Implement a Dynamic Array/Vector

I would start by defining a class with an internal array, a current size counter, and a capacity tracker. The core logic lies in the append operation. Before adding an element, I check if the current size equals the capacity. If it does, I trigger a resize. Instead of increasing capacity by one, which leads to O(n^2) total time for n appends, I double the capacity. This geometric growth is crucial. I allocate a new array twice the size, copy existing elements over, and update the reference. Now, let's analyze the cost. A single append is O(1) unless a resize occurs. When a resize happens, it takes O(k) where k is the current number of elements. However, because we only resize when full and double the space, the expensive copy operations become exponentially less frequent. Using the accounting method, we can assign two credits to each inserted item: one for the insertion itself and one saved to pay for moving this item during future resizes. Since every element is moved at most once per doubling phase, the total cost for n appends is proportional to n, proving the amortized time complexity is O(1). This balance between memory usage and performance is exactly what Microsoft values in system design.