Project Euler solutions in Python 2 www.projecteuler.net/

• Done! 1/21/2013
• projecteuler.net/problem=1
• Implemented list comprehension in sum() to find the sum of the multiples of 3 and 5 up to 1000

• Done! 1/21/2013
• projecteuler.net/problem=2
• Implemented common Fibonacci series generator

• Done! 1/22/2013
• projecteuler.net/problem=3
• Made one function to check if an int is prime
• Another function to find prime factors of a given int
• OverflowError solved by using the square root of the given int as the end of the range

• Done! 7/13/2013
• projecteuler.net/problem=4
• Used integers as strings to determine if the product was a palindrome.
• Decided to make the program scalable also by using integeres as strings (concatenated char zeroes)

• Done! 7/13/2013
• projecteuler.net/problem=5
• Took optimization advice from StackOverflow

• Done! 7/13/2013
• projecteuler.net/problem=6
• Too easy.

• Done! 7/13/2013
• projecteuler.net/problem=7
• Simple stuff. Used the same function from problem 3
• Added a counter and a while loop to find the nth prime number

• Done! 7/13/2013
• projecteuler.net/problem=8
• Converted thousand digit number into string in order to create a list of its digits
• Then simply made another list of sublists of five consecutive numbers incrementally
• Used operator module tip from StackOverflow to return a list of the products of each sublist

• Done! 7/13/2013
• projecteuler.net/problem=9
• Tried multiples of 3, 4, and 5; unsuccessful
• Resorted to Pythagorean Triples construct:
• Where n and m are any two positive integers (m < n):
• 
• 
• 

• Done! 7/13/2013
• projecteuler.net/problem=10
• Used same fuctions from problem 3 and 7
• In is_prime(), I made the end of the range the square root of the given int to drastically speed up the program
• Earned 'Decathlete' award: completed 10 consecutive problems

• Done! 7/14/2013
• projecteuler.net/problem=11
• Turned in string into grid of integers
• Grouped factors into sublists of horizontal, vertical, diagonal left and right
• Changed range limits to fix index issues

• Done! 7/16/2013
• projecteuler.net/problem=12
• Need to optimize
• get_number_of_factors() is problematic
• Fixed! 7/16/2013
• Optimized by using xrange() instead of range() to reduce resource usage
• get_number_of_factors() refactored with advice from codereview.stackexchange.com

• Done! 7/19/2013
• projecteuler.net/problem=13
• Took a while to figure out what the problem was asking
• Fairly straight forward after figured that out
• Used list comprehension to get sum of the 50-digit numbers and printed the first ten digits

• Done! 7/20/2013
• projecteuler.net/problem=14
• Used a for loop to iterate the starting numbers and a while loop to find/count the chain
• Had an 'Off-by-one' error when counting the chain

• Done! 7/21/2013
• projecteuler.net/problem=15
• Used a horrific brute force method at first
• Problem most likely lies in the random generator of the next move
• With many, many trials and lots of brainstorming, I concluded that the total number of moves is equal to twice the size of the grid (20 Right, 20 Down)
• Left script running overnight and still no result
• After a bit of research in combinations and permutations, I found a formula for the total number of non-repeating combinations:
• Binomial Coefficient (where n is the number of things to choose from, and you choose r of them and repetition and order don't matter)
• 
• Combinations and Permutations
• Implentation of formula and refactoring produced immensely faster results:
• Brute force method: inconclusive (runtime > 10 hours)
• Binomial Coefficient: 0.002 seconds

• Done! 7/17/2013
• projecteuler.net/problem=16
• Another one-liner

• Done! 7/17/2013
• projecteuler.net/problem=17
• Could be done better. Mostly hardcoded.
• Used a dictionary to store number words
• Used similar concept from problem 16

