## C++, math, n_bonacci.cpp

``````/**
* @file
* @brief Implementation of the
* [N-bonacci](http://oeis.org/wiki/N-bonacci_numbers) series
*
* @details
* In general, in N-bonacci sequence,
* we generate sum of preceding N numbers from the next term.
*
* For example, a 3-bonacci sequence is the following:
* 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81
* In this code we take N and M as input where M is the number of terms
* to be printed of the N-bonacci series
*
* @author [Swastika Gupta](https://github.com/Swastyy)
*/

#include <algorithm>  /// for std::is_equal, std::swap
#include <cassert>    /// for assert
#include <iostream>   /// for IO operations
#include <vector>     /// for std::vector

/**
* @namespace math
* @brief Mathematical algorithms
*/
namespace math {
/**
* @namespace n_bonacci
* @brief Functions for the [N-bonacci](http://oeis.org/wiki/N-bonacci_numbers)
* implementation
*/
namespace n_bonacci {
/**
* @brief Finds the N-Bonacci series for the `n` parameter value and `m`
* parameter terms
* @param n is in the N-Bonacci series
* @param m is the number of terms in the N-Bonacci sequence
* @returns the n-bonacci sequence as vector array
*/
std::vector<uint64_t> N_bonacci(const uint64_t &n, const uint64_t &m) {
std::vector<uint64_t> a(m, 0);  // we create an empty array of size m

a[n - 1] = 1;  /// we initialise the (n-1)th term as 1 which is the sum of
/// preceding N zeros
a[n] = 1;  /// similarily the sum of preceding N zeros and the (N+1)th 1 is
/// also 1
for (uint64_t i = n + 1; i < m; i++) {
// this is an optimized solution that works in O(M) time and takes O(M)
// extra space here we use the concept of the sliding window the current
// term can be computed using the given formula
a[i] = 2 * a[i - 1] - a[i - 1 - n];
}
return a;
}
}  // namespace n_bonacci
}  // namespace math

/**
* @brief Self-test implementations
* @returns void
*/
static void test() {
// n = 1 m = 1 return [1, 1]
std::cout << "1st test";
std::vector<uint64_t> arr1 = math::n_bonacci::N_bonacci(
1, 1);  // first input is the param n and second one is the param m for
// N-bonacci func
std::vector<uint64_t> output_array1 = {
1, 1};  // It is the expected output series of length m
assert(std::equal(std::begin(arr1), std::end(arr1),
std::begin(output_array1)));
std::cout << "passed" << std::endl;

// n = 5 m = 15 return [0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236,
// 464]
std::cout << "2nd test";
std::vector<uint64_t> arr2 = math::n_bonacci::N_bonacci(
5, 15);  // first input is the param n and second one is the param m for
// N-bonacci func
std::vector<uint64_t> output_array2 = {
0, 0,  0,  0,  1,   1,   2,  4,
8, 16, 31, 61, 120, 236, 464};  // It is the expected output series of
// length m
assert(std::equal(std::begin(arr2), std::end(arr2),
std::begin(output_array2)));
std::cout << "passed" << std::endl;

// n = 6 m = 17 return [0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 63, 125, 248,
// 492, 976]
std::cout << "3rd test";
std::vector<uint64_t> arr3 = math::n_bonacci::N_bonacci(
6, 17);  // first input is the param n and second one is the param m for
// N-bonacci func
std::vector<uint64_t> output_array3 = {
0, 0,  0,  0,  0,   1,   1,   2,  4,
8, 16, 32, 63, 125, 248, 492, 976};  // It is the expected output series
// of length m
assert(std::equal(std::begin(arr3), std::end(arr3),
std::begin(output_array3)));
std::cout << "passed" << std::endl;

// n = 56 m = 15 return [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
std::cout << "4th test";
std::vector<uint64_t> arr4 = math::n_bonacci::N_bonacci(
56, 15);  // first input is the param n and second one is the param m
// for N-bonacci func
std::vector<uint64_t> output_array4 = {
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0};  // It is the expected output series of length m
assert(std::equal(std::begin(arr4), std::end(arr4),
std::begin(output_array4)));
std::cout << "passed" << std::endl;
}

/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
test();  // run self-test implementations
return 0;
}
``````