Check if a given number can be represented in given a no. of digits in any base in C++

Suppose we have a number n, and number of digits d. We have to check whether the number n can be represented as d digit number in any base from 2 to 32. Suppose the number n is 8, and d = 4, then this can be represented as 1000 in binary, here the d is 4.

The idea is to check all bases one by one from 2 to 32. We can follow these steps to check the base.

If the number is smaller than base, and digit is 1, then return true
if digit is more than one and number is more than base, then remove the last digit from the number by doing num/base, thus reduce the number of digits, then recursively do this again and again.
Otherwise return false.

Example

Live Demo

#include <iostream>
using namespace std;
bool isRepresentedInDDigits(int num, int d, int base) {
   if (d==1 && num < base)
      return true;
   if (d > 1 && num >= base)
      return isRepresentedInDDigits(num/base, --d, base);
      return false;
}
bool checkNumber(int num, int d) {
   // Check for all bases one by one
   for (int base=2; base<=32; base++)
      if (isRepresentedInDDigits(num, d, base))
         return true;
         return false;
}
int main() {
   int num = 8;
   int dig = 2;
   if(checkNumber(num, dig))
      cout << "Can be represented";
   else
      cout << "Can not be represented";
}