Program to find N-th term of series 1, 2, 11, 12, 21… in C++

In this problem, we are given a number N. Our task is to create a program to find N-th term of series 1, 2, 11, 12, 21… in C++.

Problem Description

To find the Nth term of the series −

1, 2, 11, 12, 21, 22, 111, 112, .... Nterms

We will find the general term of the series.

Let’s take an example to understand the problem,

Input

N = 8

Output

112

Solution Approach

To derive the general term, we need to closely observe the series. In this series, we can see that there are only 1’s and 2’s in the value. And every term is an alternation of 1 and 2. So, the general term will be,

$$T_{(N)}=T_{(n/2)}*10 + 1,\:if\:N\:is\:odd.$$ 

$$T_{(N)}= T_{((n/2)-1)}*10 + 2, if\:N\:is\:even.$$

Example

 Live Demo

#include <iostream>
using namespace std;
int findNTerm(int N) {
   if(N == 1)
   return 1;
   if(N == 2)
   return 2;
   int value;
      if(N%2 == 0){
         value = (findNTerm((N/2)-1)*10) + 2;
      }
      else
         value = (findNTerm((N/2))*10) + 1; return value;
}
int main() {
   int N = 12;
   cout<<N<<"Th term of the series is "<<findNTerm(N);
   return 0;
}

Output

12Th term of the series is 212

Ayush Gupta

Published on 04-May-2020 11:27:57