What is the time complexity of average insertion and retrieval operations in a HashMap?

The time complexity of average insertion and retrieval operations in a HashMap is O(1) because HashMap uses a hash function to map keys to specific indices in an array, allowing for constant-time average access to its elements.

When a key-value pair is inserted, the hash function computes an index where the value should be stored. If the load factor is maintained appropriately and collisions are handled efficiently (such as through chaining or open addressing), the time taken to insert or retrieve an element remains constant on average, regardless of the number of elements in the map.

However, in situations where hash collisions are frequent or when resizing occurs, the time complexity can degrade, but these cases are outliers. Thus, for well-designed HashMaps, the average time complexity for insertion and retrieval is O(1), making it a highly efficient data structure for these operations.