## Merging sorted lists

Recently I was asked to sketch out a function that combines two sorted lists into a single (sorted) list. It’s a fun question with a couple of different answers, potentially all of them correct but with different pros and cons. There are two basic and one-line solutions that come from the Python standard library, so we’ll tackle those first.

## Just sort it

Python’s sorting algorithm, Timsort [1], is pretty amazing. It’s stable (part of its mergesort heritage) and is designed to deal particularly well with partially sorted data. Which is exactly what we’ve been given: two runs that need to be merged. In fact, what we’ve been tasked with is the merge step of mergesort. So solution #1 is as simple as:

```def combine_sorted(left, right):
return sorted(left + right)
```

This is easy to understand and obviously correct (we can’t really mess up sorting), as well as very succinct. However, it has a significant memory requirement as it copies both lists into a new one. Also, isn’t sorting going to get really slow with large lists? (spoiler: no it won’t, it’ll scale almost linearly.)

## Merge them like heaps

Heaps are great! Also, sorted lists are heaps and Python has a wonderful module for dealing with heaps. In particular here we’re interested in the heapq.merge function. This takes any number of iterables and returns an iterator over the sorted output:

```from heapq import merge

def combine_sorted(left, right):
return merge(left, right)
```

This solution is again easy to comprehend, and with some knowledge of the documentation and knowing we are using the function within its contract, it’s obviously correct. As a bonus we can combine infinitely long iterators without expending any additional memory beyond a small constant. If …