N-th polite number in C++

A polite number is a positive number that can be written as the sum of 2 or more consecutive positive numbers.

The series of polite numbers are

3 5 6 7 9 10 11 12 13 14...

There exists a formula to find the n-th polite number. The formula is n + log₂(n + log₂(n)). The default log computes with base e. We need to compute using base 2. Divide the default log result with log(2) to get the value of log with base e.

Algorithm

• Algorithm to the n-th polite number is straightforward.
• Initialise the number N.
• Use the above formula to compute the n-th polite number.
• Make sure to increment the value of n by 1 before computing the n-th polite number.

Implementation

Following is the implementation of the above algorithm in C++

#include <bits/stdc++.h>
using namespace std;
double getNthPoliteNumber(double n) {
   n += 1;
   return n + (log((n + (log(n) / log(2.0))))) / log(2.0);
}
int main() {
   double n = 10;
   cout << (int)getNthPoliteNumber(n) << endl;
   return 0;
}

Output

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

14

Hafeezul Kareem

Published on 29-Jun-2021 09:12:36

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