使用Map-Reduce时Python中的惰性布尔评估

Question

I will use my example: I want to create a list of primes using the sieve of Eratosthenes. For each number, I check if it is composite, and if not, I append it to the list.

• Using "standard" programming:

   primes = [2] start = time.time() for i in xrange(3,primeRange,2): isPrime = True for p in primes: if(i % p == 0): isPrime = False break; if(isPrime): primes.append(i) print "Using C++-style: ", time.time() - start, " seconds" 

• Using reduce function:

   start = time.time() for i in xrange(3,primeRange,2): if(reduce(lambda x,y:x and y,[i % p != 0 for p in primes])): primes.append(i) print "Using map-reduce: ", time.time() - start, " seconds" 

The results for primeRange = 100000 :

Using map-reduce:  54.1150000095  seconds
Using C++-style:  4.62000012398  seconds

The 2nd case makes the code more compact, but the condition will be evaluated for the entire list and then reduced to True / False . Is there a way to avoid that?

Answer 1

You could use all with a generator expression:

if all(i % p != 0 for p in primes)

The generator expression will lazily evaluate one term at a time, and all will return early if it hits a value that doesn't satisfy the condition.

Answer 2

yes, you should do two things.

First, if you want to avoid fully evaluating a list comprehension, don't use a list comprehension, use a generator expression:

... [i % p != 0 for p in primes] ...

should be

... (i % p != 0 for p in primes) ...

second, reduce() doesn't understand that lambda x,y:x and y can fail, and there's no way to teach it that. But that doesn't matter, because python has a builtin function for exactly the fold over the conjunction monoid, all() , so the if should be

if all(i % p != 0 for p in primes):

Answer 3

Use generator,

def prime_iter(sz):
    '''
    Iterate through all the prime number in range [2,sz]
    '''
    bucket = [0]*sz
    for i in range(2,sz):
        if bucket[i]:
            continue
        for j in range(i+i,sz,i):
            bucket[j] = i
        yield i

# get all the primes from 2 to 100.
primes = list(prime_iter(100))