Hash Functions

Before we can understand how a hash table stores and retrieves data efficiently, we need to understand the mechanism that makes it all possible: the hash function.

What is a hash function?

A hash function is a function that takes a key as input and returns an integer called a hash value or hash code. This hash value is then used to determine the index at which the corresponding value will be stored inside the hash table’s internal array.

In simple terms:

For example, if you want to store the value 91 under the key "alice", the hash function takes the string "alice", performs some computation on it, and produces a number, say 3. The value 91 is then stored at index 3 of the internal array.

When you later want to retrieve the value for "alice", the same hash function is applied to "alice" again, produces 3 again, and the table goes directly to index 3. No searching required.

In this way, a hash function transforms the problem of searching for a key into the problem of computing an index. Since computation is usually much faster than searching through many elements, hash functions make fast lookup possible.

Why is the hash function so important?

The performance of a hash table largely depends on the hash function. An effective hash function enables efficient lookup operations and optimal space utilization. A poor hash function can lead to increased collisions, degrading performance and increasing memory overhead.

The hash function is important for two reasons:

• First, it determines speed. Since retrieval works by computing an index directly, the hash function must be fast to compute. If the hash function itself takes a long time, it defeats the purpose of ...