To quickly find a data item given its key, using a function that maps keys to array indices and handles collisions, what data structure would an expert typically implement?

The data structure an expert would typically implement is a hash table. A hash table is an efficient data structure that stores key-value pairs. It uses a hash function to map keys to indices in an underlying array, which is often called a hash array or bucket array. When you want to find a data item, you provide its key. The hash function takes this key and computes an integer value, which is then typically modulo the size of the array to produce a valid array index. This index points directly to a location, or 'bucket', within the array where the corresponding data item is expected to be stored. This direct computation of an index allows for very fast, average-case constant time (O(1)) lookups, insertions, and deletions, regardless of the number of items stored.

A critical aspect of hash tables is handling 'collisions'. A collision occurs when two different keys, after being processed by the hash function, map to the same array index. Since each array index can only directly hold one item, a strategy is needed to store multiple items that hash to the same bucket. There are two primary collision resolution strategies.

One common method is 'chaining'. In chaining, each bucket in the hash array does not store the data item itself, but rather a reference to a dynamic list, often a linked list, of all key-value pairs that hash to that specific index. When a collision occurs, the new item is simply added to the list associated with that bucket. To find an item, the key is hashed to get an array index, and then the linked list at that index is traversed to find the matching key. In scenarios where many keys collide into one bucket, this linked list can become long, degrading lookup performance for that bucket to proportional to the length of the list, potentially O(N) in the worst case where N is the total number of items, if all keys hash to the same bucket. To mitigate this, some advanced implementations might use a balanced binary search tree instead of a linked list within each bucket, leading to O(log K) performance within the bucket, where K is the number of items in that bucket.

The other primary method is 'open addressing'. In open addressing, all key-value pairs are stored directly within the hash array itself. When a collision occurs (meaning the calculated index is already occupied by another item), the system 'probes' for an alternative, empty slot in the array. Various probing strategies exist, such as 'linear probing' (checking the next sequential slot), 'quadratic probing' (checking slots at increasing quadratic offsets), or 'double hashing' (using a second hash function to determine the step size for probing). To find an item, the key is hashed, and if the item is not at the calculated index, the probe sequence is followed until the item is found or an empty slot is encountered (indicating the item is not present). Open addressing can suffer from 'clustering', where occupied slots tend to group together, potentially lengthening probe sequences and degrading performance.