Why hash tables enable O(1) lookup in Data Structures Theory - Quick Recap

Recall & Review

beginner

What is a hash table?

A hash table is a data structure that stores data in an array format, using a special function called a hash function to compute an index where the data is stored or retrieved.

beginner

What role does the hash function play in a hash table?

The hash function converts a key into an index in the array, allowing quick access to the data stored at that position.

intermediate

Why do hash tables provide O(1) lookup time on average?

Because the hash function directly computes the index where the data is stored, the lookup does not require searching through the entire data set, making it very fast and close to constant time.

intermediate

What is a collision in a hash table?

A collision happens when two different keys produce the same index from the hash function. Hash tables use methods like chaining or open addressing to handle collisions.

intermediate

How do collisions affect the lookup time in a hash table?

Collisions can slow down lookup time because multiple items share the same index, requiring extra steps to find the correct item. However, with good hash functions and collision handling, lookup remains close to O(1).

What does a hash function do in a hash table?

A Stores data in a linked list

B Sorts the data alphabetically

C Converts a key into an array index

D Removes duplicate data

A hash function converts a key into an index where the data is stored or retrieved.

Why is lookup in a hash table usually O(1)?

A Because it uses a hash function to find data directly

B Because it searches the entire array

C Because it sorts data before searching

D Because it uses binary search

The hash function computes the exact index, so lookup is direct and fast.

What is a collision in a hash table?

A When the hash function fails

B When data is deleted

C When the table is empty

D When two keys map to the same index

A collision occurs when different keys produce the same index.

Which method can handle collisions in a hash table?

A Chaining

B Sorting

C Binary search

D Recursion

Chaining stores collided items in a list at the same index.

If many collisions happen, what happens to lookup time?

A It becomes faster

B It becomes slower than O(1)

C It stays exactly O(1)

D It becomes zero

More collisions mean more items to check, slowing down lookup.

Explain how a hash table uses a hash function to achieve fast lookup.

Think about how you find a book quickly in a library using a catalog number.

Describe what a collision is in a hash table and how it can affect performance.

Imagine two people trying to sit in the same chair at the same time.