Mastering Algorithms with C

Chapter 8. Hash Tables

Hash tables support one of the most efficient types of searching: hashing. Fundamentally, a hash table consists of an array in which data is accessed via a special index called a key. The primary idea behind a hash table is to establish a mapping between the set of all possible keys and positions in the array using a hash function. A hash function accepts a key and returns its hash coding, or hash value. Keys vary in type, but hash codings are always integers.

Since both computing a hash value and indexing into an array can be performed in constant time, the beauty of hashing is that we can use it to perform constant-time searches. When a hash function can guarantee that no two keys will generate the same hash coding, the resulting hash table is said to be directly addressed. This is ideal, but direct addressing is rarely possible in practice. For example, imagine a phone-mail system in which eight-character names are hashed to find messages for users in the system. If we were to rely on direct addressing, the hash table would contain more than 26⁸ = (2.09)10¹¹ entries, and the majority would be unused since most character combinations are not names.

Typically, the number of entries in a hash table is small relative to the universe of possible keys. Consequently, most hash functions map some keys to the same position in the table. When two keys map to the same position, they collide. A good hash function minimizes collisions, but we must still be prepared ...