Project Euler

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 x d₁₀ x d₁₀₀ x d₁₀₀₀ x d₁₀₀₀₀ x d₁₀₀₀₀₀ x d_1000000

The Catch

How to quickly construct the irrational number by concatenating incremented-positive-integers.

The Light

Use Java's StringBuilder class to concatenate incremented-positive-integers. Since there is no actual calculation involved, the construction should be very quick. Once the irrational number is constructed, pick out requested indexed-digits and find their product.

The Code

public class Problem40
{
  public static void main(String[] args)
  {
    StringBuilder sb = new StringBuilder(1000000);
    int i = 1;
    int result = 1;

    while(i <= 1000000)
    {
      sb = sb.append(i++);
    }
    String s = sb.toString();

    for(i = 1; i <= 1000000; i *= 10)
    {
      result *= Character.getNumericValue(s.charAt(i - 1));
    }
    System.out.println("Result = " + result);
  }
}