In-Place or Not? Classifying Python List Reversal: O(1) Space, Auxiliary Buffers, and Stack Use

Learn why a buffer-based Python list reversal isn't in-place or O(1) space, then see strict in-place alternatives and how auxiliary structures affect space.

When we talk about space complexity and “in-place” behavior, the lines often blur once dynamic arrays, stack frames, and intermediate structures enter the picture. A tiny snippet that looks innocuous can trigger a surprisingly nuanced discussion. Consider a function that drains a list into another and then moves everything back. Is it in-place? Is it O(1) space? Or does the temporary list change the classification entirely?

Problem setup

Here’s a minimal function that reverses a list by popping into a secondary list and then restores it by popping back. It ends up where it started but allocates an extra list along the way.

def flip_twice(seq):
    buf = []
    while seq:
        buf.append(seq.pop())
    while buf:
        seq.append(buf.pop())

The immediate intuition might be that because the total number of elements stays constant and at any moment len(seq) + len(buf) equals the original size, the extra memory is somehow “constant.” But the classification hinges on how memory is actually used, not just conserved in aggregate.

What the definitions actually say

There are three relevant lenses to look through. An algorithm is called in-place if it uses only a fixed amount of additional memory (auxiliary space) and transforms its input where it resides. A stricter notion—strict in-place—excludes any implicit extra memory, such as stack growth from recursion or generator chains. Finally, space O(1) means the auxiliary memory required does not scale with input size, even if that memory moves around during the computation. These are well-defined terms, though in practice people sometimes disagree about which flavors of space—auxiliary arrays versus call stack—should be counted. That disagreement is exactly why being explicit about definitions matters.

Why the example is not in-place and not O(1)

The function above allocates a new list and fills it with as many elements as are in the original. Even though the source list shrinks as the buffer grows, you are not explicitly reusing the same storage; you are allocating additional space to hold the elements in the temporary list. As the input gets bigger, so does the temporary structure. That makes the auxiliary space scale with input size. By the definitions, it is not in-place, it is not strict in-place, and it is not O(1) space.

It is also worth noting that during execution the original list is drained and rebuilt, so all the data effectively leaves the input container before being written back. That reinforces the point that the work is not performed in-place. Discussions sometimes get tangled in implementation details of dynamic arrays, memory contiguity, or how append behaves; those considerations do not change the classification here. Some developers also debate whether append() should be counted as O(1), which further complicates time analysis—but the space argument stands on its own.

A truly in-place alternative

You can achieve the same observable mid-execution state—list reversed halfway through—without allocating a second list. The following version swaps symmetric elements in-place, then does it again, leaving the list as it started.

def spin_twice(items):
    for k in range(len(items) // 2):
        items[k], items[-k - 1] = items[-k - 1], items[k]
    for k in range(len(items) // 2):
        items[k], items[-k - 1] = items[-k - 1], items[k]

This approach operates entirely within the original storage. It is in-place because all changes happen where the data lives. It is strict in-place because there is no recursion or other implicit stack growth. And it uses O(1) auxiliary space because the amount of extra memory needed does not depend on input size; the iteration machinery itself is bounded. If you print the temporary state halfway through the first pass and compare it to the earlier buffer-based function halfway through its first phase, you will observe the same reversed order.

A non-strict in-place variant

If you express the same swap logic recursively, you keep the in-place property but lose strictness due to growing call depth. Depending on the exact definition used, stack space may or may not be counted toward O(1); either way, the recursion depth clearly scales with input size.

def spin_twice_rec(items, idx = 0):
    items[idx], items[-idx - 1] = items[-idx - 1], items[idx]
    if idx < len(items) // 2:
        spin_twice_rec(items, idx + 1)
    items[idx], items[-idx - 1] = items[-idx - 1], items[idx]

This remains in-place because it modifies the list directly without allocating auxiliary containers. It is no longer strict in-place because recursion introduces implicit stack growth as the input grows. Whether one labels this O(1) in space depends on whether stack frames are included in the accounting; one reasonable stance is that it is not O(1).

Why the distinction matters

Space complexity calls often get muddled by implementation details or informal language like “only one extra list.” Clear, shared definitions let you evaluate code without guessing. If you need to justify a design decision, review algorithmic guarantees, or audit memory usage, the difference between allocating a temporary buffer and swapping in-place is material. Moreover, people sometimes claim O(1) space for patterns that do allocate extra memory, likely by focusing on conservation of elements rather than the mechanics of where those elements live during execution. When you pin the discussion to auxiliary space, implicit stack, and in-place transformation, the classification becomes straightforward.

Takeaways

Classify space by stating what you count. If your definition includes auxiliary data structures and implicit stack frames, the buffer-based approach is neither in-place nor O(1), while the iterative swap version is strict in-place and O(1). If you choose a definition that excludes stack space, the recursive swap may still be called in-place but would not be strict. If you need to convince yourself about mid-execution states, instrument both variants to print halfway through and compare the observable list ordering. Most importantly, agree on definitions up front to avoid talking past each other.