Find n’th number in a number system with only 3 and 4 in C++

In this problem, we are given an element N. we need to find the N’th number in a number system with only 3 and 4.

The number system consists of elements 3, 4, 33, 34, 43, 44, 333, 334, 343, 344, …

Let’s take an example to understand the problem,

Input

N = 6

Output

44

Explanation

The numbers of the number system are − 3, 4, 33, 34, 43, 44...

Solution Approach

The number system is similar to the binary number system but the number 0 is replaced by 3 and number 1 is replaced by 4.

Let’s say this as sBinary.

So, number Nth number is (n-1)’s Sbinary conversion.

With this knowledge, we can easily solve the problem by finding the binary equivalent of (N-1) and then adding each digit of the binary number found by 3.

How to Convert Decimal to Binary?

Program to illustrate the working of our solution,

Example

#include<iostream>
using namespace std;
void findNThTermNumberSystem(int N) {
   if(N == 1 || N == 2) {
      cout<<(N-1) + 3;
      return;
   }
   N -= 1;
   findNThTermNumberSystem(N/2);
   cout<<((N % 2) + 3);
}
int main(){
   int N = 12;
   cout<<N<<"th term of the number system is ";
   findNThTermNumberSystem(N);
   return 0;
}

Output

12th term of the number system is 434