Recursive Implementation of Merge Sort C++
First off, I'd use typedef rather than #define.

You don't really need to reference vec.end(); you know mid &lt;= right &lt;= 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&lt;T&gt; has a constructor that copies from an iterator. Your push_back for loop could be simplified to

vector&lt;int&gt; left_vec(left, mid);
vector&lt;int&gt; 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&lt;int&gt;::iterator;

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

    //make vector right with elements from mid to right-1 inclusive
    vector&lt;int&gt; 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() &amp;&amp; right_src != right.end()) {
        // pick the iterator with the smallest current value
        itr&amp; least_src = (*left_src &lt; *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);
}