Problem 43 : Sub-string divisibility

The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.

Let d₁ be the 1^st digit, d₂ be the 2^nd digit, and so on. In this way, we note the following:

d₂d₃d₄=406 is divisible by 2
d₃d₄d₅=063 is divisible by 3
d₄d₅d₆=635 is divisible by 5
d₅d₆d₇=357 is divisible by 7
d₆d₇d₈=572 is divisible by 11
d₇d₈d₉=728 is divisible by 13
d₈d₉d₁₀=289 is divisible by 17

Find the sum of all 0 to 9 pandigital numbers with this property.

#include <iostream>
 

#include <string>
#include <sstream>
#include <algorithm>  // next_permutation()
#include <cassert>    // assert()
#include <ctime>      // clock()

using namespace std;

// #define UNIT_TEST

struct _SubStrDivisibility
{
    int pos;   // sub-string start position
    int d;     // divisor
 

} subStrDiv[] = {{8, 17}, {7, 13}, {6, 11}, {5, 7}, {4, 5}, {3, 3}, {2, 2}};
    
class PE0043
{
private:
    static const int m_maxSubStrLength = 3;
    static const int max_digits = 10;
    string m_digitsString;  

    long long getLongLongInt() const;
    bool checkNumberOfSubString(int starting, int divisor);
    bool checkPandigitalNumber();

public:
    long long getSumOfProperPandigitalNumbers();
};

bool PE0043::checkPandigitalNumber()
{
    for(int i=0; i<sizeof(subStrDiv)/sizeof(_SubStrDivisibility); i++)
    {
        if (false == checkNumberOfSubString(subStrDiv[i].pos,subStrDiv[i].d))
        {
            return false;
        }
    }

    return true;
} 

bool PE0043::checkNumberOfSubString(int startPos, int divisor)
{
    int digit;
    int subStringNumber = 0;
    
    for (int i=startPos; i<startPos+m_maxSubStrLength; i++)
    {
        digit = m_digitsString[i-1] - '0';
        subStringNumber = 10*subStringNumber + digit;  
    }
    
    if (0 == subStringNumber % divisor)
    {
        return true;
    }

    return false;
}

long long PE0043::getLongLongInt()  const 
{
    long long n;
    stringstream os;

    os << m_digitsString;
    os >> n;

    return n;
}

long long PE0043::getSumOfProperPandigitalNumbers()
{
    m_digitsString = "1406357289";
    assert(true == checkPandigitalNumber());
    
    long long factorial_n = max_digits;
    for( long long n=factorial_n-1; n>=1; n-- ) 
    {
        factorial_n *= n; 
    }

    long long int sum = 0;

    for(int i=1; i<=factorial_n; i++)
    {
        if (true == checkPandigitalNumber())
        {
#ifdef UNIT_TEST
            cout << m_digitsString << endl;
#endif
            sum += getLongLongInt();
        }
        next_permutation(m_digitsString.begin(), m_digitsString.end());
    }
 
    return sum;
}
    
int main()
{
    clock_t start = clock(); 

    PE0043 pe0043;

    cout << "The sum of all 0 to 9 pandigital numbers with this property is "; 
    cout << pe0043.getSumOfProperPandigitalNumbers() << endl;

    clock_t finish = clock();
    double duration = (double)(finish - start) / CLOCKS_PER_SEC;
    cout << "C/C++ application running time: " << duration << " seconds" << endl;

    return 0;
}