How is the efficiency of searching for an element by key in a HashMap data structure evaluated?

In the HashMap data structure, searching for an element by key is usually performed in amortized O(1) time. This is achieved by using a hash function that converts the key into an array index where the value is stored.

However, in the worst case, if many keys hash to the same bucket (collision), the search can degrade to O(n), where n is the number of elements in the bucket. Modern implementations, such as in Java and Kotlin, use balanced trees within buckets when there are many collisions, which improves the worst-case scenario to O(log n).

Thus, the efficiency of search in HashMap is usually very high and close to constant.