Why is accessing by index in data structures performed quickly?

Accessing by index in data structures is fast because indices allow direct calculation of the memory address of the desired element without the need for sequential traversal.

For example, in arrays, elements are stored contiguously, and to get the element at index i, it is enough to calculate the address: base_address + i * element_size. This operation has constant time complexity (O(1)).

In contrast, data structures without direct access (such as linked lists) require traversing the elements up to the desired index, which takes more time.