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98 lines
2.9 KiB
Python
98 lines
2.9 KiB
Python
#!/usr/bin/env python
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'''
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Created on 10 feb. 2012
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@author: Julien Lengrand-Lambert
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DESCRIPTION: Solves problem 49 of Project Euler
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The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways:
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(i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
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There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property,
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but there is one other 4-digit increasing sequence.
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What 12-digit number do you form by concatenating the three terms in this sequence?
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'''
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import pickle
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import itertools
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# list of primes up to one million.
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plist = pickle.load(open("primes_list.dup", "rb"))
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def fourLengthPrime():
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"""
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Returns the list of all prime numbers of length 4
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"""
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return[val for val in plist if len(str(val)) == 4]
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def isPrime(val):
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"""
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Returns True if the number is prime
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"""
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return (val in plist)
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def all_permutations(seq):
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"""permutate a sequence and return a list of the permutations"""
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if not seq:
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return [seq] # is an empty sequence
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else:
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temp = []
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for k in range(len(seq)):
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part = seq[:k] + seq[k+1:]
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for m in all_permutations(part):
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temp.append(seq[k:k+1] + m)
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return temp
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def getPrimesPermutations(primes, length):
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"""
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Returns all the lists of primes that are permutations from one another,
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of size 3 and that make an arithmetic suite.
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"""
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res = []
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idx = 0
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for prime in primes :
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idx += 1
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print "%d / %d" % (idx, len(primes))
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perms = findPrimePerms(prime)
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# gets all length 3 prime combinations
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els = None
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if perms > 2:
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els = [list(x) for x in itertools.combinations(perms, 3)]
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if els != None:
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for primeList in els:
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if isArithmetic(primeList):
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res.append(primeList)
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return res # removes duplicates
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def isArithmetic(aList):
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"""
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Returns true if the list is arithmetic.
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Elements of the list are expected to be numbers.
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"""
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diffs = [a - b for a, b in zip(aList[1:], aList[:-1])]
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res = list(set(diffs)) # removes duplicates
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return (len(res) == 1)
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def findPrimePerms(prime):
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"""
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Returns all the list of primes that are permutations from prime
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"""
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perms = [int(val) for val in all_permutations(str(prime)) if (isPrime(int(val)) and len(str(int(val))) == 4)]
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res = list(set(perms)) # removes duplicates
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if len(res) > 2:
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return res
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if __name__ == '__main__':
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primes = fourLengthPrime()
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print getPrimesPermutations(primes, 3)
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#itertools.combinations(lst, i)]
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#getPrimesPermutations(primes, 3)
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# try:
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# while primes.next():
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# print primes.next()
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# except StopIteration:
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# print "Reached end of list"
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#print "Answer : %d " % (last_ten()) |