How is amortized operation complexity in a hash table, approaching O(1), ensured?

Amortized complexity of operations in a hash table is achieved through infrequent rehashing and uniform distribution of elements across buckets.

Key points:

• When adding elements, the hash table stores them in an array of buckets based on the hash of the key.
• If the number of elements exceeds a certain threshold (load factor), rehashing occurs — a new larger array is created, and all elements are redistributed.
• Although rehashing is an expensive operation (O(n)), it happens rarely.
• Most insert, search, and delete operations are performed in O(1) on average.

Thus, the amortized complexity is the average time per operation considering the rare costs of rehashing, providing efficient hash table performance.