merge sort c 2b 2b vector

1#include "tools.hpp"
2/*   >>>>>>>> (Recursive function that sorts a sequence of) <<<<<<<<<<<< 
3     >>>>>>>> (numbers in ascending order using the merge function) <<<<                                 */
4std::vector<int> sort(size_t start, size_t length, const std::vector<int>& vec)
5{
6	if(vec.size()==0 ||vec.size() == 1)
7	return vec;
8
9	vector<int> left,right; //===>  creating left and right vectors 
10
11	size_t mid_point = vec.size()/2; //===>   midle point between the left vector and the right vector 
12
13	for(int i = 0 ; i < mid_point; ++i){left.emplace_back(vec[i]);} //===>  left vector 
14	for(int j = mid_point; j < length; ++j){ right.emplace_back(vec[j]);} //===>  right vector 
15
16	left = sort(start,mid_point,left); //===>  sorting the left vector 
17	right = sort(mid_point,length-mid_point,right);//===>  sorting the right vector 
18	
19
20	return merge(left,right); //===>   all the function merge to merge between the left and the right
21}
22/*
23
24>>>>> (function that merges two sorted vectors of numberss) <<<<<<<<<                                    */ 
25vector<int> merge(const vector<int>& a, const vector<int>& b)
26{
27	vector<int> merged_a_b(a.size()+b.size(),0); // temp vector that includes both left and right vectors
28	int i = 0;
29	int j = 0;
30	int k = 0;
31	int left_size = a.size();
32	int right_size = b.size();
33	while(i<left_size && j<right_size) 
34	{
35		if(a[i]<b[j])
36		{
37			merged_a_b[k]=a[i];
38			i++;
39		}
40		else
41		{
42			merged_a_b[k]=b[j];
43			j++;
44		}
45		k++;
46	}
47	while(i<left_size)
48	{
49		merged_a_b[k]=a[i];
50		i++;
51		k++;
52	}
53	while(j<right_size)
54	{
55		merged_a_b[k]=b[j];
56		j++;
57		k++;
58	}
59	
60	return merged_a_b;
61
62}