Maximum Average Subarray I – Sliding Window Optimization Explained While solving LeetCode – Maximum Average Subarray I , I initially implemented a straightforward sliding window solution. Although the logic was correct, it resulted in a Time Limit Exceeded (TLE) error. This problem became a good learning example of why optimization matters and how prefix sums can drastically improve performance. Initial Approach (Naive Sliding Window) My first solution calculated the average of every window of size k by slicing the array and computing the sum each time. Array slicing takes O(k) Summing also takes O(k) This happens for each window → O(n) times Overall time complexity becomes O(n × k) , which causes TLE for large inputs. This solution works logically but is inefficient due to repeated recalculation of sums. Optimized Approach Using Prefix Sum To avoid recalculating sums, I switched to using a prefix sum array . Each index in the prefix array stores...
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