How is the time complexity of updating an element in a map data structure determined?

In data structures like map (for example, HashMap in Dart or other languages), the operation of updating an element usually has an amortized time complexity of O(1). This is because the map is implemented based on a hash table, where access to an element by key occurs in constant time on average.

However, in the worst case, if there are many hash collisions, the time can degrade to O(n), where n is the number of elements in the map. But thanks to good hash functions and collision resolution mechanisms, in practice, updates are very fast.

Example of updating a value by key in Dart:

var map = {'key1': 'value1', 'key2': 'value2'};
map['key1'] = 'newValue'; // updating the value by key

Here, the update operation is performed in amortized O(1).