Problem 40 : Champernowne’s constant

An irrational decimal fraction is created by concatenating the positive integers:

0.123456789101112131415161718192021…

It can be seen that the 12^th digit of the fractional part is 1.

If d_n represents the n^th digit of the fractional part, find the value of the following expression.

d₁ × d₁₀ × d₁₀₀ × d₁₀₀₀ × d₁₀₀₀₀ × d₁₀₀₀₀₀ × d_1000000

#include <iostream>
#include <cmath>
#include <cassert>
#include <ctime>

using namespace std;

// #define UNIT_TEST

class PE0040
{
private:
    static const int MAX = 1000000;
    int m_digits[10];

    int getDigits(int number);

public:
    int findValueOfExpression
 
();
};


int PE0040::getDigits(int number)
{
    int numOfDigits = 0;

    while(number> 0)
    {
        m_digits[numOfDigits++] = number%10;
        number /= 10; 
    }

    return numOfDigits;
}

int PE0040::findValueOfExpression()
{
    int numOfDigits;
    int numOfFractionDigits = 0;

    short *irrationalDecimalFractionDigits =
 
 new short[MAX+1];    
    
    for(int number=1; numOfFractionDigits<=MAX; number++)
    {
        numOfDigits = getDigits(number);

        for(int i=numOfDigits-1; i>=0 && numOfFractionDigits<=MAX; i--)
        {
            irrationalDecimalFractionDigits[numOfFractionDigits++] = m_digits[i];
        }
    }

    assert (1 == irrationalDecimalFractionDigits[12]);

    int index;
    int product = 1;

    for(int exp = 0; exp<7; exp++)
    {
        index = (int)pow(10.0, exp);  // 10^0, 10^1, 10^2, 10^3, 10^4, 10^5, 10^6

#ifdef UNIT_TEST
        cout << "d" << index << " : " << irrationalDecimalFractionDigits[index-1]<<endl;
#endif
        product *= irrationalDecimalFractionDigits[index-1];
    }    

    delete [] irrationalDecimalFractionDigits;

    return product;
}

int main()
{
    clock_t start = clock();

    PE0040 pe0040;

    cout << "d1 x d10 x d100 x d1000 x d10000 x d100000 x d1000000 = ";
    cout << pe0040.findValueOfExpression() << endl;

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

    return 0;
}