#!/usr/bin/env python
'''
Created on 10 feb. 2012

@author: Julien Lengrand-Lambert

DESCRIPTION: Solves problem 49 of Project Euler
The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways:
(i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.

There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property,
but there is one other 4-digit increasing sequence.

What 12-digit number do you form by concatenating the three terms in this sequence?
'''
import pickle
import itertools

# list of primes up to one million.
plist = pickle.load(open("primes_list.dup", "rb"))

def fourLengthPrime():
    """
    Returns the list of all prime numbers of length 4
    """
    return[val for val in plist if len(str(val)) == 4]

def isPrime(val):
    """
    Returns True if the number is prime
    """
    return (val in plist)

def all_permutations(seq):
    """permutate a sequence and return a list of the permutations"""
    if not seq:
        return [seq]  # is an empty sequence
    else:
        temp = []
        for k in range(len(seq)):
            part = seq[:k] + seq[k+1:]
            for m in all_permutations(part):
                temp.append(seq[k:k+1] + m)
        return temp

def getPrimesPermutations(primes, length):
    """
    Returns all the lists of primes that are permutations from one another,
    of size 3 and that make an arithmetic suite.
    """
    res = []
    idx = 0
    for prime in primes :
        idx += 1
        print "%d / %d" % (idx, len(primes))
        perms = findPrimePerms(prime)

        # gets all length 3 prime combinations
        els = None
        if perms > 2:
            els = [list(x) for x in itertools.combinations(perms, 3)]

        if els != None:
            for primeList in els:
                if isArithmetic(primeList):
                    res.append(primeList)
    return res # removes duplicates

def isArithmetic(aList):
    """
    Returns true if the list is arithmetic.
    Elements of the list are expected to be numbers.
    """
    diffs = [a - b for a, b in zip(aList[1:], aList[:-1])]
    res = list(set(diffs)) # removes duplicates
    return (len(res) == 1)

def findPrimePerms(prime):
    """
    Returns all the list of primes that are permutations from prime
    """
    perms = [int(val) for val in all_permutations(str(prime)) if (isPrime(int(val)) and len(str(int(val))) == 4)]
    res = list(set(perms)) # removes duplicates
    if len(res) > 2:
        return res

if __name__ == '__main__':
    primes = fourLengthPrime()
    print getPrimesPermutations(primes, 3)
    #print "Answer : %d " % (last_ten())