feat: Add count_of_trailing_ciphers_in_factorial_n (TheAlgorithms#1543)

* zeroes

* Update bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

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

* Update bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

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

* Update bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

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

* Update bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

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

* Update bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

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

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for 537cd7e

* Update count_of_trailing_ciphers_in_factorial_n.cpp

* Update bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

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

* Update bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

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

* Update bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

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

* Update bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

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

* clang-format and clang-tidy fixes for a8c85e2

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com>

Author: 4 people

DIRECTORY.md

@@ -14,6 +14,7 @@
 
 ## Bit Manipulation
   * [Count Of Set Bits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/count_of_set_bits.cpp)
+  * [Count Of Trailing Ciphers In Factorial N](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp)
   * [Hamming Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/hamming_distance.cpp)
 
 ## Ciphers

bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

@@ -0,0 +1,98 @@
+/**
+ * @file
+ * @brief [Count the number of
+ * ciphers](https://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus) in `n!` implementation
+ * @details
+ * Given an integer number as input. The goal is to find the number of trailing
+ zeroes in the factorial calculated for
+ * that number. A factorial of a number N is a product of all numbers in the
+ range [1, N].
+
+ * We know that we get a trailing zero only if the number is multiple of 10 or
+ has a factor pair (2,5). In all factorials of
+ * any number greater than 5, we have many 2s more than 5s in the prime
+ factorization of that number. Dividing a
+ * number by powers of 5 will give us the count of 5s in its factors. So, the
+ number of 5s will tell us the number of trailing zeroes.
+ * @author [Swastika Gupta](https://github.com/Swastyy)
+ */
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
+
+/**
+ * @namespace bit_manipulation
+ * @brief Bit manipulation algorithms
+ */
+namespace bit_manipulation {
+/**
+ * @namespace count_of_trailing_ciphers_in_factorial_n
+ * @brief Functions for the [Count the number of
+ * ciphers](https://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus)
+ * in `n!` implementation
+ */
+namespace count_of_trailing_ciphers_in_factorial_n {
+/**
+ * @brief Function to count the number of the trailing ciphers
+ * @param n number for which `n!` ciphers are returned
+ * @return count, Number of ciphers in `n!`.
+ */
+uint64_t numberOfCiphersInFactorialN(uint64_t n) {
+    // count is to store the number of 5's in factorial(n)
+    uint64_t count = 0;
+
+    // Keep dividing n by powers of
+    // 5 and update count
+    for (uint64_t i = 5; n / i >= 1; i *= 5) {
+        count += static_cast<uint64_t>(n) / i;
+    }
+
+    return count;
+}
+}  // namespace count_of_trailing_ciphers_in_factorial_n
+}  // namespace bit_manipulation
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // 1st test
+    std::cout << "1st test ";
+    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
+               numberOfCiphersInFactorialN(395) == 97);
+    std::cout << "passed" << std::endl;
+
+    // 2nd test
+    std::cout << "2nd test ";
+    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
+               numberOfCiphersInFactorialN(977) == 242);
+    std::cout << "passed" << std::endl;
+
+    // 3rd test
+    std::cout << "3rd test ";
+    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
+               numberOfCiphersInFactorialN(871) == 215);
+    std::cout << "passed" << std::endl;
+
+    // 4th test
+    std::cout << "4th test ";
+    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
+               numberOfCiphersInFactorialN(239) == 57);
+    std::cout << "passed" << std::endl;
+
+    // 5th test
+    std::cout << "5th test ";
+    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
+               numberOfCiphersInFactorialN(0) == 0);
+    std::cout << "passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}

math/check_prime.cpp

@@ -22,11 +22,11 @@ template <typename T>
 bool is_prime(T num) {
     bool result = true;
     if (num <= 1) {
-        return 0;
+        return false;
     } else if (num == 2) {
-        return 1;
+        return true;
     } else if ((num & 1) == 0) {
-        return 0;
+        return false;
     }
     if (num >= 3) {
         for (T i = 3; (i * i) <= (num); i = (i + 2)) {
@@ -47,7 +47,7 @@ int main() {
     assert(is_prime(50) == false);
     assert(is_prime(115249) == true);
 
-    int num;
+    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);