Minimum Swaps to Group All 1's Together

Minimum Swaps to Group All 1's Together

What is this problem about?

The Minimum Swaps to Group All 1's Together problem gives you a binary array containing only 0s and 1s. Your task is to find the minimum number of swap operations needed to move all the 1s into one contiguous group. A swap exchanges any two elements. This Minimum Swaps to Group All 1's Together coding problem is a clean application of the fixed-size sliding window technique on binary arrays.

Why is this asked in interviews?

Microsoft, TikTok, and Expedia ask this because it tests whether candidates can reframe an operation-based problem into an observation-based one. Instead of simulating swaps directly, the insight is to count how many 1s need to move into a target window. The array and sliding window interview pattern is fundamental here, and this problem is an ideal gateway to a whole class of window-based optimization challenges.

Algorithmic pattern used

The approach is a fixed-size sliding window. Count the total number of 1s in the array — call it k. This is the window size (since all 1s must fit in a contiguous segment of length k). Slide a window of size k across the array. For each window, count how many 0s are inside — those 0s represent 1s that need to swap in from outside. Track the minimum zero-count across all windows.

Example explanation

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

• Window [0..2] = [0,1,0]: zeros = 2 → 2 swaps.
• Window [1..3] = [1,0,1]: zeros = 1 → 1 swap.
• Window [2..4] = [0,1,1]: zeros = 1 → 1 swap.
• Window [3..5] = [1,1,0]: zeros = 1 → 1 swap.
• Window [4..6] = [1,0,0]: zeros = 2 → 2 swaps. Minimum swaps = 1.

Common mistakes candidates make

• Simulating actual swap operations instead of using the window observation.
• Using window size = total array length instead of total count of 1s.
• Counting 1s instead of 0s inside the window as the cost.
• Not initializing the first window count before sliding.

Interview preparation tip

"Minimum swaps to group elements" problems almost always reduce to a sliding window of size equal to the target element count. Once you internalize this reframing, you can solve the entire family of problems: grouping 0s, grouping specific values, or grouping elements satisfying a condition. After this problem, practice the circular variant (the array wraps around) to strengthen your ability to adapt linear algorithms to circular constraints.