << std::endl;
      }
    }
  }
}

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