using merge sort with vectors c++ code example

Example: merge sort c++ vector

#include "tools.hpp"
/*   >>>>>>>> (Recursive function that sorts a sequence of) <<<<<<<<<<<< 
     >>>>>>>> (numbers in ascending order using the merge function) <<<<                                 */
std::vector<int> sort(size_t start, size_t length, const std::vector<int>& vec)
{
	if(vec.size()==0 ||vec.size() == 1)
	return vec;

	vector<int> left,right; //===>  creating left and right vectors 

	size_t mid_point = vec.size()/2; //===>   midle point between the left vector and the right vector 

	for(int i = 0 ; i < mid_point; ++i){left.emplace_back(vec[i]);} //===>  left vector 
	for(int j = mid_point; j < length; ++j){ right.emplace_back(vec[j]);} //===>  right vector 

	left = sort(start,mid_point,left); //===>  sorting the left vector 
	right = sort(mid_point,length-mid_point,right);//===>  sorting the right vector 
	

	return merge(left,right); //===>   all the function merge to merge between the left and the right
}
/*

>>>>> (function that merges two sorted vectors of numberss) <<<<<<<<<                                    */ 
vector<int> merge(const vector<int>& a, const vector<int>& b)
{
	vector<int> merged_a_b(a.size()+b.size(),0); // temp vector that includes both left and right vectors
	int i = 0;
	int j = 0;
	int k = 0;
	int left_size = a.size();
	int right_size = b.size();
	while(i<left_size && j<right_size) 
	{
		if(a[i]<b[j])
		{
			merged_a_b[k]=a[i];
			i++;
		}
		else
		{
			merged_a_b[k]=b[j];
			j++;
		}
		k++;
	}
	while(i<left_size)
	{
		merged_a_b[k]=a[i];
		i++;
		k++;
	}
	while(j<right_size)
	{
		merged_a_b[k]=b[j];
		j++;
		k++;
	}
	
	return merged_a_b;

}