Hash Tables


In computer science, a hash table (also called a hash map or hash set) is a data structure that efficiently implements an associative array or a dictionary. This abstract data type maps keys to values, allowing for fast lookups of values based on their associated keys. Hash tables achieve this by using a hash function to compute an index (called a hash code or just hash) within an array of buckets or slots. The value is then stored at the index corresponding to its key.

Key Concepts

  • Hash Function: A hash function transforms the key into an integer index pointing to a location within the hash table's array. A good hash function should distribute keys relatively evenly across the array to avoid excessive collisions.
  • Collision Handling: Collisions occur when multiple keys map to the same index within the array. Common collision handling techniques include:
    • Separate Chaining: Storing multiple key-value pairs at an index using a linked list or similar data structure.
    • Open Addressing: Finding an alternative placement within the array using methods like linear probing, quadratic probing, or double hashing.
  • Load Factor: The ratio between the number of occupied buckets to the total number of buckets in the hashtable. A high load factor leads to increased collisions, slowing down operations.
  • Rehashing: The process of resizing the hash table to improve its performance when the load factor grows too high. Rehashing involves creating a new larger array and re-inserting all elements from the smaller array by recalculating their hash values.

Time Complexity

Assuming a well-designed hash function and load factor management, hash tables offer a significant performance advantage:

  • Search: O(1) on average.
  • Insert: O(1) on average.
  • Delete: O(1) on average.

In the worst-case scenario, with a poor hash function or excessive collisions, these operations can degrade to O(n).


Hash tables have numerous applications in computing:

  • Caching: Storing frequently accessed data for quick retrieval.
  • Database Indexing: Providing efficient data lookups in databases.
  • Sets: Enforcing uniqueness and offering fast membership checks.
  • Symbol Tables (in compilers): Managing identifiers and their attributes.
  • Object Representation: Implementing object properties in some programming languages.
  • Graph Algorithms: Used in adjacency list representations.

Programming Language Implementations

Many programming languages provide built-in hash table implementations:

  • Python: Dictionaries (dict)
  • Java: HashMap (java.util.HashMap)
  • C++: Unordered map (std::unordered_map)
  • JavaScript: Maps and Objects


  • Security: Hash tables can potentially be vulnerable to hash flooding attacks if a predictable hash function is used with attacker-controlled inputs.
  • Ordering: Hash tables do not maintain any inherent ordering of elements. If order is important, consider a sorted data structure.