// Finding fermion basis states using next_permutation
#include <iostream>
#include <vector>
#include <algorithm>
#include <iomanip>

namespace my {
  template<typename T>
  struct State{
    T i;
    std::vector<T> v;
    State(T ind,std::vector<T> vec) {i=ind; v=std::move(vec);}
    void print(){
      std::cout<<"state # "<<std::setw(10)<<std::left<<i<<std::left<<" = ";
      for(auto x:v) std::cout<<x;
      std::cout<<std::endl;
    }
  };
}

int main () {
  const int Nstates=8; // single-particle states
  const int N=5; // number of fermions
  std::cout<<"All "<<N<<"-fermion states for a system of "<<Nstates<<" single-particle states\n";
  std::vector<my::State<int>> states;
  std::vector<int> vec(Nstates,0); // 0 occupation by default
  for (int i=0; i!=N; ++i) {vec[i]=1;} // occupy single-fermion states
  std::sort(vec.begin(),vec.end()); // make sure next_permutation starts OK
  int i = 1;
  do {
    states.push_back(my::State(i,vec));
    ++i;
  } while (next_permutation (vec.begin(),vec.end()));
  for (auto s:states) s.print();
}