Merge Sort

#include <concepts>
#include <iostream>
#include <limits>
#include <vector>

namespace codiga::sort {
template <typename T>
requires std::totally_ordered<T> 
void merge(std::vector<T>& array, std::vector<T>& auxiliary, int begin, 
           int middle, int end) {
  for (auto i = begin, j = begin, k = middle + 1; i <= end; i++) {
    if (k > end || (j <= middle && auxiliary[j] <= auxiliary[k])) {
      array[i] = auxiliary[j++];
    }
    else {
      array[i] = auxiliary[k++];
    }
  }
}
template <typename T>
requires std::totally_ordered<T> 
void merge_sort(std::vector<T>& array, std::vector<T>& auxiliary, int begin, 
                int end){
  if (begin >= end) {
    return;
  }
  auto middle = begin + (end - begin) / 2;
  merge_sort(auxiliary, array, begin, middle);
  merge_sort(auxiliary, array, middle + 1, end);
  merge(array, auxiliary, begin, middle, end);
}
template <typename T>
requires std::totally_ordered<T> void merge_sort(std::vector<T>& array){
  std::vector<T> auxiliary(array.begin(), array.end());
  merge_sort(array, auxiliary, 0, array.size() - 1);
}
}