vector of vectors of all combinations of -1, +1 - c++

Question

For any given n, I need to create a vector of vectors of length n std::vector<std::vector<int>>, containing all possible combinations of -1 and +1. For example, for n=3 I need
std::vector<std::vector<int>> v = {
{ 1, 1, 1},
{ 1, 1, -1},
{ 1, -1, 1},
{ 1, -1, -1},
{-1, 1, 1},
{-1, 1, -1},
{-1, -1, 1},
{-1, -1, -1}
};
Any hints?

Answer 1

Simple solution using the binary representation, and testing the bit value. I used std::bitset although you can also use the simple C-Style bit manipulations.
#include <bitset>
int main(){
int n=3;
int to = pow(2,n);
std::vector<std::vector<int>> result;
for (int i=0; i < to; i++){
std::bitset<32> b(i);
std::vector<int> vec1;
for (int j=0; j < n; j++){
int value = b.test(j) ? 1 : -1;
vec1.push_back(value);
}
result.push_back(vec1);
}
// Printing out result
for (auto& vec : result){
for (auto val : vec){
cout << val;
}
cout << endl;
}
}
Test Example

Answer 2

For larger values of (n), you might want to improve the efficiency:
std::vector<std::vector<int>> v;
v.reserve(1 << n);
for (unsigned int i = 0; i < (1 << n); i++)
{
std::vector<int> vi (n, 0);
for (unsigned int j = 0; j < n; j++)
vi[n - 1 - j] = (i & (1 << j)) ? (-1) : (+1);
v.push_back(vi);
}
I'm sure someone can come up with a template meta-program that can construct (v) at compile-time for a constant (n).

Answer 3

Following #sascha's suggestion, here's a method that appends +-1 to a given set of lists.
#include <vector>
#include <iostream>
std::vector<std::vector<int>>
append_plus_minus(const std::vector<std::vector<int>> & in)
{
auto out = in;
out.insert(out.end(), in.begin(), in.end());
for (std::size_t i=0; i < in.size(); i++) {
out[i].push_back(+1);
out[i+in.size()].push_back(-1);
}
return out;
}
int main() {
const int n = 5;
std::vector<std::vector<int>> b_combinations = {{}};
for (std::size_t i=0; i < n; i++) {
b_combinations = append_plus_minus(b_combinations);
}
for (std::size_t i=0; i < b_combinations.size(); i++) {
for (std::size_t j=0; j < b_combinations[i].size(); j++) {
std::cout << b_combinations[i][j] << " ";
}
std::cout << std::endl;
}
return 0;
}