Insertion sort in C++

insertion_sort.cpp

#include <iostream>
#include <vector>

void insertion_sort(std::vector<int> & v) {
  // invariant: the first i elements of v are sorted
  for(size_t i = 1; i < v.size(); ++i) {
    int value = v[i];
    size_t j = i-1;
    // invariant: elements of v from j+1 to i inclusive are sorted and >= value
    for(; j >= 0 && v[j] > value; --j) {
      v[j+1] = v[j];
    }
    v[j+1] = value;
  }
}

void insertion_sort_no_copies(std::vector<int> & v) {
  // invariant: the first i elements of v are sorted
  for(size_t i = 1; i < v.size(); ++i) {
    // invariant: elements of v from j+1 to i inclusive are sorted and >= value
    for(size_t j = i-1; j >= 0 && v[j] > v[j+1]; --j) {
      std::swap(v[j],v[j+1]);
    }
  }
}

int main() {
  std::vector<int> v{6, 3, 5, 4, 2, 1};
  insertion_sort_no_copies(v);
  for(int const x : v) {
    std::cout << x << std::endl;
  }
  return 0;
}