Scope 列表中的 Python - Project Euler 007

Question

first question here. I am trying to learn python by stepping through project euler, and I've run into a roadblock. The following method (returns a list of prime factors) works fine for a single call:

def findPrimeFactors(num, primeFactors = []):
    '''Find the prime factors of an arbitrary positive integer

        input: num to factorize
        returns: a list containing the prime factors of the number
    '''
    pIndex = 2

    while (num >= pIndex):
        if num % pIndex == 0:
            num /= pIndex
            primeFactors.append(pIndex)
            return FindPrimes.findPrimeFactors(num, primeFactors)

        else:
            pIndex += 1

    return primeFactors

However when I use it in a loop, like so (this method may not be complete yet, currently results in infinite loop since more primes cannot be found):

def countPrimes(n = 1001):
    '''find n amount of unique primes ascending

        input: number of primes to find
        returns: list of n primes starting from 2   '''

    primes = []
    i = 2

    while len(primes) < n:
        primeFactors = FindPrimes.findPrimeFactors(i)
        print(primeFactors) #verify method behavior

        if len(primeFactors) is 1:
            primes.append(primeFactors[0])   
        i += 1

    return primes

The result is that the first loop returns [2], the next returns [2, 3], and so on, appending the new results to the list that I Wanted to have been empty on the first recursive call. It seems that my list is persisting, but I'm not sure exactly why? I read Python Class scope & lists as well which gives me some clues but the recursion complicates it more.

Recursive also means I cannot simply assign an empty set to it either. Coming from a C++ background, my expectation was that the primeFactors variable should be reinitialized each time the function is called from my program. Still a baby snake here.

EDIT: This is the iterative version of findPrimeFactors I wrote. I know it is not optimal - but I would like to at least make it efficient enough to meet Project Euler's 1 minute rule. Any suggestions for improvement or clarity are appreciated.

PRIMES = [2,3,5,7,11,13,17,19]
import math

class FindPrimes():

    '''V2 iterative'''
    def findPrimeFactors(n, primeFactors = None):
        '''Find the prime factors of an arbitrary positive integer

            input: num to factorize
            returns: a list containing the prime factors of the number
        '''

        if primeFactors is None:
            primeFactors = []

        num = n
        ceil = math.sqrt(n) #currently unused

        global PRIMES
        knownPrimes = PRIMES

        #check known primes for divisors first, then continue searching for primes by brute force
        while True:

            factorFound = False
            for prime in knownPrimes:   

                if num % prime == 0:
                    primeFactors.append(prime)
                    num /= prime
                    factorFound = True
                    break       #ensure that the list returned has ascending primes

            if not factorFound:
                break

        #once attempts have been made to reduce using known primes
        #search for new primes if the number is not fully reduced

        i = knownPrimes[-1] + 2

        while num != 1:

            if num % i == 0:
                knownPrimes.append(i)
                primeFactors.append(i)
                num /= i

            i += 2          

        return primeFactors


    def countPrimes(n = 10001):
        '''find n amount of unique primes ascending

            input: number of primes to find
            returns: list of n primes starting from 2   '''

        primes = []
        i = 2

        while len(primes) < n:

            primeFactors = FindPrimes.findPrimeFactors(i)

            if len(primeFactors) == 1:
                primes.append(primeFactors[0])
                #print(primeFactors[-1])

            i += 1

        print(len(primes))
        return primes

nth = 10001
print(FindPrimes.countPrimes(nth)[nth-1])   #print the largest prime found

Answer 1

See "Least Astonishment" and the Mutable Default Argument

Answer 2

The default value of primeFactors is being shared between calls, so when you change it, it stays changed for future calls.

Example:

def foo(bar = []):
    bar.append(1)
    return bar

print foo()
print foo()

Output:

[1]
[1, 1]

You should return a new list instead of changing the default:

def foo(bar = []):
    return bar + [1]

print foo()
print foo()

Output:

[1]
[1]

Answer 3

As mentioned by hammar, the default value is only created once, when the function is defined, and shared between calls.

The usual way around that is to use a marker value as the default:

def findPrimeFactors(num, primeFactors=None):
    if primeFactors is None:
        primeFactors = []
    ...

Off-topic, but your function findPrimeFactor() will recurse once for every prime factor found. Python doesn't do tail call removal, so you should probably rewrite this using iteration instead of recursion.