PROJECT EULER SOLUTION # 40

Solution to problem number 40 of Project Euler.

Question #40

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

Solution #40

/***********************************************************************************************************/

#include<stdio.h>

#include<conio.h>

#include<time.h>

#include<stdlib.h>

#include<math.h>

long count_digits(long);

long count_digits_upto(long);

int d(long);

int ith(long,long);

int main()

{

       long product=1;

       int i;

       for(i=0;i<7;i++)

              product*=d((long)pow(10.0,i));

       printf("%ld\n",product);

       printf("EXECUTION TIME = %f\n",clock()/(float)CLK_TCK);

       system("pause");

}

int d(long n)

{

       int ans;

       long i,tmp;

       i=getNumber(n);

       tmp=count_digits_upto(i-1);

       ans=ith(n-tmp,i);

       return ans;

}

int ith(long i,long n)

{

       int digits,j;

       digits=count_digits(n);

       for(j=0;j<digits-i;j++)

              n/=10;

       return n%10;

}

long count_digits_upto(long n)

{

       long counter=0,i;

       for(i=1;i<=n;i++)

              counter+=count_digits(i);

       return counter;

}

long getNumber(long n)

{

       long i,counter=0,product;

       for(i=1;i<=n;i++)

       {

              counter+=count_digits(i);

              if(counter>=n)

                     break;

       }

       return i;

}

long count_digits(long i)

{

       int counter=0;

       while(i)

       {

              counter++;

              i/=10;

       }

       return counter;

}

/***********************************************************************************************************/