How do I generate all vectors of size n where each element may contain 1 of m different values? - c++

Question

Sorry if this is a duplicate, but I did not find any answers which match mine.
Consider that I have a vector which contains 3 values. I want to construct another vector of a specified length from this vector. For example, let's say that the length n=3 and the vector contains the following values 0 1 2. The output that I expect is as follows:
0 0 0
0 0 1
0 0 2
0 1 0
0 1 1
0 1 2
0 2 0
0 2 1
0 2 2
1 0 0
1 0 1
1 0 2
1 1 0
1 1 1
1 1 2
1 2 0
1 2 1
1 2 2
2 0 0
2 0 1
2 0 2
2 1 0
2 1 1
2 1 2
2 2 0
2 2 1
2 2 2
My current implementation simply constructs for loops based on nand generates the expected output. I want to be able to construct output vectors of different lengths and with different values in the input vector.
I have looked at possible implementations using next_permutation, but unfortunately passing a length value does not seem to work.
Are there time and complexity algorithms that one can use for this case? Again, I might have compute this for up to n=17and sizeof vector around 6.
Below is my implementation for n=3. Here, encis the vector which contains the input.
vector<vector<int> > combo_3(vector<double>enc,int bw){
vector<vector<int> > possibles;
for (unsigned int inner=0;inner<enc.size();inner++){
for (unsigned int inner1=0;inner1<enc.size();inner1++){
for (unsigned int inner2=0;inner2<enc.size();inner2++){
cout<<inner<<" "<<inner1<<" "<<inner2<<endl;
unsigned int arr[]={inner,inner1,inner2};
vector<int>current(arr,arr+sizeof(arr)/sizeof(arr[0]));
possibles.push_back(current);
current.clear();
}
}
}
return possibles;
}

Answer 1

What you are doing is simple counting. Think of your output vector as a list of a list of digits (a vector of a vector). Each digit may have one of m different values where m is the size of your input vector.
This is not permutation generation. Generating every permutation means generating every possible ordering of an input vector, which is not what you're looking for at all.
If you think of this as a counting problem the answer may become clearer to you. For example, how would you generate all base 10 numbers with 5 digits? In that case, your input vector has size 10, and each vector in your output list has length 5.