• Done! 7/31/2013
• projecteuler.net/problem=18
• Tried altering the algorithm from problem 17, but was inconclusive
• Tried a simpler approach. Start from the bottom and add the numbers upwards to ensure the highest possible sum
• Issue with comparing sums: iteration goes out of bounds
• [Fixed!] Made a seperate function, largest_sum(), to simplify things
• Got rid of the useless row size counter. Only made it more complicated.
• Used the same concepts in C++ solution

• Done! 8/3/2013
• projecteuler.net/problem=19
• In C++ [Incomplete], stuck in infinite recursion
• Counter did not increment in recursion. Used pass-by-reference to fix
• In Python, tried a completely different approach. Still used same isLeapYear() function
• Seems more efficent, however it produces the wrong final answer.
• Off-by-one error somewhere
• [Temp fix] Started counter at 1

• Done! 7/18/2013
• projecteuler.net/problem=20
• Pretty much straight forward
• Used the factorial formula given in problem description: n! = n * (n - 1)
• Turned the factorial into a string to get the sum of digits

• Done! 8/2/2013
• projecteuler.net/problem=21
• Completed Level 1!
• Used a dictionary to store number[key] and sum of divisors[value]
• Reduced to list comprehensions
• Applying similar concepts to C++ solution, but is difficult to replace dictionaries
• Getting float-value error

• Done! 8/4/2013
• projecteuler.net/problem=22
• Fairly straight forward
• Used list comprehensions, enumerate(), and, the recently learned, replace()

• Incomplete 8/4/2013
• projecteuler.net/problem=23
• Need to optimize isAbundant(); does not complete in a reasonable amount of time
• After some research, I've learned about generators to get factors of an int
• 8/5/2013 When run, outputs "KILLED"

• Done! 7/18/2013
• projecteuler.net/problem=25
• Used the same fibonacci series generator from problem 2 with slight refactorization

• Done! 8/11/2013
• Took forever to figure out
• After some research, I found and implemented Fermat's little theorem
• Off by one error somehow. Kludged it for now

• Done! 8/15/2013
• projecteuler.net/problem=28
• Made a generator for the spiral
• The numbers added were only the corners; not including 1
• 1st round skipped 1 number, 2nd round skipped 3, and so forth

• Done! 7/24/2013
• projecteuler.net/problem=29
• Completed in both Python and C++. Was a lot easier to code in Python
• Implemented recently learned concept of vectors (still not confident with them yet)

• Done! 8/15/2013
• projecteuler.net/problem=30
• Completed in C++
• Found upper bound and number of digits by multiplying 9 to the nth (i.e. 9^4 is the max of one digit)

• Done! 10/12/2013
• projecteuler.net/problem=34
• Completed in Java
• Fairly straight forward
• Could have hardcoded the factorials (digits only 0...9) but used a simple function instead
• Classic off-by-one error in factsum()

• Done! 10/13/2013
• projecteuler.net/problem=35
• Completed in Java
• Used strings to rotate numbers

• Done! 1/13/2016
• projecteuler.net/problem=35
• Straight forward. Just applied Pythagorean theorem.

• Done! 1/9/2016
• projecteuler.net/problem=35
• Very easy. Don't know why I didn't complete it earlier
• Created string of the irrational and multiplied indices requested
• Used reduce() and list comprehensions. Not very readable though

• Done! 10/16/2013
• projecteuler.net/problem=42
• Completed in Java
• Learned more Java string methods e.g. contains()
• Created a list of the triangle numbers
• Calculated word value using a string and letter index values

• Done! 7/24/2013
• Used a brute force method
• Fairly easy, however, limiting the range to the sqrt of num doesn't print the correct answer
• Could use a lot of optimization: runtime > 1500 seconds

• Done! 7/23/2013
• Another easy one
• Could have done a one-liner but opted for readability instead

• Done! 1/3/2016
• Used a similar strategy as problem 18, but didn't store each path as arrays. Instead, I started with the largest number, added the largest adjacent number, and so on until reaching the top of the triangle.