Let us suppose the design of a module mananging a key$/$value dictionary with the following properties:

Data types : integer for both the keys and their associated values

Unicity of keys: there is no possible duplicates of any given key value

Underlying data structure: the dictionary uses a two$-$dimensional array $($a matrix$)$ for its internal management.

The internal array memory management is driven in linear amortised constant time, which limits the operation complexity asymptotically at $.$

Data management: there is no sorting of the array when inserting a new key$/$value pair

What is the algorithmic complexity of the insertion algorithm for a new key$/$value pair in this dictionary?