# Python set based solution to Subset Sum

Working on the 2 element subset sum problem (finding two numbers in a list that sum to a given value), I came up with a relatively short solution code-wise.

The code could fit on a single line but I'm not super familiar with python so is this is a naive way to solve/implement it?

How efficient is creating a set and intersecting it with a list vs using a loop?

l = [10, 7, 11, 3, 5, 11]
k = 22

#create a set of the differences between K and L including duplicate elements that sum to K
diff = {k-x for i, x in enumerate(l) if k != 2*x or x in l[i+1:len(l)]}

#Return true if an element of Diff is in L
print(bool(diff.intersection(l)))


Usually Python is not terribly fast when it comes to "hand-written" loops. So my prediction (also supported by some preliminary profiling using timeit, see below) would be that a "hand-written" loop is slower than the C loop used in the implementation of set.intersection. The effect should/will become more significant for larger lists.

A quick non-performance related note: you can substitute l[i+1:len(l)] by l[i+1:]. This is because the end of a slice defaults to the end of the sequence.

import timeit

SETUP = """
l = [10, 7, 11, 3, 5, 11]
k = 22

diff = {k-x for i, x in enumerate(l) if k != 2*x or x in l[i+1:]}
"""
print(
sum(timeit.repeat("bool(diff.intersection(l))", setup=SETUP,
repeat=10, number=100000)) / 10
)
print(
sum(timeit.repeat("bool([i for i in l if i in diff])", setup=SETUP,
repeat=10, number=100000)) / 10
)

#create a set of the differences between K and L including duplicate elements that sum to K
diff = {k-x for i, x in enumerate(l) if k != 2*x or x in l[i+1:len(l)]}


The slice can be simplified:

diff = {k-x for i, x in enumerate(l) if k != 2*x or x in l[i+1:]}


In my opinion, the or x in l[i+1:] is a bit too tricky to use without further explanation. My immediate reaction on seeing it was that it undermined the whole point of using a set by creating a quadratic worst case. On further reflection I see that (assuming Python is sensibly implemented, which I think is a safe assumption here) it doesn't, but it's better to preempt the doubt with a comment.

Alternatively, handle the special case separately by checking whether k is even and if so counting instances of k // 2.

As an optimisation, you can keep only the half of each pair in diff:

diff = {k-x for x in l if 2*x < k}


#Return true if an element of Diff is in L
print(bool(diff.intersection(l)))


This is a bit cryptic. I think it might be more pythonic to use any:

print(any(x in l if x in diff))


That's also potentially faster, because it can abort on finding the first solution.

• i is used in the second condition in the original set construction so it cannot be dropped so easily at this stage in the optimization. – AlexV May 4 '19 at 14:29
• @AlexV, oops. Thanks. – Peter Taylor May 4 '19 at 17:14