c++ quick sort comparison query

c++ quick sort comparison query

For some reason it's taken me a while to get my head around this one, but
there's one bit I'm still not sure about.
In the code below, this bit:
a.at(first) = a.at(last);
a.at(last) = a.at(++first);
a.at(first) = pivot;
My question is, when a.at(++first) is swapped with a.at(last), it hasn't
been compared, has it? a.at(last) is lower that the pivot, so is being
moved, but there is no way of knowing if a.at(++first) is greater than or
equal to pivot, is there? Or am I missing something?
#include <iostream>
#include <vector>
using namespace std;
void quick(vector<int>&);
void quick_helper(vector<int>&, int, int);
void print(vector<int>);
int main(){
vector<int>v(10);
v.at(0) = 8;
v.at(1) = 3;
v.at(2) = 7;
v.at(3) = 2;
v.at(4) = 5;
v.at(5) = 9;
v.at(6) = 1;
v.at(7) = 4;
v.at(8) = 0;
v.at(9) = 6;
cout << "Before sorting:\n";
print(v);
quick (v);
cout << "After sorting:\n";
print(v);
return 0;
}
void print(vector<int> a)
{
for (int i = 0; i < static_cast<int>(a.size()); i++)
cout << a[i] << " ";
cout << "\n";
}
void quick(vector<int>& a){
quick_helper(a, 0, static_cast<int>(a.size() - 1));
}
void quick_helper(vector<int>& a, int l, int r){
int i, first, last, pivot;
if (r>l){
first = l;
last = r;
i = (l+r)/2;
pivot = a.at(i);
a.at(i) = a.at(first);
a.at(first) = pivot;
while (last > first){
if (a.at(last) >= pivot){
last--;
} else {
a.at(first) = a.at(last);
a.at(last) = a.at(++first);
a.at(first) = pivot;
}
}
pivot = first;
quick_helper(a, l, pivot-1);
quick_helper(a, pivot+1, r);
}
return;
}