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Keith Number Program in C++

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In this tutorial, we will write a Keith number in C++. It is one of the most asked questions in an interview. Before that, you may go through the following topic in C programming.

What is Keith Number?

A positive n digit number x is called a Keith number or repfigit number (repetitive Fibonacci-like digit) if it is arranged in a special number sequence generated using its digits. This sequence has n terms as digit of x and the next term is determined by the sum of previous n terms and so on. And if the number x falls under this sequence then x is a Keith Number. Example: 19, 742, etc

Explanation: Consider the number 742. Go through the following steps:

First separate the digit, 7, 4, 2.

To find the next term, add the digits, 7+4+2 = 13
New Series: 7, 4, 2, 13.

To find the next term, add the last three digits of the above sequence, 13+2+4=19
New Series: 7, 4, 2, 13, 19.

To find the next term, add the last three digits of the above sequence, 19+13+2=34
New Series: 7, 4, 2, 13, 19, 34.

To find the next term, add the last three digits of the above sequence, 34+19+13=66
New Series: 7, 4, 2, 13, 19, 34, 66.

To find the next term, add the last three digits of the above sequence, 66+34+19=119
New Series: 7, 4, 2, 13, 19, 34, 66, 119.

To find the next term, add the last three digits of the above sequence, 119+66+34=219
New Series: 7, 4, 2, 13, 19, 34, 66, 119, 219.

To find the next term, add the last three digits of the above sequence, 219+119+66=404
New Series: 7, 4, 2, 13, 19, 34, 66, 119, 219, 404.

To find the next term, add the last three digits of the above sequence, 404+219+119=742
New Series: 7, 4, 2, 13, 19, 34, 66, 119, 219, 404, 742.

Now we will stop as we got the number 742 as the term of the series. Hence 742 is a Keith Number.

C++ Program to check whether the Number is Keith Number or not 

#include <bits/stdc++.h>
using namespace std;

int digitCount(int n)
{
  int counter = 0;
  while (n > 0)
  {
    n = n / 10;
    counter++;
  }

  return counter;
}

int main()
{
  int num1 = 0, arr1[10], temp = 0, flag = 0, i = 0, sum = 0;

  cout << "Enter a number: ";
  cin >> num1;

  temp = num1;

  for (i = digitCount(temp) - 1; i >= 0; i--)
  {
    arr1[i] = num1 % 10;
    num1 /= 10;
  }

  while (flag == 0)
  {
    for (i = 0; i < digitCount(temp); i++)
      sum += arr1[i];
    if (sum == temp)
    {
      cout << "The entered number is a Keith Number\n";
      flag = 1;
    }

    if (sum > temp)
    {
      cout << "The entered number is NOT a Keith Number\n";
      flag = 1;
    }

    for (i = 0; i < digitCount(temp); i++)
    {
      if (i != digitCount(temp) - 1)
        arr1[i] = arr1[i + 1];
      else
        arr1[i] = sum;
    }

    sum = 0;
  }
}

Output:

//Run 1
Enter a number: 197
The entered number is a Keith Number

//Run 2
Enter a number: 15
The entered number is NOT a Keith number

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