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 its predecessor to a circular binary array. The same goal applies — group all 1s into a contiguous segment — but now the array wraps around, so a valid segment can span the end and beginning of the array. This Minimum Swaps to Group All 1's Together II coding problem tests circular sliding window implementation.

Why is this asked in interviews?

IBM and Josh Technology use this to test whether candidates can adapt a known linear algorithm to a circular constraint. Handling circularity correctly — without just doubling the array, which wastes space — is the key skill. The array and sliding window interview pattern applies with the added circular twist.

Algorithmic pattern used

Circular sliding window using modular indexing. Count total 1s (ones) to determine window size. Slide the window of size ones across the circular array using index i % n. Maintain a count of 1s (or 0s) inside the current window as it slides. Update by removing the outgoing element and adding the incoming element using modulo. Track the minimum zero-count across all window positions.

Example explanation

Array: [0, 1, 1, 1, 0, 0, 1, 1, 0]. Total 1s = 5. Window size = 5.

• Linear windows: check positions 0-4, 1-5, ..., 4-8 → count zeros in each.
• Circular windows: position 5-4 (wrapping): [0,0,1,1,0] → 3 zeros.
• Position 6-5 (wrap): [1,1,0,0,1] → 2 zeros.
• Best window = 2 zeros → minimum 2 swaps.

Common mistakes candidates make

• Doubling the array (works but uses O(2n) space unnecessarily).
• Forgetting to use modular indexing for circular wrapping.
• Incorrectly handling the window boundary at the array's end.
• Not handling the edge case where all elements are already 1s (zero swaps).

Interview preparation tip

Circular array problems always bring the question: should I double the array or use modular arithmetic? Doubling is simpler to implement but less space-efficient; modulo is cleaner and more scalable. Practice both approaches, but prefer modulo in interviews to signal awareness of space complexity. After Minimum Swaps to Group All 1's Together II, practice other circular sliding window problems — they appear frequently in scheduling and buffer-management interview scenarios.