How do I sort a std::vector by the values of a different std::vector?

friol's approach is good when coupled with yours. First, build a vector consisting of the numbers 1…n, along with the elements from the vector dictating the sorting order:

typedef vector<int>::const_iterator myiter;

vector<pair<size_t, myiter> > order(Index.size());

size_t n = 0;
for (myiter it = Index.begin(); it != Index.end(); ++it, ++n)
    order[n] = make_pair(n, it);

Now you can sort this array using a custom sorter:

struct ordering {
    bool operator ()(pair<size_t, myiter> const& a, pair<size_t, myiter> const& b) {
        return *(a.second) < *(b.second);
    }
};

sort(order.begin(), order.end(), ordering());

Now you've captured the order of rearrangement inside order (more precisely, in the first component of the items). You can now use this ordering to sort your other vectors. There's probably a very clever in-place variant running in the same time, but until someone else comes up with it, here's one variant that isn't in-place. It uses order as a look-up table for the new index of each element.

template <typename T>
vector<T> sort_from_ref(
    vector<T> const& in,
    vector<pair<size_t, myiter> > const& reference
) {
    vector<T> ret(in.size());

    size_t const size = in.size();
    for (size_t i = 0; i < size; ++i)
        ret[i] = in[reference[i].first];

    return ret;
}

typedef std::vector<int> int_vec_t;
typedef std::vector<std::string> str_vec_t;
typedef std::vector<size_t> index_vec_t;

class SequenceGen {
  public:
    SequenceGen (int start = 0) : current(start) { }
    int operator() () { return current++; }
  private:
    int current;
};

class Comp{
    int_vec_t& _v;
  public:
    Comp(int_vec_t& v) : _v(v) {}
    bool operator()(size_t i, size_t j){
         return _v[i] < _v[j];
   }
};

index_vec_t indices(3);
std::generate(indices.begin(), indices.end(), SequenceGen(0));
//indices are {0, 1, 2}

int_vec_t Index = { 3, 1, 2 };
str_vec_t Values = { "Third", "First", "Second" };

std::sort(indices.begin(), indices.end(), Comp(Index));
//now indices are {1,2,0}

Now you can use the "indices" vector to index into "Values" vector.

Put your values in a Boost Multi-Index container then iterate over to read the values in the order you want. You can even copy them to another vector if you want to.