Final answer:
Using ensureCapacity(manyItems + 1) would technically work for array resizing but is less efficient because it may lead to many resizing operations; doubling the size each time minimizes these operations and optimizes performance.
Step-by-step explanation:
The question relates to whether the ensureCapacity method would work correctly if it is used with ensureCapacity(manyItems + 1) instead of doubling the capacity, which implies a context of dynamic array management in programming, specifically in cases where the size of a collection needs to be increased to accommodate more elements.
Using ensureCapacity(manyItems + 1) would increase the capacity by just one element, which is a linear approach to resizing an array. While this would work correctly in the sense that it will provide enough space for the immediate addition of an element, it is not efficient for the performance when adding many elements because it may result in frequent resizing operations and, consequently, more computational overhead. The common practice is to grow the array capacity by a factor (often doubling the size) to ensure that the number of resizing operations is minimized, thus optimizing performance over time.
If a program used ensureCapacity(manyItems + 1) without the *2 factor, it could lead to poor performance due to the constant resizing of the array if elements are added frequently.