Merge branch 'master' into factorial

math/check_factorial.cpp

@@ -1,64 +1,73 @@
 /**
  * @file
- * @brief A simple program to check if the given number is a factorial of some
- * number or not.
+ * @brief A simple program to check if the given number is a
+ * [factorial](https://en.wikipedia.org/wiki/Factorial) of some number or not.
+ *
+ * @details A factorial number is the sum of k! where any value of k is a
+ * positive integer. https://www.mathsisfun.com/numbers/factorial.html
+ *
  * @author [Divyajyoti Ukirde](https://github.com/divyajyotiuk)
+ * @author [ewd00010](https://github.com/ewd00010)
  */
-#include <cassert>
-#include <iostream>
+#include <cassert>   /// for assert
+#include <iostream>  /// for cout
 
 /**
- * Function to check if the given number is factorial of some number or not.
- * @param n number to be checked.
- * @return if number is a factorial, returns true, else false.
+ * @namespace
+ * @brief Mathematical algorithms
+ */
+namespace math {
+/**
+ * @brief Function to check if the given number is factorial of some number or
+ * not.
+ * @param n number to be checked.
+ * @return true if number is a factorial returns true
+ * @return false if number is not a factorial
  */
-
 bool is_factorial(uint64_t n) {
-    if (n <= 0) {
+    if (n <= 0) {  // factorial numbers are only ever positive Integers
         return false;
     }
-    for (uint32_t i = 1;; i++) {
-        if (n % i != 0) {
-            break;
-        }
-        n = n / i;
-    }
-    if (n == 1) {
-        return true;
-    } else {
-        return false;
-    }
-}
 
-/** Test function
+    /*!
+     * this loop is basically a reverse factorial calculation, where instead
+     * of multiplying we are dividing. We start at i = 2 since i = 1 has
+     * no impact division wise
+     */
+    int i = 2;
+    while (n % i == 0) {
+        n = n / i;
+        i++;
+    }
+
+    /*!
+     * if n was the sum of a factorial then it should be divided until it
+     * becomes 1
+     */
+    return (n == 1);
+}
+}  // namespace math
+
+/**
+ * @brief Self-test implementations
  * @returns void
  */
-void tests() {
-    std::cout << "Test 1:\t n=50\n";
-    assert(is_factorial(50) == false);
-    std::cout << "passed\n";
+static void tests() {
+    assert(math::is_factorial(50) == false);
+    assert(math::is_factorial(720) == true);
+    assert(math::is_factorial(0) == false);
+    assert(math::is_factorial(1) == true);
+    assert(math::is_factorial(479001600) == true);
+    assert(math::is_factorial(-24) == false);
 
-    std::cout << "Test 2:\t n=720\n";
-    assert(is_factorial(720) == true);
-    std::cout << "passed\n";
-
-    std::cout << "Test 3:\t n=0\n";
-    assert(is_factorial(0) == false);
-    std::cout << "passed\n";
-
-    std::cout << "Test 4:\t n=479001600\n";
-    assert(is_factorial(479001600) == true);
-    std::cout << "passed\n";
-
-    std::cout << "Test 5:\t n=-24\n";
-    assert(is_factorial(-24) == false);
-    std::cout << "passed\n";
+    std::cout << "All tests have successfully passed!" << std::endl;
 }
 
-/** Main function
+/**
+ * @brief Main function
  * @returns 0 on exit
  */
 int main() {
-    tests();
+    tests();  // run self-test implementations
     return 0;
 }

math/check_prime.cpp

@@ -1,62 +1,84 @@
 /**
- * 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
  */
-template <typename T>
-bool is_prime(T num) {
-    bool result = true;
+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
+     */
     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;
 }