Question

I am working on Project Euler problem 5 and am using the following:

def findLCM(k):
start=time.time()
primes=[2,3,5,7,11,13,17,19,23]
factors=[]
for factor in range(2,k):
    if factor in primes:
        factors.append(factor)
    else:
        factorization=[]
        while factor!=1:
            for prime in primes:
                lastFactor=prime
                if factor%prime==0:
                    factor/=prime
                    factorization.append(lastFactor)
                    break
        tmpFactors=[]
        for tmpFactor in factorization:
            if tmpFactor not in factors:
                factors.append(tmpFactor)
            else:
                tmpFactors.append(tmpFactor)
                factors.remove(tmpFactor)
        for tmpFactor in tmpFactors:
            factors.append(tmpFactor)
        print factors
product=1
for factor in factors:
    product*=factor
factors.sort()
end=time.time()
fnTime=end-start
return product, fnTime, factors

Is there a Python function with which I can combine factorization and factors like this function does? For example, if factors=[2, 3, 5] and factorization=[2, 2, 3], the combined list should be [2, 2, 3, 5].

Answer 1

The terminology is “union of multisets“.

It is implemented in Python using collections.Counter:

>>> from collections import Counter
>>> combined = Counter([2, 3, 5]) | Counter([2, 2, 3])
>>> list(combined.elements())
[2, 2, 3, 5]