A hash table is a data structure that stores data as key-value pairs and uses a hash function to quickly compute the storage location.

When we write:

set("abc") = "xyz"

Internally, it becomes:

index = hash("abc") % array_size
A[index] = ("abc", "xyz")

This means: - The key (“abc”) is passed into a hash function - The hash function converts it into a number - That number is reduced into a valid array index using modulo (%) - The value is stored together with the key at that index

We store both key and value because different keys can produce the same index (collision).

Example:

"abc" → index 2
"def" → index 2

If we store only values:

A[2] = "xyz"   ❌ (data will be overwritten)

Instead, we store:

A[2] = [
  ("abc", "xyz"),
  ("def", "123")
]

This method is called “chaining”.

The correct way to think about a hash table is:

key → hash(key) → index → A[index] = (key, value)

or in real systems:

A[index] = list of (key, value)

- Hash table maps keys to values using a hash function - Index is computed as: hash(key) % array_size - Each slot stores (key, value), not just value - Collisions are handled using a list (chaining) - Average time complexity for get/set is O(1)

Hash tables are fast because they avoid searching through all elements by directly jumping to a computed index.