why are the answers different?

[Mahendra Kariya]

I was solving Problem 40 of Project Euler. I tried it in two different ways. But I was getting an incorrect answer for one of the ways. Can someone tell me what is the mistake?

My code follows:

    
/*********************************************************************
we have to find the number at the nth place.

so iterate thru the all the numbers from 1 to some upper bound.
keep track of how many digits hav passed by.
if the no of digits is a multiple of 10, find out it is for which no.
if it is slightly gr8er than the multiple of 10, say 1002 or so, take 
the required digit.
*********************************************************************/

public class Prob40
{
	int product = 1;

	//method to find the no of digits
	int noOfDigits(long n)
	{
		if(n < 10)
			return 1;
		else if(n < 100)
			return 2;
		else if(n < 1000)
			return 3;
		else if(n < 10000)
			return 4;
		else if(n < 1000000)
			return 5;
		return 0;
	}


	//to check no of digits hav reached a multiple of 10.
	//if yes find out the digit which is the required
	boolean targetReached(long digits, long milestone, long i)
	{

		long temp; //the required digit. i.e. the 10th or 100th or whatever.
			  //i is that number for which we achieved the milestone.
			  //digits is no of digits

			if(digits == milestone) //if digits is exactly equal to milestone, take the last digit.
			{
				temp = i%10;
				System.out.println("temp = "+temp);				
				System.out.println("i = "+i);				
				System.out.println("digits = "+digits);
				return true;
			}
			else if(digits > milestone) //if digits is slightly more than milestone, remove the not required digits frm the end
			{
				temp = i;
				for(int k = 0;k<digits%milestone;k++)
					temp /= 10;
				temp %= 10;
				System.out.println("temp = " +temp);	
				System.out.println("i = "+i);							
				System.out.println("digits = "+digits);
				return true;
			}
		return false;

	}

	public static void main(String args[])
	{
		Prob40 p = new Prob40();

		long digits = 0;
		long milestone = 10;

		for(long i = 1;i<205000;i++)		
		{
			digits += p.noOfDigits(i);
			if(p.targetReached(digits,milestone,i))
			{
				milestone *= 10; //if one milestone is achieved higher the milestone
				System.out.println();
			}
		}
		System.out.println(digits);

	}
}

">

[Himanshu Kansal]

Is the condition at line 50 correct?

digits can have a max value of 5 and milestone has a value of 10 and increases only.

Regards

[Mahendra Kariya]

Himanshu Kansal wrote:Is the condition at line 50 correct?

digits can have a max value of 5 and milestone has a value of 10 and increases only.

The output shows that only the last one is incorrect. I mean the millionth digit. Rest all are correct. I cross checked with the second method.

[Himanshu Kansal]

i think it should be:

  digits < milestone  

well i don't know what the actual problem is, but I am just trying to shoot the trouble through your code.

[Mahendra Kariya]

Himanshu Kansal wrote:i think it should be:

  digits < milestone  

This will be a frequent case. Suppose we want to find the 100th digit. We have the milestone set to 100. If we check digits<milestone, then this condition will be true for every case. But if it is what I have done, this condition will be true once the milestone is reached. And once we reach a particular milestone, we increase it.

I guess your condition will result in an infinite loop!

[Himanshu Kansal]

Could you please post the problem statement?

[Mahendra Kariya]

Himanshu Kansal wrote:Could you please post the problem statement?

Problem statement is available at http://projecteuler.net/index.php?section=problems&id=40

Still I have put it here for convenience.

------------------------
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.

d(1) × d(10) × d(100) × d(1000) × d(10000) × d(100000) × d(1000000)
-------------------------

[Sean Clark]

Hey,

I'm not sure if this makes a difference, but line 27 - 28

else if(n < 1000000)   
return 5; 

if n < 1000000 then number of digits could be 6 as well??

Dunno if that helps though.

Sean

[Mahendra Kariya]

Sean Clark wrote:
I'm not sure if this makes a difference, but line 27 - 28

else if(n < 1000000)   
return 5; 

if n < 1000000 then number of digits could be 6 as well??

Thanks Sean, this was the error. At line 27-28, it should be something like this.

else if(n < 100000)   
return 5;
else if(n < 1000000)   
return 6;
 

Thank you Sean and Himanshu.