Problem 40 Project Euler Solution with python

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

This problem requires a small homework to set the upper limit for the for loop. This is general mathematics.

We have 9, 1 digit numbers
90, 2 digit numbers
900, 3 digit numbers
9000, 4 digit numbers
90000, 5 digit numbers
900000, 6 digit numbers

Which will total to 5888889 digits. But we only need 1000000, so that
9 x 1 digit
90 x 2 digit
900 x 3 digit
9000 x 4 digit
90000 x 5 digit
n x 6 digit

= 9*1 + 90*2 + 900*3+ 9000*4 + 90000*5 + n*6 = 1000000
So the value of n is approximately 85186 that means that we will have to do iterations until 185186.

The same thing has been used in the program directly.

Program

File: pep40.py ------------------------- # http://radiusofcircle.blogspot.com # time module for calculating execution time import time # time at the start of program execution start = time.time() # variable to store the values a = '' # for loop for i in xrange(1, 185186): a += str(i) # d1 d1 = int(a[0]) # d10 d10 = int(a[9]) # d100 d100 = int(a[99]) # d1000 d1000 = int(a[999]) # d10000 d10000 = int(a[9999]) # d100000 d100000 = int(a[99999]) # d1000000 d1000000 = int(a[999999]) # printing the solution print d1*d10*d100*d1000*d10000*d100000*d1000000 # time at the end of program execution end = time.time() # total time for execution print end - start

Remember that the strings are indexed from 0 on wards.

As always you can download the source code from Github Gist pep40.py

This solution also satisfies PEP8 standard.

Output

Summary

I don't really have any big comments on this problem. But this problem demanded some homework and usage of basic mathematics to make it optimized and work faster. Performance wise I am satisfied and I have not tried optimizing the code. The code I have presented to you is the first draft. You can write a better code and share it with me, if possible.

As always if you have any doubt or didn't understand anything then you can comment in the comment box below, I will be glad to help you.

Please do comment if you have found any typo or have any better program or have a different program or have any suggestion. I will be glad to view each of them.

You can also contact me.

Thank you, have a nice day😃.

RADIUS OF CIRCLE

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