Approach

When tasked with designing a hash table from scratch without using any built-in libraries, it's essential to follow a structured framework to ensure clarity and effectiveness. Here’s how to approach this question:

1. Understand the Concept of Hash Tables

• Define what a hash table is.

• Explain its purpose and common applications.

• Outline the Components of a Hash Table

• Discuss the core elements: keys, values, and the underlying array.

• Explain how hashing works.

• Design the Hash Function

• Describe how to create a hash function that converts a key into an index.

• Discuss considerations for minimizing collisions.

• Implementing Collision Resolution Strategies

• Introduce collision handling methods like chaining and open addressing.

• Explain the pros and cons of each method.

• Define Core Operations

• Outline how to implement insert, delete, and search operations.

• Consider Performance and Resizing

• Discuss the time complexity of operations.

• Explain how to handle resizing the hash table when it reaches capacity.

Key Points

• Hash Table Definition: A hash table is a data structure that implements an associative array, mapping keys to values for efficient data retrieval.

• Hash Function: A critical component that determines the index for storing key-value pairs.

• Collision Resolution: Techniques to handle situations where multiple keys hash to the same index.

• Efficiency: Aim for average-case time complexity of O(1) for insert, delete, and search operations.

• Resizing: Essential for maintaining performance as the number of items grows.

Standard Response

Here’s how to effectively answer the question, “How would you design a hash table from scratch without utilizing any built-in libraries?”:

To design a hash table from scratch, we begin by understanding the basic components and operations involved in this data structure.

• Define the Hash Table Structure:

A hash table consists of an array where each index corresponds to a slot for storing key-value pairs. The size of this array is crucial for performance, as it affects the load factor—the ratio of stored items to the array size.

• Create the Hash Function:

 def hash_function(key, array_size):
 return sum(ord(char) for char in key) % array_size

The hash function transforms a key into an index in the array. A simple hash function might take the modulo of the key's ASCII value:

• Implement Collision Resolution:

Since multiple keys can hash to the same index, we need a strategy to handle collisions. We can use chaining (storing multiple items at each index using a linked list) or open addressing (finding another open slot).

 class HashTable:
 def __init__(self, size=10):
 self.size = size
 self.table = [[] for _ in range(size)]
 
 def insert(self, key, value):
 index = hash_function(key, self.size)
 for pair in self.table[index]:
 if pair[0] == key:
 pair[1] = value
 return
 self.table[index].append([key, value])

For chaining:

• Define Core Operations:

• Insert: Add a new key-value pair, using the hash function to find the appropriate index.

• Search: Retrieve the value associated with a key:

• Delete: Remove a key-value pair by locating it with the hash function and removing it from the list.

• Consider Performance and Resizing:

The average time complexity for each operation (insert, search, delete) is O(1). However, if the load factor exceeds a certain threshold (commonly 0.7), we should resize the array—typically doubling its size and rehashing existing keys to distribute them evenly.

 def resize(self):
 old_table = self.table
 self.size *= 2
 self.table = [[] for _ in range(self.size)]
 for bucket in old_table:
 for key, value in bucket:
 self.insert(key, value)

By following these steps, we've created a functional hash table that efficiently handles key-value pairs while managing collisions and optimizing performance.

Tips & Variations

Common Mistakes to Avoid

• Neglecting Collision Resolution: Failing to address collisions can lead to an inefficient hash table.

• Using Non-Uniform Hash Functions