Comparison of two class instances not having members as unique identifiers

Question

Consider two classes, Node and Edge, representing the nodes and the edges of a multigraph, respectively (see my MWE code below). My intention is to to use three unordered_maps:

(a) from Node variables to Edge data,

(b) from Edge variables to Node data, and

(c) from Node pairs to double variables.

I tried to write bool operator==() functions for Node* and Edge* and hash functions for Node*, Edge*, and pair<Node*,Node*>.

My first problem is related to the bool operator==() function of Edge. Although the labels of the Nodes are certainly unique, this bool operator==() function is not correct for multiple edges having the same starts and ends (). Is there any chance to construct correct bool operator==() function using, e.g., the memory address of the Edges?

The second question is whether these functions result in saving only the different Node/Edge/pair<Node,Node> objects if only simple edges are assumed.

So, my MWE is as follows:

#include<string>
#include<vector>
#include<utility>
#include<unordered_map>
#include<iostream>
#include <bits/stdc++.h> 

using namespace std;


class Node
{
   public:
      Node(){};
      string label;
      bool operator==(const Node* other) const
      {return label == other->label;};
};

class Edge
{
   public:
      Edge(){};
      Node *start, *end;
      double weight;
      bool operator==(const Edge* other) const
      {return start->label == other->start->label && 
       end->label == other->end->label;};
      //{return this == *other;}
};

namespace std
{
   template <>
   struct hash<Node*>
   {
      size_t operator()(const Node* node) const
      {return hash<string>()(node->label);}
   };

   template <>
   struct hash<Edge*>
   {
      size_t operator()(const Edge* edge) const
      {
         auto hash1 = hash<Node*>()(edge->start);
         auto hash2 = hash<Node*>()(edge->end);
         return hash1 ^ hash2; 
      }
   };

   template <>
   struct hash<pair<Node*,Node*>>
   {
      size_t operator()(const pair<Node*, Node*>& p) const
      { 
          auto hash1 = hash<Node*>()(p.first); 
          auto hash2 = hash<Node*>()(p.second);
          return hash1 ^ hash2; 
      } 
   };
}; 

int main()
{
   Edge* edge;
   Node* node;

   unordered_map<Node*,Edge> n2e;
   unordered_map<Edge*,Node> e2n;
   unordered_map<pair<Node*,Node*>,double> np2w;

   edge = new Edge();
   edge->weight = 1.0;
   edge->start = new Node();
   edge->start->label = "A";
   edge->end = new Node();
   edge->end->label = "B";

   n2e[edge->start] = *edge;
   e2n[edge] = *(edge->start);
   np2w[make_pair(edge->start, edge->end)] = edge->weight;

   edge = &n2e[edge->start];
   node = &e2n[edge];

   return 0;
}

Answer 1

You mostly define operator==(const Edge&, const Edge*),
whereas you would need operator==(const Edge*, const Edge*), but the latter cannot be defined.

You have to write class which define operator()(const Edge*, const Edge*) const and provide it in std::unordered_map.

struct MyEdgeComp
{
    bool operator()(const Edge* lhs, const Edge* rhs) const {
        return *lhs == *rhs; // Assuming you implement it
    }
};

std::unordered_map<Edge*, Node, std::hash<Edge*>, MyEdgeComp> e2n;