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Keith Number in C++
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.
#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.
Updated on: 09-Apr-2021
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