fix: Adding documentations, tests, and amending algorithm for gcd_of_n_numbers.cpp

math/gcd_of_n_numbers.cpp

@@ -1,41 +1,112 @@
 /**
  * @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. gcd(a, b, c) = gcd(gcd(a, b), c)
+ * Euclidean algorithm helps calculate the GCD of each pair of numbers efficiently
+ * 
  * @see gcd_iterative_euclidean.cpp, gcd_recursive_euclidean.cpp
  */
-#include <iostream>
+#include <iostream>  /// for IO operations
+#include <cassert>  /// for assert
+#include <algorithm>  /// for std::abs
 
-/** 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
+ */
+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 array are 0
+ * @param a Array of numbers
+ * @param n Number of elements in array
+ * @return 'True' if all elements are 0
+ * @return 'False' if not all elements are 0
+ */
+bool check_all_zeros(int a[], size_t n) {
+    // Check for the undefined GCD cases
+    int zero_count = 0;
+    for (int i = 0; i < n; ++i) {
+        if (a[i] == 0) {
+            ++zero_count;
+        }
+    }
+
+    // return whether all elements in array are 0
+    return zero_count == n;
+}
+/** 
+ * @brief Main program to compute GCD using division algorithm
+ * @param a Array of integers to compute GCD for
+ * @param n number of integers in the array
+ * @return GCD of the numbers in the array
  */
-int gcd(int *a, int n) {
-    int j = 1;  // to access all elements of the array starting from 1
+int gcd(int a[], size_t n) {
+    // GCD is undefined if all elements in the array are 0
+    if (check_all_zeros(a, n))
+        return -1;  // since gcd is positive, use -1 to mark undefined gcd
+
     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
+    for(int i = 1; i < n; i++) {
+        gcd = gcd_two(gcd, a[i]);
+        if (std::abs(gcd) == 1) 
+            break;  // if gcd is already 1, further computations still result in gcd of 1
     }
-    return gcd;
+
+    return std::abs(gcd);  // divisors can be negative, and we only want positive value
 }
+} // namespace gcd_of_n_numbers
+} // namespace math
 
-/** Main function */
-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];
+/**
+ * @brief Self-test implementation
+ * @return void
+ */
+static void test() { 
+    int array_1[1] = {0};
+    int array_2[1] = {1};
+    int array_3[2] = {0, 2};
+    int array_4[3] = {-60, 24, 18};
+    int array_5[4] = {100, -100, -100, 200};
+    int array_6[5] = {0, 0, 0, 0, 0};
+    int array_7[7] = {90, -120, 0, 135, 660, -280, 900}; 
+    int array_8[7] = {90, -120, 0, 4000, 0, 0, 111};
 
-    std::cout << "GCD of entered n numbers:" << gcd(a, n) << std::endl;
+    assert(math::gcd_of_n_numbers::gcd(array_1, 1) == -1);
+    assert(math::gcd_of_n_numbers::gcd(array_2, 1) == 1); 
+    assert(math::gcd_of_n_numbers::gcd(array_3, 2) == 2);
+    assert(math::gcd_of_n_numbers::gcd(array_4, 3) == 6);
+    assert(math::gcd_of_n_numbers::gcd(array_5, 4) == 100);
+    assert(math::gcd_of_n_numbers::gcd(array_6, 5) == -1);
+    assert(math::gcd_of_n_numbers::gcd(array_7, 7) == 5);
+    assert(math::gcd_of_n_numbers::gcd(array_8, 7) == 1);
+}
 
-    delete[] a;
+/**
+ * @brief Main function
+ * @return 0 on exit
+ */
+int main() {
+    test();  // run self-test implementation
     return 0;
 }