From adccfdfa41cc99f21ccf367bd44581794dfc3297 Mon Sep 17 00:00:00 2001
From: Swastika Gupta <gupta.swastika521@gmail.com>
Date: Wed, 21 Jul 2021 08:54:28 +0000
Subject: [PATCH] n-bonacci

---
 math/n_bonacci.cpp | 98 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 98 insertions(+)
 create mode 100644 math/n_bonacci.cpp

diff --git a/math/n_bonacci.cpp b/math/n_bonacci.cpp
new file mode 100644
index 000000000..90302131d
--- /dev/null
+++ b/math/n_bonacci.cpp
@@ -0,0 +1,98 @@
+/**
+ * @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<int> N_bonacci(int n, unsigned int m) {
+    std::vector<int> 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 (int 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<int> 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<int> 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<int> 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<int> 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<int> 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<int> 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<int> 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<int> 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;
+}
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