python - 2 lists, and finding maximum product from 2 lists

Question

I have two lists made of numbers(integers); both have 2 million unique elements.

I want to find number a from list 1 and b from list 2, that -

1)a*b should be maximized.
2)a*b has to be smaller than certain limit.

here's what I came up with:

maxpq = 0
nums = sorted(nums, reverse=True)
nums2 = sorted(nums2, reverse=True)
for p in nums:
    n = p*dropwhile(lambda q: p*q>sqr, nums2).next()
    if n>maxpq:
        maxpq=n
print maxpq

any suggestions? edit : my method is too slow. It would take more than one day.

Answer 1

Here's a linear-time solution (after sorting):

def maximize(a, b, lim):
    a.sort(reverse=True)
    b.sort()
    found = False
    best = 0
    j = 0
    for i in xrange(len(a)):
        while j < len(b) and a[i] * b[j] < lim:
            found = True
            if a[i]*b[j] > best:
                best, n1, n2 = a[i] * b[j], a[i], b[j]
            j += 1
    return found and (best, n1, n2)

Simply put:

• start from the highest and lowest from each list
• while their product is less than the target, advance the small-item
• once the product becomes bigger than your goal, advance the big-item until it goes below again

This way, you're guaranteed to go through each list only once. It'll return False if it couldn't find anything small enough, otherwise it'll return the product and the pair that produced it.

Sample output:

a = [2, 5, 4, 3, 6]
b = [8, 1, 5, 4]
maximize(a, b, 2)   # False
maximize(a, b, 3)   # (2, 2, 1)
maximize(a, b, 10)  # (8, 2, 4)
maximize(a, b, 100) # (48, 6, 8)