Minimum Swaps to Group All 1's Together II

Minimum Swaps to Group All 1's Together II

What is this problem about?

The Minimum Swaps to Group All 1's Together II problem extends the classic grouping problem to a circular binary array. The 1s can wrap around — a valid group can span the end and beginning of the array. Your goal is still to find the minimum swaps needed to gather all 1s into a contiguous circular segment. This Minimum Swaps to Group All 1's Together II interview question tests circular sliding window implementation.

Why is this asked in interviews?

Companies like Arcesium, Microsoft, Amazon, TikTok, IBM, Google, and Bloomberg ask this to verify that candidates can extend a known linear algorithm to circular constraints. Handling circularity — where the window can wrap around the end of the array — tests implementation precision. The array and sliding window interview pattern applies with the added circular dimension.

Algorithmic pattern used

Circular sliding window with modular indexing. Count total 1s (call it k) to define the window size. Instead of treating the array linearly, imagine it doubled (or use index % n). Slide a window of size k using i % n for index access. Maintain the count of 0s (or 1s) in the current window using an add/remove step at each slide. Track the minimum zero-count. This avoids the need to physically double the array.

Example explanation

Array: [1, 1, 0, 0, 1]. Total 1s = 3. Window size = 3.

• Window starting at 0: [1,1,0] → zeros = 1.
• Window at 1: [1,0,0] → zeros = 2.
• Window at 2: [0,0,1] → zeros = 2.
• Window at 3 (wrapping): [0,1,1] → zeros = 1.
• Window at 4 (wrapping): [1,1,1] → zeros = 0. Minimum swaps = 0 (already a valid circular group).

Common mistakes candidates make

• Not using modular arithmetic, causing index-out-of-bounds errors.
• Physically doubling the array (works but wasteful; modulo is preferred).
• Forgetting the wrap-around window positions entirely.
• Using the wrong window size (should equal count of 1s, not array length).

Interview preparation tip

For circular arrays, always decide early: double the array (simple but O(2n) space) or use modular indexing (O(n) space, slightly more complex). For interviews, demonstrating modular indexing shows stronger algorithmic awareness. After mastering this problem, generalize: any sliding window problem on a circular array uses the same i % n trick. Practice this technique on other circular problems like circular buffer management and ring-road scheduling.