ProjEuler - Python Base

#!/usr/bin/python
#====================================================================
# Project Euler Base File - for those who want to try
#
# By Charc
#
# Projects can be found at: https://projecteuler.net/problems
# Some of the projects have also been provided with Titles
# and Project aims.
# This porgram accepts an input for which project you would like to
# check the solution for.
# A link with solutions is also provided in the comments below.
# With Problem 0 (unofficial & my own) solved to give an example.
# For convinience's sake, please don't run with -OO
#====================================================================

#=======SOLUTIONS - BEWARE===========================================
# Proj 0: 145;
# http://www.tsm-resources.com/alists/trip.html
# Ctrl-F if you don't believe me.
# Proj >0:
# https://code.google.com/p/projecteuler-solutions/wiki/ProjectEulerSolutions
#====================================================================


#====================================================================
#   Valid Input
#   TODO make the valid input block more pretty
#====================================================================
import sys

if len(sys.argv) > 2:
    print "Try again with a whole number."
    sys.exit(-1)
try:
    n = int(sys.argv[1])
except IndexError:
    n = 0
except ValueError:
    print "Try again with a whole number."
    sys.exit(-1)

print "You have chosen question {0}.".format(n)

#====================================================================
#   General solutions for the problems defined as functions
#====================================================================
import math as m

def prob0(x):
    """Given the right angle with a sidelength 12, the largest
hypotenuse part of an integer pythagorean triple is 37.
Given a sidelength of 24, what's the largest value for the
hypotenuse part of an integer pythagorean triangle?"""
    # Exactly as asked -- We want the largest int Hyp given
    # one length is x -- can be shown this is only the case
    # for primitive triangles TODO find proof of this?

    # There is an m, n formula by Euclid
    # A = a^2 - b^2, B = 2ab, C = a^2 + b^2
    # a!=b (mod 2) and gcd(a, b)=1 gives all primitive triangles
    # We can simply work out all such solutions and take max
    # by defn of A, a > b
    ans = 0
    if x % 2 == 0:
    # So x is the even side, i.e. B
    # a > b --> sqrt(B/2) > b
        for b in range(1, int((m.sqrt(x/2)))+1):
            if x/2 % b == 0:
                ans = max(ans, (x/(2*b))**2 + b*b)
        return ans
    else:
    # x is on the odd side, i.e. A
    # now (a-b)(a+b) = A, so:
        for i in range(1, int(m.sqrt(n))):
            if n%i == 0:
                p = (i + n/i)/2
                q = n/i -p
                ans = max(ans, p*p + q*q)
    return ans


def prob1(x):
    """If we list all the natural numbers below 10 that are multiples of
3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000."""
    return x


def prob2(x):
    """Each new term in the Fibonacci sequence is generated by
adding the previous two terms. By starting with 1 and 2, the first
10 terms will be:
             1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do
not exceed four million, find the sum of the even-valued terms."""
    return x


def prob3(x):
    """The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?"""
    return x


def prob4(x):
    """A palindromic number reads the same both ways. The largest
palindrome made from the product of two 2-digit numbers is
9009 = 91 * 99.
Find the largest palindrome made from the product of two 3-digit
numbers."""
    return x
#====================================================================
#   Printing questions and answers
#====================================================================
t = "Problem number {0}?!".format(n)
q = "Sorry, I haven't done that one.\nYet!"
z = "going to be ready soon!\nhttps://projecteuler.net/problem={0}".format(n)

if n == 0:
    t = "Largest hypotenuse"
    q = prob0.__doc__
    z = prob0(24)
elif n == 1:
    t = "Multiples of 3 and 5"
    q = prob1.__doc__
    z = prob1(1000)
elif n == 2:
    t = "Even Fibonacci numbers"
    q = prob2.__doc__
    z = prob2(4000000)
elif n == 3:
    t = "Largest prime factor"
    q = prob3.__doc__
    z = prob3(600851475143)
elif n == 4:
    t = "Largest palindrome product"
    q = prob4.__doc__
    z = prob4(3)
print "\n{ti}\n\n{qu}\n\nMy solution is {ans}.".format(ti=t, qu=q, ans = z)