What is time requirement for insert operation one dimensional array state average and worst case time management?

Answer 1

The time-complexity of an insert operation upon an array is O(n-k), where n is the number of elements in the array (such that n>=0), and k is the position where the insertion will occur (such that k<=n). The time-complexity arises due to the need to move the last n-k elements in the array to make room for the new element. Thus inserting at or near the start of the array will take more time than inserting at or near the end of the array. Inserting at the end of an array is a constant-time operation, O(1).

However, all of this presumes that the array has one or more unused elements at the end of the array to allow for expansion. If the array is full (no unused elements), the entire array must be re-allocated. For optimal performance, implementations will typically grow an array by increasing the allocation by 50% - 100%, thus time-complexity is said to be amortized rather than finite due to the occasional need to re-allocate.

Note that the number of dimensions is immaterial since all arrays are intrinsically one-dimensional. That is; a two-dimensional array is nothing more than a one-dimensional array where every element is itself a one-dimensional array. The length of each element will affect the actual time taken to complete an insertion, however it does not affect the time-complexity.