fix: Adding documentations, tests, and amending algorithm for gcd_of_n_numbers.cpp (#2766)

* Update gcd_of_n_numbers.cpp

* Update gcd_of_n_numbers.cpp

Reformatting code, comment and test cases, change array data type.

* Update gcd_of_n_numbers.cpp

* Update gcd_of_n_numbers.cpp

* Update gcd_of_n_numbers.cpp

* Update gcd_of_n_numbers.cpp

math/gcd_of_n_numbers.cpp

@@ -1,41 +1,114 @@
 /**
  * @file
- * @brief This program aims at calculating the GCD of n numbers by division
- * method
+ * @brief This program aims at calculating the GCD of n numbers
+ *
+ * @details
+ * The GCD of n numbers can be calculated by
+ * repeatedly calculating the GCDs of pairs of numbers
+ * i.e. \f$\gcd(a, b, c)\f$ = \f$\gcd(\gcd(a, b), c)\f$
+ * Euclidean algorithm helps calculate the GCD of each pair of numbers
+ * efficiently
  *
  * @see gcd_iterative_euclidean.cpp, gcd_recursive_euclidean.cpp
  */
-#include <iostream>
+#include <algorithm> /// for std::abs
+#include <array>     /// for std::array
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
 
-/** Compute GCD using division algorithm
- *
- * @param[in] a array of integers to compute GCD for
- * @param[in] n number of integers in array `a`
+/**
+ * @namespace math
+ * @brief Maths algorithms
  */
-int gcd(int *a, int n) {
-    int j = 1;  // to access all elements of the array starting from 1
-    int gcd = a[0];
-    while (j < n) {
-        if (a[j] % gcd == 0)  // value of gcd is as needed so far
-            j++;              // so we check for next element
-        else
-            gcd = a[j] % gcd;  // calculating GCD by division method
+namespace math {
+/**
+ * @namespace gcd_of_n_numbers
+ * @brief Compute GCD of numbers in an array
+ */
+namespace gcd_of_n_numbers {
+/**
+ * @brief Function to compute GCD of 2 numbers x and y
+ * @param x First number
+ * @param y Second number
+ * @return GCD of x and y via recursion
+ */
+int gcd_two(int x, int y) {
+  // base cases
+  if (y == 0) {
+    return x;
+  }
+  if (x == 0) {
+    return y;
+  }
+  return gcd_two(y, x % y); // Euclidean method
+}
+
+/**
+ * @brief Function to check if all elements in the array are 0
+ * @param a Array of numbers
+ * @return 'True' if all elements are 0
+ * @return 'False' if not all elements are 0
+ */
+template <std::size_t n>
+bool check_all_zeros(const std::array<int, n> &a) {
+  // Use std::all_of to simplify zero-checking
+  return std::all_of(a.begin(), a.end(), [](int x) { return x == 0; });
+}
+
+/**
+ * @brief Main program to compute GCD using the Euclidean algorithm
+ * @param a Array of integers to compute GCD for
+ * @return GCD of the numbers in the array or std::nullopt if undefined
+ */
+template <std::size_t n>
+int gcd(const std::array<int, n> &a) {
+  // GCD is undefined if all elements in the array are 0
+  if (check_all_zeros(a)) {
+    return -1; // Use std::optional to represent undefined GCD
+  }
+
+  // divisors can be negative, we only want the positive value
+  int result = std::abs(a[0]);
+  for (std::size_t i = 1; i < n; ++i) {
+    result = gcd_two(result, std::abs(a[i]));
+    if (result == 1) {
+      break; // Further computations still result in gcd of 1
     }
-    return gcd;
+  }
+  return result;
+}
+} // namespace gcd_of_n_numbers
+} // namespace math
+
+/**
+ * @brief Self-test implementation
+ * @return void
+ */
+static void test() {
+  std::array<int, 1> array_1 = {0};
+  std::array<int, 1> array_2 = {1};
+  std::array<int, 2> array_3 = {0, 2};
+  std::array<int, 3> array_4 = {-60, 24, 18};
+  std::array<int, 4> array_5 = {100, -100, -100, 200};
+  std::array<int, 5> array_6 = {0, 0, 0, 0, 0};
+  std::array<int, 7> array_7 = {10350, -24150, 0, 17250, 37950, -127650, 51750};
+  std::array<int, 7> array_8 = {9500000, -12121200, 0, 4444, 0, 0, 123456789};
+
+  assert(math::gcd_of_n_numbers::gcd(array_1) == -1);
+  assert(math::gcd_of_n_numbers::gcd(array_2) == 1);
+  assert(math::gcd_of_n_numbers::gcd(array_3) == 2);
+  assert(math::gcd_of_n_numbers::gcd(array_4) == 6);
+  assert(math::gcd_of_n_numbers::gcd(array_5) == 100);
+  assert(math::gcd_of_n_numbers::gcd(array_6) == -1);
+  assert(math::gcd_of_n_numbers::gcd(array_7) == 3450);
+  assert(math::gcd_of_n_numbers::gcd(array_8) == 1);
 }
 
-/** Main function */
+/**
+ * @brief Main function
+ * @return 0 on exit
+ */
 int main() {
-    int n;
-    std::cout << "Enter value of n:" << std::endl;
-    std::cin >> n;
-    int *a = new int[n];
-    int i;
-    std::cout << "Enter the n numbers:" << std::endl;
-    for (i = 0; i < n; i++) std::cin >> a[i];
-
-    std::cout << "GCD of entered n numbers:" << gcd(a, n) << std::endl;
-
-    delete[] a;
-    return 0;
+  test(); // run self-test implementation
+  return 0;
 }