Project Euler Problem 28 diagonals

root@www ~]# python twentyeight.py
669171001
Started at: Wed Oct 8 22:40:25 2008 Ended at: Wed Oct 8 22:40:25 2008
[root@www ~]# cat twentyeight.py
# -*- coding: utf-8 -*-
"""
<+ MODULE_NAME +>
Project Euler Problem Set
<+ DESCRIPTION +>
Solutions in Python to the problems at http://projecteuler.net

Licensed under the Creative Commons license; see http://creativecommons.org for more details. In short, this means you can freely reuse, modify and distribute this program, also commercially, for as long you provide a proper attribution.

Copyright by Jonathan Mark, jonathanmark.com/aristede.com, jmark@aristede.com

>>> print 881 + 1
882

"""
import time
starttime = time.asctime()


def listOddSquare(N):
"""
Returns list of odd squares for the first N odd numbers starting
at 3

>>> sum(listOddSquare(2))
34

>>> sum(listOddSquare(1))
9

"""

x = range(1,(N +1) * 2)
oddSquare = map(lambda x: x * x, x)
oddSquare = filter(lambda x: x % 2 == 1, oddSquare)
oddSquare = oddSquare[1:]
return oddSquare

def listEvenSquarePlusOne(N):
"""
Returns list of square-plus-one for the first N even numbers starting
at 2.

>>> sum(listEvenSquarePlusOne(2))
22

>>> sum(listEvenSquarePlusOne(1))
5

"""
evenSquarePlusOne = filter(lambda x: x % 2 == 0, range(1,(N + 1) * 2 ))
evenSquarePlusOne = map(lambda x: x*x + 1, evenSquarePlusOne)
return evenSquarePlusOne

def listUpperLeft(N):
"""
for returning average of listOddSquare and listEvenSquarePlusOne

>>> upperLeft(2)
28

>>> upperLeft(1)
7

"""


return listOddSquare(N) + listEvenSquarePlusOne(N)

def upperLeft(N):
return sum(listUpperLeft(N))/2

def listLowerRight(N):
"""Returns n-th element of listEvenSquarePlusOne minus n

>>> sum(listLowerRight(2))
16

>>> sum(listLowerRight(1))
3

"""
return [listEvenSquarePlusOne(N)[i] - (2*(i + 1) ) for i in range(N)]

def total(N):
"""Return sum of diagonals except that center is only counted once

>>> total(2)
101


"""

return sum(listEvenSquarePlusOne(N) + listOddSquare(N) + listLowerRight(N)) + upperLeft(N) + 1

print total(500)

print "Started at: ", starttime, " Ended at: ",time.asctime()

if __name__ == "__main__":
import doctest
doctest.testmod()
[root@www ~]#