n_bonacci.cpp File Reference

Implementation of the N-bonacci series. More...

#include <cassert>
#include <iostream>
#include <vector>

Include dependency graph for n_bonacci.cpp:

Namespaces
namespace	math
	for IO operations
namespace	n_bonacci
	Functions for the N-bonacci implementation.

Functions
std::vector< uint64_t >	math::n_bonacci::N_bonacci (const uint64_t &n, const uint64_t &m)
	Finds the N-Bonacci series for the n parameter value and m parameter terms.
static void	test ()
	Self-test implementations.
int	main ()
	Main function.

Detailed Description

Implementation of the N-bonacci series.

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

Function Documentation

main()

int main

(

void

)

Main function.

Returns

0 on exit

           {
    test();  // run self-test implementations
    return 0;
}

Here is the call graph for this function:

N_bonacci()

std::vector< uint64_t > math::n_bonacci::N_bonacci	(	const uint64_t &	n,
		const uint64_t &	m )

Finds the N-Bonacci series for the n parameter value and m parameter terms.

Parameters

n	is in the N-Bonacci series
m	is the number of terms in the N-Bonacci sequence

Returns

the n-bonacci sequence as vector array

we initialise the (n-1)th term as 1 which is the sum of preceding N zeros

similarily the sum of preceding N zeros and the (N+1)th 1 is also 1

                                                                    {
    std::vector<uint64_t> a(
        m, 0);  // we create an array of size m filled with zeros
    if (m < n || n == 0) {
        return a;
    }
 
    a[n - 1] = 1;  /// we initialise the (n-1)th term as 1 which is the sum of
                   /// preceding N zeros
    if (n == m) {
        return a;
    }
    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;
}

Here is the call graph for this function:

test()

static void test ( )

static

Self-test implementations.

Returns

void

                   {
    struct TestCase {
        const uint64_t n;
        const uint64_t m;
        const std::vector<uint64_t> expected;
        TestCase(const uint64_t in_n, const uint64_t in_m,
                 std::initializer_list<uint64_t> data)
            : n(in_n), m(in_m), expected(data) {
            assert(data.size() == m);
        }
    };
    const std::vector<TestCase> test_cases = {
        TestCase(0, 0, {}),
        TestCase(0, 1, {0}),
        TestCase(0, 2, {0, 0}),
        TestCase(1, 0, {}),
        TestCase(1, 1, {1}),
        TestCase(1, 2, {1, 1}),
        TestCase(1, 3, {1, 1, 1}),
        TestCase(5, 15, {0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236, 464}),
        TestCase(
            6, 17,
            {0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 63, 125, 248, 492, 976}),
        TestCase(56, 15, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})};
 
    for (const auto &tc : test_cases) {
        assert(math::n_bonacci::N_bonacci(tc.n, tc.m) == tc.expected);
    }
    std::cout << "passed" << std::endl;
}

Here is the call graph for this function: