SumOfFactorialDigits

Calculate all digits of given factorial

How it works

The main idea behind the algorithm it's to calculate using the last digit. We will incress the list with all digits of factorial. This is list starts with 1, because it's the starting point. When we end on iteration on all digits and we still have a rest, we need to add to list.

First, we iterate over all numbers between 1 and the expected factorial number.

Look at the code:

int rest = 0;
for(int i = 0; i < currentDigitSize; ++i)
{
    int result = rest + digits[i] * iCurrentFactorial;

    digits[i] = result % 10;
    rest = result / 10;
}

We update every digit on list with the rest mod of 10 and saving the left number.

Imagine the loop with iCurrentFactorial being 5. The digits.Count will be 1 and digits[0] = 6.
Result will be 24.
The digits[0] will be replaced with mod of ten: 4
The rest with 2.

We have a rest different from 0 so, at this point, we add to the list. On next iteration (if exists), we calculate over all the digits again.