feat: Add n_bonacci.cpp in math section (TheAlgorithms#1544)

* n-bonacci

* Update math/n_bonacci.cpp

Co-authored-by: David Leal <[email protected]>

* Update math/n_bonacci.cpp

Co-authored-by: David Leal <[email protected]>

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for f30cb37

* Update math/n_bonacci.cpp

Co-authored-by: David Leal <[email protected]>

* clang-format and clang-tidy fixes for 4af9dc3

* Update n_bonacci.cpp

Co-authored-by: David Leal <[email protected]>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Abhinn Mishra <[email protected]>

DIRECTORY.md

@@ -181,6 +181,7 @@
   * [Modular Division](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_division.cpp)
   * [Modular Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_exponentiation.cpp)
   * [Modular Inverse Fermat Little Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_inverse_fermat_little_theorem.cpp)
+  * [N Bonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/n_bonacci.cpp)
   * [N Choose R](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/n_choose_r.cpp)
   * [Ncr Modulo P](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/ncr_modulo_p.cpp)
   * [Number Of Positive Divisors](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/number_of_positive_divisors.cpp)

math/n_bonacci.cpp

@@ -0,0 +1,123 @@
+/**
+ * @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;
+}