template<typename Value>
std::vector<std::pair<double, Value>> to_search_vector(std::vector<std::pair<Value, double>> const& weighted_values)
{
   std::vector<std::pair<double, Value>> value_map;
   value_map.reserve(weighted_values.size());

   double summed_weights = 0.0;
   for (auto const& weighted_value: weighted_values)
   {
      summed_weights += weighted_value.second;
      value_map.emplace_back(summed_weights, weighted_value.first);
   }
   return value_map;
}