What is the time complexity of inserting an element at the end of an array?

Inserting an element at the end of an array is a common operation in computer programming, especially for dynamic data structures that require frequent updates. The time complexity of this operation depends on the length of the array, as well as the implementation of the data structure.

In an array with a fixed size, inserting an element at the end of the array requires copying all the elements of the array to a new array with a larger size, and then adding the new element to the end of the new array. This operation takes linear time, or O(n), where n is the length of the array, because each element of the array must be copied to the new array.

In an array with a dynamic size, such as an ArrayList in Java, inserting an element at the end of the array is more efficient. The ArrayList maintains an internal array that has a certain capacity, which can be increased dynamically as needed. When an element is added to the end of the ArrayList and the internal array is full, a new, larger array is created and all the elements of the original array are copied to the new array, along with the new element. The time complexity of this operation is amortized constant time, or O(1), on average, because most of the time the internal array has enough free space to accommodate the new element, and there is no need to copy the elements to a new array.

In summary, the time complexity of inserting an element at the end of an array depends on the implementation of the data structure. In an array with a fixed size, this operation takes linear time, while in an array with a dynamic size, it takes amortized constant time on average. It is important to choose the appropriate data structure for the application based on the expected frequency of updates and the size of the data set, in order to ensure efficient and scalable performance.