Euler Fourteen MLC | Python Fiddle

# -*- coding: utf-8 -*-
"""
Created on Sun Apr 07 01:10:52 2013

@author: Matthew Cordrey
"""
#The following iterative sequence is defined for the set of positive integers:
    #n > n/2 (n is even)
    #n > 3n + 1 (n is odd)
#Using the rule above and starting with 13, we generate the following sequence:
#13  40  20  10  5  16  8  4  2  1
#It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms.
#Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1
#Which starting number, under one million, produces the longest chain?
#NOTE: Once the chain starts the terms are allowed to go above one million.

def collatz(x):
    terms = 1
    termsList = [x]
    while x > 1:    
        if x % 2: x = 3*x+1
        else: x = x/2
        termsList.append(x)
        terms += 1
    return terms

chains = {}    
for i in range(1000001): chains[i] = collatz(i)     
analysis = sorted(chains.items(), key=lambda k: k[1], reverse=True)
print "\nThe Winner >>>>> Start Number: ",analysis[0][0], " | Chain Length: ",analysis[0][1]

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