feat: added log code for counting digits (#2234)

* added log code for counting digits

* one space removed

* fix: CI warnings (hopefully)

* fix: revert for now

* decoupled test functions

* Update math/finding_number_of_digits_in_a_number.cpp

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

* Update math/finding_number_of_digits_in_a_number.cpp

typo changes

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

* uint64_t changed to double to resolve clang-tidy warnings

* clang-format and clang-tidy fixes for 61bb2dea

* comment improvement

* clang-format and clang-tidy fixes for 39ebc33d

* guarded required function

---------

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions[bot] <github-actions@users.noreply.github.com>

math/finding_number_of_digits_in_a_number.cpp

@@ -9,18 +9,21 @@
  * number i.e, we can use it by inputting values whether it can be a
  * positive/negative value, let's say: an integer. There is also a second
  * method: by using "K = floor(log10(N) + 1)", but it's only applicable for
- * numbers (not integers).
+ * numbers (not integers). The code for that is also included
- * For more details, refer to the
+ * (finding_number_of_digits_in_a_number_using_log). For more details, refer to
+ * the
  * [Algorithms-Explanation](https://github.com/TheAlgorithms/Algorithms-Explanation/blob/master/en/Basic%20Math/Finding
  * the number of digits in a number.md) repository.
  */
 
 #include <cassert>   /// for assert
+#include <cmath>     /// for log calculation
 #include <iostream>  /// for IO operations
 
 /**
  * @brief The main function that checks
  * the number of digits in a number.
+ * TC : O(number of digits)
  * @param n the number to check its digits
  * @returns the digits count
  */
@@ -40,11 +43,34 @@ uint64_t finding_number_of_digits_in_a_number(uint64_t n) {
     return count;
 }
 
+/**
+ * @brief This function finds the number of digits
+ * in constant time using logarithmic function
+ * TC: O(1)
+ * @param n the number to check its digits
+ * @returns the digits count
+ */
+double finding_number_of_digits_in_a_number_using_log(double n) {
+    // log(0) is undefined
+    if (n == 0) {
+        return 0;
+    }
+
+    // to handle the negative numbers
+    if (n < 0) {
+        n = -n;
+    }
+
+    double count = floor(log10(n) + 1);
+
+    return count;
+}
+
 /**
  * @brief Self-test implementations
  * @returns void
  */
-static void test() {
+static void first_test() {
     assert(finding_number_of_digits_in_a_number(5492) == 4);
     assert(finding_number_of_digits_in_a_number(-0) == 0);
     assert(finding_number_of_digits_in_a_number(10000) == 5);
@@ -52,15 +78,25 @@ static void test() {
     assert(finding_number_of_digits_in_a_number(100000) == 6);
     assert(finding_number_of_digits_in_a_number(13) == 2);
     assert(finding_number_of_digits_in_a_number(564) == 3);
-
-    std::cout << "All tests have successfully passed!\n";
 }
 
+static void second_test() {
+    assert(finding_number_of_digits_in_a_number_using_log(5492) == 4);
+    assert(finding_number_of_digits_in_a_number_using_log(-0) == 0);
+    assert(finding_number_of_digits_in_a_number_using_log(10000) == 5);
+    assert(finding_number_of_digits_in_a_number_using_log(9) == 1);
+    assert(finding_number_of_digits_in_a_number_using_log(100000) == 6);
+    assert(finding_number_of_digits_in_a_number_using_log(13) == 2);
+    assert(finding_number_of_digits_in_a_number_using_log(564) == 3);
+}
 /**
  * @brief Main function
  * @returns 0 on exit
  */
 int main() {
-    test();  // run self-test implementations
+    // run self-test implementations
+    first_test();
+    second_test();
+    std::cout << "All tests have successfully passed!\n";
     return 0;
 }