Hash Tables and Hashing

 

Hash Tables and Hashing

A hash table is a data structure that maps keys to values for efficient data retrieval. The underlying concept is based on hashing, which involves using a hash function to compute an index (or hash code) for each key. This index determines where the value associated with the key will be stored in the table.


Key Features of Hash Tables

  1. Fast Lookup: Hash tables offer average O(1) time complexity for lookups, insertions, and deletions.
  2. Key-Value Pair Storage: Data is stored as key-value pairs.
  3. Dynamic Size: Many implementations dynamically resize the hash table as the number of elements grows.

How Hashing Works

  1. A hash function converts a key into a numerical hash code.
  2. The hash code is mapped to an index in an array (or bucket) of fixed size.
  3. If two keys produce the same hash code (a collision), a collision resolution strategy is used, such as:
    • Chaining: Store multiple values in a linked list or similar structure at the same index.
    • Open Addressing: Find the next available slot in the array.

Hash Tables in Python: Dictionaries

In Python, the dictionary is implemented as a hash table. Python dictionaries are highly optimized for performance.

Key Features of Python Dictionaries

  1. Hash Function: Each key in a Python dictionary is hashed using Python's built-in hash() function.
  2. Dynamic Resizing: The dictionary grows automatically as the number of elements increases.
  3. Collision Handling: Python uses open addressing to resolve collisions.

Python Dictionary: Internal Implementation

  1. Hashing:

    • When a key-value pair is added, the key is hashed to produce an index.
    • Example: hash(key) % table_size.

  2. Indexing:

    • The value is stored at the computed index in the dictionary's internal array.

  3. Collision Resolution:

    • If two keys hash to the same index, Python uses probing to find an open slot.

  4. Performance:

    • Average O(1) for lookups.
    • Worst-case O(n) if there are excessive collisions (rare with good hash functions).

Example: Python Dictionary Implementation

# Creating a dictionary
phone_book = {
    "Alice": "123-456-7890",
    "Bob": "987-654-3210",
    "Charlie": "555-555-5555"
}

# Accessing a value
print(phone_book["Alice"])  # Output: 123-456-7890

# Adding a new key-value pair
phone_book["Diana"] = "444-444-4444"

# Removing a key-value pair
del phone_book["Charlie"]

# Iterating through a dictionary
for name, number in phone_book.items():
    print(f"{name}: {number}")

Applications of Hash Tables

  1. Data Indexing: Used in database indexing to retrieve records quickly.
  2. Caching: Storing frequently accessed data for quick retrieval.
  3. Symbol Tables: Storing variable/function names in compilers and interpreters.
  4. Sets: Python sets are also implemented using hash tables.
  5. Load Balancers: Mapping requests to servers.


Advantages and Limitations

Advantages:

  • Extremely fast for lookups and insertions.
  • Simple and efficient implementation.

Limitations:

  • Inefficient memory usage due to possible empty slots (sparse table).
  • Performance degrades with excessive collisions.
  • Keys must be hashable (immutable types like strings, numbers, tuples).


Understanding Hash Function in Python

Python’s hash() function is used internally:

# Example of Python's hash function
print(hash("Alice"))  # Output: A large integer unique to "Alice"

# Using hash() to implement a simple hash table
table_size = 10
key = "Alice"
index = hash(key) % table_size
print(f"Index for key '{key}': {index}")

Python's dictionary implementation ensures high efficiency, making it a cornerstone for many programming tasks.



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