Project Euler problem 40

Problem 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

Firstly I completed this in Coldfusion. I got the correct answer by brute-forcing it, but the solution was slow. This took about 11 minutes on a CF 5 server; it would undoubtedly be a lot quicker on any CFMX server. I then rewrote it in Python, which spits out the correct answer within a couple of seconds.

I thought it might be interesting to do a code comparison between the two languages.
CFML:

<cfset fraction = "">
<cfset total = 1>

<cfloop index="i" from="1" to="1000000">
<!--- we're going to break out of the loop sooner than that --->
	<cfset fraction = fraction & i>
	
	<cfif Len(fraction) GTE 1000000>
		<cfbreak>
	</cfif>
</cfloop>

<cfset total = total *	Mid(fraction, 1, 1) * 
	Mid(fraction, 10, 1) * 
	Mid(fraction, 100, 1) * 
	Mid(fraction, 1000, 1) * 
	Mid(fraction, 10000, 1) * 
	Mid(fraction, 100000, 1) * 
	Mid(fraction, 1000000, 1)>

<cfoutput>#total#</cfoutput>

Python:

fraction = ""
total = 1

for i in range(1,1000000):
    fraction = fraction + str(i)

    if len(fraction) >= 1000000:
        break

total = total * \
        int(fraction[0]) * \
        int(fraction[9]) * \
        int(fraction[99]) * \
        int(fraction[999]) * \
        int(fraction[9999]) * \
        int(fraction[99999]) * \
        int(fraction[999999])

print(total)

Almost identical code. I’m still not anywhere near writing pythonic code, but it’s early days.

Basically I loop from 1 to 1000000 (not really that far, because I break out of the loop once our string has length of 1000000). As I go I append each loop counter to the string.

Then I just multiply together the 1st, 10th, 100th etc values from the string. That part could also have been done in a loop to simplify the code slightly. The whole thing’s not particularly clever, but it works.

If you’re coming to this from a Coldfusion background, you’re maybe wondering why I’m doing a DIV between each of the values before multiplying them. Because whitespace is important in Python, the \ can be used to join two lines together where the line length gets too long.