Multiple STL containers referencing same object in C++

main.cpp

#include <set>
#include <iostream>
#include <vector>

/*
 * How to order a set<vector<A>::iterator>.
 */

struct A
{
  int value;
  A(int value): value(value){};
  // When storing objects of this struct in an STL container,
  // this operator will be used for ordering,
  // e.g. set<A>.
  //
  // It will not be used to order set<vector<A>::iterator>;
  // these will be ordered by pointer addresses.
  bool operator<(const A& a) const {
    return this->value < a.value;
  }
};

int main()
{
  // Vector holding struct objects: source of truth.
  std::vector<A> v;
  // Set holding iterators, without comparator.
  // Appears unsorted, i.e. is sorted by pointer value, not by value inside struct.
  std::set<std::vector<A>::iterator> s1;
  // Set holding values, ordering uses "operator<" defined in struct A.
  std::set<A> s2;
  // Set holding iterators, with custom C++20 comparator.
  // Ordered by value inside struct.
  // From: https://stackoverflow.com/a/46128321/92049
  auto cmp = [](std::vector<A>::iterator a, std::vector<A>::iterator b){ return a->value < b->value; };
  std::set<std::vector<A>::iterator, decltype(cmp)> s3; 

  // Insert values into vector<A>.
  v.push_back(A(1));
  v.push_back(A(3));
  v.push_back(A(2));
  
  for (auto e: v) {
    std::cout << e.value << " ";
  }
  std::cout << "=> vector<A>: " << std::endl;

  // Insert element iterators into containers:
  // set<vector<A>::iterator>
  // set<A>
  // set<vector<A>::iterator> + comparator
  for (auto e=v.begin(); e!=v.end(); e++) {
    s1.insert(e);
    s2.insert(*e);
    s3.insert(e);
  }

  // set<vector<A>::iterator> seems unordered;
  // that's because it is ordered by poiner addresses.
  for (auto e: s1) {
    std::cout << e->value << " ";
  }
  std::cout << "=> set<vector<A>::iterator>: " << std::endl;

  // set<A> is ordered by value,
  // using operator<() from struct A
  for (auto e: s2) {
    std::cout << e.value << " ";
  }
  std::cout << "=> set<A>: " << std::endl;

  // set<vector<A>::iterator> is ordered
  // using custom comparator specified when creating the set.
  for (auto e: s3) {
    std::cout << e->value << " ";
  }
  std::cout << "=> set<vector<A>::iterator> + cmp: " << std::endl;
};

// Output:
// 1 3 2 => vector<A>: 
// 1 3 2 => set<vector<A>::iterator>: 
// 1 2 3 => set<A>: 
// 1 2 3 => set<vector<A>::iterator> + cmp: