Howto create combinations of several vectors without hardcoding loops in C++?

You can implement this like an odometer, which leads to the following (works for different-sized vectors):

Say you have K vectors in an array v: v[0], v[1], ... v[K-1]

Keep an array of iterators it (size K) into your vectors, starting with it[i] = v[i].begin(). Keep incrementing it[K-1] in a loop. When any iterator hits the end() of the corresponding vector, you wrap it around to begin() and increment the previous iterator also (so when it[K-1] wraps around, you increment it[K-2]). These increments may "cascade" so you should do them in a loop backwards. When it[0] wraps around, you're done (so your loop condition could be something like while (it[0] != v[0].end())

Putting all that together, the loop that does the work (after setting up the iterators) should be something like:

while (it[0] != v[0].end()) {
  // process the pointed-to elements

  // the following increments the "odometer" by 1
  ++it[K-1];
  for (int i = K-1; (i > 0) && (it[i] == v[i].end()); --i) {
    it[i] = v[i].begin();
    ++it[i-1];
    }
  }

If you're interested in complexity, the number of iterator increments that get performed is easy to calculate. For simplicity here I'll assume each vector is the same length N. The total number of combinations is N^K. The last iterator gets incremented each time, so that is N^K, and moving back through the iterators this count gets divided by N each time, so we have N^K + N^K-1 + ... N¹; this sum equals N(N^K - 1)/(N-1) = O(N^K). This also means that the amortized cost per-combination is O(1).

Anyway, in short, treat it like an odometer spinning its digit wheels.

A C++0x solution. Provided, of course, your compiled supports it (currently GCC 4.5 and VS2010, I think).

The following compiles and works with GCC 4.5 using -std=c++0x switch. The use of variadic templates makes it possible to combine arbitrary number of containers. I am sure you can come up with a more idiomatic solution.

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

typedef std::vector<std::string> myvec;

// Base case.
void combine2(const std::string &row) {
    std::cout << row << std::endl;
}

// Recursive variadic template core function.
template<class T0, class ...T>
void combine2(const std::string &row, const T0& cont0, T...cont_rest) {
    for (auto i = cont0.begin(); i != cont0.end(); ++i) {
        std::stringstream ss;
        ss << row << *i;
        combine2(ss.str(), cont_rest...);
    }
}

// The actual function to call.
template<class ...T>
void combine(T...containers) {
    combine2("", containers...);
}

int main() {
    myvec v1 = {"T", "C", "A"}, v2 = {"C", "G", "A"}, v3 = {"C", "G", "T"};

    combine(v1);
    combine(v1, v2);
    combine(v1, v2, v3);

    // Or even...
    std::vector<std::string> v4 = {"T", "C", "A"};
    std::vector<char> v5 = {'C', 'G', 'A'};
    std::vector<int> v6 = {1 ,2 ,3};

    combine(v4);
    combine(v4, v5);
    combine(v4, v5, v6);

    return 0;
}

This will do the trick:

void printAll(const vector<vector<string> > &allVecs, size_t vecIndex, string strSoFar)
{
    if (vecIndex >= allVecs.size())
    {
        cout << strSoFar << endl;
        return;
    }
    for (size_t i=0; i<allVecs[vecIndex].size(); i++)
        printAll(allVecs, vecIndex+1, strSoFar+allVecs[vecIndex][i]);
}

Call with:

printAll(allVecs, 0, "");

The basic difficulty with recursion here is that you need to keep track of the entire list of indices (or else construct the string incrementally, as another question points out).

An expedient way to handle this problem without constructing additional objects inside the loops is to hand your recursive function a vector of indices, of the same length as the vector of vectors:

void printcombos(const vector<vector<string> >&vec,vector<int>&index,int depth) {
  if(depth==index.length()) {
    for(int i=0; i<depth; ++i) {
      cout<<vec[i][index[i]];
    }
    cout<<endl;
  } else {
    const vector<string> &myvec= vec[depth];
    int mylength= myvec.length();
    for(int i=0; i<mylength; ++i) {
      index[depth]=i;
      printcombos(vec,index,depth+1);
    }
  }
}