Why does a hash table provide fast access to data?

A hash table provides fast access to data because it does not search elements sequentially, like a list, but computes their address directly using a hash function.

How this happens:

1. When looking up an element, its key is taken.
2. The hash function computes an index, the position where this element should be.
3. The table accesses that slot directly and returns the value.

So instead of scanning all elements (O(n)), only a single computation and a single memory access happen (O(1) on average).

Example:

The speed comes from the fact that lookup reduces to an arithmetic operation, rather than comparing keys one by one.

Exception: when collisions occur, the time can grow, but with a good hash function and a correct implementation the average complexity stays O(1).