Finding Number of Digits in a Number

```/**
* @author [aminos ðŸ‡®ðŸ‡³](https://github.com/amino19)
* @file
*
* @brief [Program to count digits
* in an
* integer](https://www.geeksforgeeks.org/program-count-digits-integer-3-different-methods)
* @details It is a very basic math of finding number of digits in a given
* 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). The code for that is also included
* (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
*/
uint64_t finding_number_of_digits_in_a_number(uint64_t n) {
uint64_t count = 0;  ///< the variable used for the digits count

// iterate until `n` becomes 0
// remove last digit from `n` in each iteration
// increase `count` by 1 in each iteration
while (n != 0) {
// we can also use `n = n / 10`
n /= 10;
// each time the loop is running, `count` will be incremented by 1.
++count;
}

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 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);
assert(finding_number_of_digits_in_a_number(9) == 1);
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);
}

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() {
// run self-test implementations
first_test();
second_test();
std::cout << "All tests have successfully passed!\n";
return 0;
}
```