Merge pull request #1318 from neha-hasija17/patch-3

feat: Create magic_number.cpp

DIRECTORY.md

@@ -144,6 +144,7 @@
   * [Large Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_number.h)
   * [Lcm Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/lcm_sum.cpp)
   * [Least Common Multiple](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/least_common_multiple.cpp)
+  * [Magic Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/magic_number.cpp)
   * [Miller Rabin](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/miller_rabin.cpp)
   * [Modular Inverse Fermat Little Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_inverse_fermat_little_theorem.cpp)
   * [Number Of Positive Divisors](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/number_of_positive_divisors.cpp)

math/magic_number.cpp

@@ -0,0 +1,80 @@
+/**
+ * @file
+ * @brief A simple program to check if the given number is a magic number or
+ * not. A number is said to be a magic number, if the sum of its digits are
+ * calculated till a single digit recursively by adding the sum of the digits
+ * after every addition. If the single digit comes out to be 1,then the number
+ * is a magic number.
+ *
+ * This is a shortcut method to verify Magic Number.
+ * On dividing the input by 9, if the remainder is 1 then the number is a magic
+ * number else not. The divisibility rule of 9 says that a number is divisible
+ * by 9 if the sum of its digits are also divisible by 9. Therefore, if a number
+ * is divisible by 9, then, recursively, all the digit sums are also divisible
+ * by 9. The final digit sum is always 9. An increase of 1 in the original
+ * number will increase the ultimate value by 1, making it 10 and the ultimate
+ * sum will be 1, thus verifying that it is a magic number.
+ * @author [Neha Hasija](https://github.com/neha-hasija17)
+ */
+#include <cassert>   /// for assert
+#include <iostream>  /// for io operations
+
+/**
+ * @namespace math
+ * @brief Mathematical algorithms
+ */
+namespace math {
+/**
+ * Function to check if the given number is magic number or not.
+ * @param n number to be checked.
+ * @return if number is a magic number, returns true, else false.
+ */
+bool magic_number(const uint64_t &n) {
+    if (n <= 0) {
+        return false;
+    }
+    // result stores the modulus of @param n with 9
+    uint64_t result = n % 9;
+    // if result is 1 then the number is a magic number else not
+    if (result == 1) {
+        return true;
+    } else {
+        return false;
+    }
+}
+}  // namespace math
+
+/**
+ * @brief Test function
+ * @returns void
+ */
+static void tests() {
+    std::cout << "Test 1:\t n=60\n";
+    assert(math::magic_number(60) == false);
+    std::cout << "passed\n";
+
+    std::cout << "Test 2:\t n=730\n";
+    assert(math::magic_number(730) == true);
+    std::cout << "passed\n";
+
+    std::cout << "Test 3:\t n=0\n";
+    assert(math::magic_number(0) == false);
+    std::cout << "passed\n";
+
+    std::cout << "Test 4:\t n=479001600\n";
+    assert(math::magic_number(479001600) == false);
+    std::cout << "passed\n";
+
+    std::cout << "Test 5:\t n=-35\n";
+    assert(math::magic_number(-35) == false);
+    std::cout << "passed\n";
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    tests();  // execute the tests
+    return 0;
+}