# Keith Number in C++

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In this tutorial, we are going to write a program that checks whether the given number is Keith Number or not.

The number n is called Keith number if it appears in the sequence generated using its digits. The sequence has first n terms as digits of the number n and other terms are recursively evaluated as sum of previous n terms.

Let's see the steps to solve the problem.

• Initialise the number n.
• Initialise an empty vector elements to store the sequence.
• Count the digits and add every digit to the vecor.
• Reverse the digits vector.
• Initialise a variable with 0 called next element.
• Write a loop that iterate till the next element is less than n.
• Add the last n digits to get the next element.
• Add the next element to the vector.
• Return true if the next element is equal to n else false.

## Example

Let's see the code.

Live Demo

#include<bits/stdc++.h>
using namespace std;
bool isKeithNumber(int n) {
vector<int> elements;
int temp = n, digitsCount = 0;
while (temp > 0) {
elements.push_back(temp % 10);
temp = temp / 10;
digitsCount++;
}
reverse(elements.begin(), elements.end());
int nextElement = 0, i = digitsCount;
while (nextElement < n) {
nextElement = 0;
for (int j = 1; j <= digitsCount; j++) {
nextElement += elements[i - j];
}
elements.push_back(nextElement);
i++;
}
return nextElement == n;
}
int main() {
isKeithNumber(43) ? cout << "Yes" << endl : cout << "No" << endl;
isKeithNumber(14) ? cout << "Yes" << endl : cout << "No" << endl;
isKeithNumber(197) ? cout << "Yes" << endl : cout << "No" << endl;
return 0;
}

## Output

If you run the above code, then you will get the following result.

No
Yes
Yes

## Conclusion

If you have any queries in the tutorial, mention them in the comment section.