Transform iterative function to recursive function - c++

Question

I was having a discussion with a coworker about how to transform the following iterative function into a strictly recursive function. We know that all iterative functions can be transformed into recursive functions; however, my coworker remembered that this particular implementation used only three parameters. We can't re-solve this problem. Are we remembering incorrectly? Or are we missing something simple?
void iterative_function (char a, char b, int width) {
int i = width;
while (i > 0) {
cout << string(i, a) << string(width-i, b) << endl;
i -= 2;
}
i = width % 2;
while (i <= width) {
cout << string(i, a) << string(width-i, b) << endl;
i += 2;
}
}
Where the output looks something like below when called like iterative_function('X', '-', 5).
XXXXX
XXX--
X----
XXX--
XXXXX
EDIT: Here is a small skeleton of what the recursive version might look like:
void recursive_function (char a, char b, int width) {
if (width > -1) {
cout << string(width, a) << endl;
recursive(a, b, width - 2);
cout << string(width, a) << endl;
}
}
Except the problem here is filling the right side out with, say, hyphens.

Answer 1

Here is the recursive function, I just add another len to your function you can see in here, that its output is exactly like the output of your code here.
#include <iostream>
using namespace std;
void i_f(char a, char b, int width,int len) {
if(len <0 || width < 0)
return;
cout <<string(width, a) << string(len, b) << endl;
i_f(a,b,width-2,len+2);
cout <<string(width, a) << string(len, b) << endl;
}
int main() {
i_f('X', '-', 5,0);
return 0;
}
your code output:
XXXXX
XXX--
X----
X----
XXX--
XXXXX
my code output:
XXXXX
XXX--
X----
X----
XXX--
XXXXX
P.S After I posted my answer I saw your edit, although you edited your question 10 minutes before my answer, and I can see that you choose a path like my answer yourself.