[feat/docs/fix]: fit check_prime.cpp to guidelines (#2460)

* check_prime_update

docs: added links to file @brief and @details. moved previous @brief to be with function, made comments easier to read in general and added boilerplate documentation to functions.
chore: removed bool result and most brackets in is_prime. Moved assert tests to their own function and added more in, test success now returns message.

* Delete cmake-build-debug directory

* clang-format

* original box_stacking documentation

start point

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Delete box_stacking.cpp

* Update check_prime.cpp

improved files @details text, removed generic t template - replaced with long long

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update check_prime.cpp

removed cin/cout interaction

* Update check_prime.cpp

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update math/check_prime.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update math/check_prime.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update check_prime.cpp

* Update math/check_prime.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

---------

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>
Co-authored-by: David Leal <halfpacho@gmail.com>

math/check_prime.cpp

@@ -1,62 +1,83 @@
 /**
- * Copyright 2020 @author omkarlanghe
- *
  * @file
- * A simple program to check if the given number if prime or not.
- *
  * @brief
- * Reduced all possibilities of a number which cannot be prime.
- * Eg: No even number, except 2 can be a prime number, hence we will increment
- * our loop with i+6 jumping and check for i or i+2 to be a factor of the
- * number; if it's a factor then we will return false otherwise true after the
- * loop terminates at the terminating condition which is (i*i<=num)
+ * A simple program to check if the given number is [Prime](https://en.wikipedia.org/wiki/Primality_test) or not.
+ * @details
+ * A prime number is any number that can be divided only by itself and 1. It must
+ * be positive and a whole number, therefore any prime number is part of the
+ * set of natural numbers. The majority of prime numbers are even numbers, with
+ * the exception of 2. This algorithm finds prime numbers using this information.
+ * additional ways to solve the prime check problem:
+ * https://cp-algorithms.com/algebra/primality_tests.html#practice-problems
+ * @author [Omkar Langhe](https://github.com/omkarlanghe)
+ * @author [ewd00010](https://github.com/ewd00010)
  */
 
 #include <cassert>   /// for assert
 #include <iostream>  /// for IO operations
 
 /**
- * Function to check if the given number is prime or not.
- * @param num number to be checked.
- * @return if number is prime, it returns @ true, else it returns @ false.
+ * @brief Mathematical algorithms
+ * @namespace
+ */
+namespace math {
+    /**
+     * @brief Function to check if the given number is prime or not.
+     * @param num number to be checked.
+     * @return true if number is a prime
+     * @return false if number is not a prime.
+     */
+    bool is_prime(int64_t num) {
+        /*!
+         * Reduce all possibilities of a number which cannot be prime with the first
+         * 3 if, else if conditionals. Example: Since no even number, except 2 can
+         * be a prime number and the next prime we find after our checks is 5,
+         * we will start the for loop with i = 5. then for each loop we increment
+         * i by +6 and check if i or i+2 is a factor of the number; if it's a factor
+         * then we will return false. otherwise, true will be returned after the
+         * loop terminates at the terminating condition which is i*i <= num
          */
-template <typename T>
-bool is_prime(T num) {
-    bool result = true;
         if (num <= 1) {
             return false;
         } else if (num == 2 || num == 3) {
             return true;
-    } else if ((num % 2) == 0 || num % 3 == 0) {
+        } else if (num % 2 == 0 || num % 3 == 0) {
             return false;
         } else {
-        for (T i = 5; (i * i) <= (num); i = (i + 6)) {
-            if ((num % i) == 0 || (num % (i + 2) == 0)) {
-                result = false;
-                break;
+            for (int64_t i = 5; i * i <= num; i = i + 6) {
+                if (num % i == 0 || num % (i + 2) == 0) {
+                    return false;
                 }
             }
         }
-    return (result);
+        return true;
+    }
+}  // namespace math
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void tests() {
+    assert(math::is_prime(1) == false);
+    assert(math::is_prime(2) == true);
+    assert(math::is_prime(3) == true);
+    assert(math::is_prime(4) == false);
+    assert(math::is_prime(-4) == false);
+    assert(math::is_prime(7) == true);
+    assert(math::is_prime(-7) == false);
+    assert(math::is_prime(19) == true);
+    assert(math::is_prime(50) == false);
+    assert(math::is_prime(115249) == true);
+
+    std::cout << "All tests have successfully passed!" << std::endl;
 }
 
 /**
- * Main function
+ * @brief Main function
+ * @returns 0 on exit
  */
 int main() {
-    // perform self-test
-    assert(is_prime(50) == false);
-    assert(is_prime(115249) == true);
-
-    int num = 0;
-    std::cout << "Enter the number to check if it is prime or not" << std::endl;
-    std::cin >> num;
-    bool result = is_prime(num);
-    if (result) {
-        std::cout << num << " is a prime number" << std::endl;
-    } else {
-        std::cout << num << " is not a prime number" << std::endl;
-    }
-
+    tests();  // perform self-tests implementations
     return 0;
 }