指定したキーでソートするstd::sort ref: http://qiita.com/piyo7/items/e23670cd89502680649c

file0.cpp

std::sort(idols.begin(), idols.end(),
  [](const Idol& lhs, const Idol& rhs){ return lhs.production_id < rhs.production_id; });

file1.cpp

#include <algorithm>
#include <iostream>
#include <string>
#include <vector>

template<
  typename Inputs,
  typename Functor,
  typename T = typename Inputs::value_type>
void sort_by(Inputs& inputs, Functor f) {
  std::sort(std::begin(inputs), std::end(inputs),
    [&f](const T& lhs, const T& rhs){ return f(lhs) < f(rhs); });
}

struct Idol {
  std::string name;
  int production_id;
};

int main() {
  std::vector<Idol> idols = {
    {"Takane", 961},
    {"Kotori", 765},
    {"Mai",    876}
  };

  sort_by(idols, [](const Idol& idol){ return idol.production_id; });

  for (const auto& idol : idols) {
    std::cout << idol.name << std::endl;
  }

  return 0;
}

file1.txt

Kotori
Mai
Takane

file2.txt

Kotori
Mai
Takane