Need help understanding recursion - c++

Question

So in my class we are studying recursive functions. But I just do not understand how they work.
I'll use this code as an example.
// n is written to the screen vertically
// with each digit on a separate line.
void write_vertical(int n) {
if (n < 10)
{
cout << n << endl;
}
else // n is two or more digits long
{
write_vertical(n/10);
cout << (n % 10) << endl;
}
}
So if int n = 123; it will print each digit on its own line.How does this happen? how does this function work step by step?

Answer 1

Testing by random number (13)
Let's take 13 for an example. Well it's not less than 10, so it will execute the else block, and it will immediately execute the function itself with 13/10, which (as an integer) is 1. Now 1 is less than 10, so it will print 1 onto the screen with a new line because of endl. Now it will return back to the previous function call it had (before calling the function again with argument 1) and execute 13%10. 13 modulus 10 is 3, since its remainder becomes 3, with a new line (again because of endl). And voila, you printed the number in a vertical line!
For future
You should use a pencil and a paper, and debug it yourself manually just like we did above. OR even better use a debugger like GDB! This is an excellent quick startup on how to debug with GDB.

Answer 2

Recursion is simple. Assume you've already written your function; then use it.
Here it's the other way around - you are trying to figure out what the function does. Just the same, when you call it, it always does the same stuff.
So, in a general case of a number n > 10, what is n/10 (integer division)? It's that number without its last decimal digit.
What's n % 10? It's the number's last decimal digit.
So, your definition reads:
doing_something for a number `n` IS
doing_it for this number without its last decimal digit
(if there's something left, that is);
then printing its last decimal digit and a newline after it.
That's all.

Answer 3

1:
if(123 < 10) // fails
cout << 123; // skipped
else
{
recurse(123 / 10); // recurse(12) converted to int
cout << 123 % 10; // i'll be back here wait
}
2:
if(12 < 10) // fails
cout << 12; // skipped
else
{
recurse(12 / 10); // recurse(1)
cout << 12 % 10; // wiat I'll be back
}
3:
if(1 < 10) // succeeds! so now else executed
cout << 1; // printed
nothing is below until return of functions so we return
to 2:
cout << 12% 10; // (12 % 10 = 2) was wating it's its time
continue below: nothing below so return from function 2 to 1:
in 1:
cout << 123 % 10; // it was waiting so now it's its time
cout << 123 % 10; // 123 % 10 = 3
go below: nothing untile the end of function so retrun to main
where function was called first time (to the line after the call )
the result: 123