When does the operation of inserting an element into an array lead to a runtime proportional to the size of the array?

Inserting an element into an array results in a runtime proportional to the size of the array when the array is implemented as a dynamic array and a reallocation occurs. For example, if the array is full and a new element needs to be added, a new larger array is created, and all elements are copied from the old array to the new one. This copying process takes time proportional to the number of elements in the array.

Additionally, if the insertion is not at the end of the array but in the middle or at the beginning, all subsequent elements need to be shifted, which also requires time proportional to the number of shifted elements.