Variadic nested loops - c++

Question

I am working on a N dimensional grid.
I would like to generate nested loops depending on any dimension (2D, 3D, 4D, etc...).
How can I do that in an elegant and fast way ? Below a simple illustration of my problem.
I am writing in C++ but I think this kind of question can be useful for other languages.
I need to know the indices (i,j,k...) in my do stuff part.
Edit : lower_bound and upper_bound represents the indexes in the grid so they are always positive.
#include <vector>
int main()
{
// Dimension here is 3D
std::vector<size_t> lower_bound({4,2,1});
std::vector<size_t> upper_bound({16,47,9});
for (size_t i = lower_bound[0]; i < upper_bound[0]; i ++)
for (size_t j = lower_bound[1]; j < upper_bound[1]; j ++)
for (size_t k = lower_bound[2]; k < upper_bound[2]; k ++)
// for (size_t l = lower_bound[3]; l < upper_bound[3]; l ++)
// ...
{
// Do stuff such as
grid({i,j,k}) = 2 * i + 3 *j - 4 * k;
// where grid size is the total number of vertices
}
}

Answer 1

Following may help:
bool increment(
std::vector<int>& v,
const std::vector<int>& lower,
const std::vector<int>& upper)
{
assert(v.size() == lower.size());
assert(v.size() == upper.size());
for (auto i = v.size(); i-- != 0; ) {
++v[i];
if (v[i] != upper[i]) {
return true;
}
v[i] = lower[i];
}
return false;
}
And use it that way:
int main() {
const std::vector<int> lower_bound({4,2,1});
const std::vector<int> upper_bound({6,7,4});
std::vector<int> current = lower_bound;
do {
std::copy(current.begin(), current.end(), std::ostream_iterator<int>(std::cout, " "));
std::cout << std::endl;
} while (increment(current, lower_bound, upper_bound));
}
Live demo

Answer 2

An iterative approach could look like this:
#include <iostream>
#include <vector>
int main()
{
std::vector<int> lower_bound({-4, -5, -6});
std::vector<int> upper_bound({ 6, 7, 4});
auto increase_counters = [&](std::vector<int> &c) {
for(std::size_t i = 0; i < c.size(); ++i) {
// This bit could be made to look prettier if the indices are counted the
// other way around. Not that it really matters.
int &ctr = c .rbegin()[i];
int top = upper_bound.rbegin()[i];
int bottom = lower_bound.rbegin()[i];
// count up the innermost counter
if(ctr + 1 < top) {
++ctr;
return;
}
// if it flows over the upper bound, wrap around and continue with
// the next.
ctr = bottom;
}
// end condition. If we end up here, loop's over.
c = upper_bound;
};
for(std::vector<int> counters = lower_bound; counters != upper_bound; increase_counters(counters)) {
for(int i : counters) {
std::cout << i << ", ";
}
std::cout << "\n";
}
}
...although whether this or a recursive approach is more elegant rather depends on the use case.

Answer 3

#include <iostream>
#include <vector>
template <typename Func>
void process(const std::vector<int>& lower, const std::vector<int>& upper, Func f)
{
std::vector<int> temp;
process(lower, upper, f, 0, temp);
}
template <typename Func>
void process(const std::vector<int>& lower, const std::vector<int>& upper, Func f,
int index, std::vector<int>& current)
{
if (index == lower.size())
{
f(current);
return;
}
for (int i = lower[index]; i < upper[index]; ++i)
{
current.push_back(i);
process(lower, upper, f, index + 1, current);
current.pop_back();
}
}
int main()
{
// Dimension here is 3D
std::vector<int> lower_bound({-4, -5, 6});
std::vector<int> upper_bound({6, 7, 4});
// Replace the lambda below with whatever code you want to process
// the resulting permutations.
process(lower_bound, upper_bound, [](const std::vector<int>& values)
{
for (std::vector<int>::const_iterator it = values.begin(); it != values.end(); ++it)
{
std::cout << *it << " ";
}
std::cout << std::endl;
});
}

Answer 4

Probably some typos an whatnot, but I'd flatten the whole range.
This is based on the idea that the range can be described as
x_0 + d_0*(x_1+d_1*(x_2+d_2....)
So we can roll our own that way
std::vector<int> lower_bound{-4,-5,6};
std::vector<int> upper_bound{6,7,4};
//ranges
std::vector<int> ranges;
for (size_t i = 0; i < lower_bound.size(); i++) {
ranges.push_back(upper_bound[i]-lower_bound[i]);
}
for (int idx = 0; idx < numel; idx++) {
//if you don't need the actual indicies, you're done
//extract indexes
int idx2 = idx;
std::vector<int> indexes;
for (int i = 0; i < ranges.size(); i++) {
indexes.push_back(idx2%ranges[i]-lower_bound[i]);
idx2 = idx2/ranges[i];
}
//do stuff
grid[idx] = 2 * indexes[0] + 3 *indexes[1] - 4 * indexes[2];
}
Edit: to be more generic:
template <typename D>
void multi_for(const std::vector<int>& lower_bound, const std::vector<int> upper_bound, D d) {
std::vector<int> ranges;
for (size_t i = 0; i < lower_bound.size(); i++) {
ranges.push_back(upper_bound[i]-lower_bound[i]);
}
size_t numel = std::accumulate(ranges.begin(), ranges.end(), std::multiplies<int,int>{});
for (int idx = 0; idx < numel; idx++) {
//if you don't need the actual indicies, you're done
//extract indexes
int idx2 = idx;
std::vector<int> indexes;
for (int i = 0; i < ranges.size(); i++) {
indexes.push_back(idx2%ranges[i]-lower_bound[i]);
idx2 = idx2/ranges[i];
}
//do stuff
d(idx,indexes);
}
}
//main
size_t* grid;//initialize to whateer
std::vector<int> lower_bound{-4,-5,6};
std::vector<int> upper_bound{6,7,4};
auto do_stuff = [grid](size_t idx, const std::vector<int> indexes) {
grid[idx] = 2 * indexes[0] + 3 *indexes[1] - 4 * indexes[2];
};
multi_for(lower_bound,upper_bound,do_stuff);

Answer 5

A recursive function may help you achieve what you want.
void Recursive( int comp )
{
if(comp == dimension)
{
// Do stuff
}
else
{
for (int e = lower_bound[comp]; e < upper_bound[comp]; e++)
Recursive(comp+1);
}
}
Some additions may be necessary in the function signature if you need to know the current indices (i,j,k,...) in your "Do Stuff" section.
This is a clean way to have access to these indices
void Recursive( int comp, int dimension )
{
static std::vector<int> indices;
if( comp == 0 ) // initialize indices
{
indices.clear();
indices.resize(dimension, 0);
}
if(comp == dimension -1)
{
// Do stuff
}
else
{
int& e = indices[comp];
for (e = lower_bound[comp]; e < upper_bound[comp]; e++)
Recursive(comp+1);
}
}
This is however not usable along multiple threads, due to the shared static vector.