# Recursive Implementation of Merge Sort C++

I am currently reading an algorithms book and I read on the insertion and merge sorts. I implemented the merge sort in C++, The first function MERGE is responsible for the merging of the two subarrays part and the function MERGE_SORT is the actual algorithm. I am interested to know whether or not my code has a good readability factor and if It can be optimized further or not?

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

using namespace std;

#define itr vector<int>::iterator
void MERGE(vector<int>& vec,itr left, itr mid, itr right){
//Make vector left with elements from left to mid inclusive
vector<int> left_vec;
for (itr i=left; i!=vec.end()&&i<=mid;i++){
left_vec.push_back(*i);
}
left_vec.push_back(numeric_limits<int>::max());//sentinel card
//make vector right with elements from mid+1 to right inclusive
vector<int> right_vec;
for (itr i=mid+1; i!=vec.end() && i<=right; i++){
right_vec.push_back(*i);
}
right_vec.push_back(numeric_limits<int>::max());//sentinel card
//Now add them in a sorted manner to vector from left to right

itr l=left_vec.begin(); itr r=right_vec.begin();
for (itr vec_itr=left;vec_itr!=vec.end()&&vec_itr<=right;vec_itr++){
if (*l<=*r){
*vec_itr=*l;
l++;
}
else{
*vec_itr = *r;
r++;
}
}
}
void MERGE_SORT(vector<int>& vec, itr left, itr right){
if(left<right){
itr mid = left + (right-left)/2;
MERGE_SORT(vec,left,mid);
MERGE_SORT(vec,mid+1,right);
MERGE(vec, left,mid,right);
}
return;
}
int main() {
int a[] = {10,8,9,7,6,3,3,9,15,4,3,2,1};
vector<int> vec(a,a+13);
MERGE_SORT(vec,vec.begin(),vec.end());
for (itr i=vec.begin();i!=vec.end();i++)cout << *i << " ";
return 0;
}


First off, I'd use typedef rather than #define.

You don't really need to reference vec.end(); you know mid <= right <= vec.end() and the fact that you're copying the same number of elements back in as you copied out, means you don't need to compare vec_itr to vec.end(). What this really means is that you don't need the vec parameter to MERGE.

vector<T> has a constructor that copies from an iterator. Your push_back for loop could be simplified to

vector<int> left_vec(left, mid);
vector<int> right_vec(mid, right);


The push_back of max() as a sentinel is not strictly needed. Instead, you can just loop until you hit the end of either left_vec or right_vec and then copy the remainder of the vectors to the left to right range.

Your variable names might be easier to understand.

typedef itr vector<int>::iterator;

void MERGE(itr left, itr mid, itr right){
//Make vector left with elements from left to mid-1 inclusive
vector<int> left(left, mid);

//make vector right with elements from mid to right-1 inclusive
vector<int> right(mid, right);

// Now concurrently loop over the left and right vectors
// and add the values back to left to right. Stop when
// either iterator runs out of elements.
itr left_src=left.begin();
itr right_src=right.begin();
itr dest = left;
while (left_src != left.end() && right_src != right.end()) {
// pick the iterator with the smallest current value
itr& least_src = (*left_src < *right_src) ? left_src : right_src;
*dest = *least_src;
least_src ++;
dest ++;
}

// copy remainder of left (maybe 0 elements)
copy(left_src, left.end(), dest);

// copy remainder of right (maybe 0 elements)
copy(right_src, right.end(), dest);
}