How is the time complexity of inserting an element into a dictionary determined?

In Python, a dictionary (dict) is implemented based on a hash table, so the operation of inserting an element usually has an amortized time complexity of O(1).

This means that on average, insertion takes constant time regardless of the size of the dictionary. However, in the worst case (for example, during hash collisions or the need to resize the internal array), the time can increase.

Example of insertion:

d = {}
d['key'] = 'value'  # amortized O(1)

Thus, for most practical tasks, inserting into a dictionary is very fast and efficient.