Stuck with this problem

[Oriol Serrabassa]

You have to write an ITERATIVE procedure write_digit(d,x) that receives a digit d and a natural number x, and writes x times the digit d in the standard output (cout). For example, the call write_digit(3,5) writes 33333, whereas the call write_digit(5,3) writes 555.

You have also to write an ITERATIVE procedure write_expanded(n) that receives a natural number n > 0, and writes in the standard output (cout) each digit of n as many times as the digit value plus 1. For instance, write_expanded(315) writes 333311555555 in the cout, whereas write_expanded(204) writes 222044444. Your implementation of write_expanded(n) must conveniently use the function write_digit(d,x).

Your implementation of both procedures must be ITERATIVE and use the following C++ code, modifying only the parts that are indicated. Notice that the main procedure below writes an end-of-line after each call to write_expanded. Thus, the procedures must not write the end-of-line.

INPUT
315
204
112233
332211
200000
456789
999999
100000

OUTPUT
333311555555
222044444
111122222233333333
333333332222221111
22200000
444445555556666666777777778888888889999999999
999999999999999999999999999999999999999999999999999999999999
1100000

#include <iostream>
using namespace std;

// define here additional functions and/or procedures
// if you need them 

// Pre: 0<=d<=9 and 0<=x.
void write_digit(int d,int x) {
    // insert here your (ITERATIVE) code
}

// Pre: 0<n.
void write_expanded(int n) {
    // insert here your (ITERATIVE) code
}

int main() {
    int n;
    while (cin >> n) {
        write_expanded(n);
        cout << endl;
    }
}

I made a program that does what the program asks but couts the inversed result. Did it intentionally because if I had done it normal it would be imposible because I do not know the number of digits the input will have.

#include <iostream>
using namespace std;

void write_digit(int d, int x) {
	for (int i = 0; i < x; ++i) cout << d;
}

void write_expanded(int n) {
	while (n != 0) {
		if (n/10 > 0) {		
			int d = n%10;
			int x = n%10 +1;
			write_digit(d,x);
			n /= 10;
			d = 0;
			x = 0;
		}
		else {
			int d = n;
			int x = n+1;
			write_digit(d,x);
			n = 0;
		}
	}
}

int main() {
	int n;
	while (cin >> n) {
		write_expanded(n);
		cout << endl;
	}
}

To try to output the correct result, I inverted the input and now it gives me the proper solution in some cases. If there are leading zeroes, the program gives incorrect output. for example:
Input: (1000 -> 0001 = 1 "inverted input")
Output: (1100000 -> 11 "cout output")

#include <iostream>
using namespace std;

void write_digit(int d, int x) {
	for (int i = 0; i < x; ++i) cout << d;
}

void write_expanded(int n) {
	int reverse = 0;	
	while (n != 0) {
        	int remainder = n%10;
        	reverse = reverse*10 + remainder;
        	n /= 10;
	}
	while (reverse != 0) {
		if (reverse/10 > 0) {		
			int d = reverse%10;
			int x = reverse%10 +1;
			write_digit(d,x);
			reverse /= 10;
			d = 0;
			x = 0;
		}
		else {
			int d = reverse;
			int x = reverse+1;
			write_digit(d,x);
			reverse = 0;
		}
	}
}

int main() {
	int n;
	while (cin >> n) {
		write_expanded(n);
		cout << endl;
	}
}

What can I do to make this program finally work as it is supposed to?