Circular Active Computers Window

Given `n` computers arranged in a circle as 0/1 states, find the maximum number of active computers in any `k` adjacent computers. Requirements Input: a circular array or string of 0 / 1 states and an integer k. Return the maximum number of 1s among any k adjacent positions on the circle. Windows can wrap from the end of the array back to the beginning. Clarify behavior for k > n; the natural answer depends on whether repeated wraparound is allowed. Notes Duplicate the array once and run a fixed-size sliding window over starts 0..n-1. If k <= n, only inspect n windows; scanning all windows in the doubled array creates duplicates but usually still works if bounded carefully. Prefix sums are also clean: build prefix over arr + arr, then compute each circular window sum in O(1). Preparation Implement both sliding-window and prefix-sum versions. Test k=1, k=n, all zeros, all ones, and a maximum window that wraps across the boundary.