n! means n × (n − 1) × … × 3 × 2 × 1

For example, 10! = 10 × 9 × … × 3 × 2 × 1 = 3628800, and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.

Find the sum of the digits in the number 100!

#include <iostream>
#include <cassert>   // assert()
#include <cstring>   // memset()
 


using namespace std;

class PE0020
{
private: 
    static const int MAX_DIGITS = 400; // estimation
    int m_digitsArray[MAX_DIGITS];

    void calculateFactorial(int n);
    void adjustDigitsArray();
    int  getSumOfDigits();

public:
    int getSumOfDigitsOfFactorial(int n);
};

int PE0020::getSumOfDigitsOfFactorial
 
(int n)
{
    calculateFactorial(n);

    return getSumOfDigits();
}

void PE0020::calculateFactorial(int n)
{
    memset(m_digitsArray, 0, sizeof(m_digitsArray)); 
    m_digitsArray[0] = 1;  // from left to right: unit, decade, hundred,...
          
    for(int i=1; i<=n; i++)
    {        
        for
 
 (int j=0; j<MAX_DIGITS; j++)
        {
            m_digitsArray[j] *= i; 
        }
        adjustDigitsArray();
    }
}

void PE0020::adjustDigitsArray()
{
    for (int j=0; j+1<MAX_DIGITS; j++)
    {
        if (m_digitsArray[j] >= 10)
        {
            m_digitsArray[j+1] += m_digitsArray[j]/10;
            m_digitsArray[j] %= 10;
        }
    }
}

int PE0020::getSumOfDigits()
{
    int sumOfDigits = 0;
    for(int i=0; i<MAX_DIGITS; i++)
    {
        sumOfDigits += m_digitsArray[i];
    } 
    
    return sumOfDigits;
}

int main()
{
    PE0020 pe0020;

    assert(27 == pe0020.getSumOfDigitsOfFactorial(10));
    
    cout << "The sum of the digits in the number 100! is ";
    cout << pe0020.getSumOfDigitsOfFactorial(100) << endl;

    return 0;    
}