A fundamental data structure used extensively in computer science and software development is the hash table. They do this by utilizing the strength of hash functions to offer an effective method of storing and retrieving data. In this post, we’ll look at hash functions and learn how they help hash tables work efficiently and effectively.

How do hash functions work?

A mathematical operation known as a hash function takes an input (or key) and outputs a fixed-length character string known as a hash value or hash code. A hash function’s main role is to convert data of any size into a fixed-size value. The generated hash code allows for quick access to the associated data by serving as an index or address in a hash table.

What Makes a Good Hash Function?

A good hash function has the following qualities:

  • Deterministic: A hash function should always provide the same hash code when given the same input. This characteristic guarantees the hashing process’ consistency and predictability.
  • Uniformity: An effective hash function should distribute hash codes equally across the complete gamut of feasible hash values. Collisions, which happen when two different inputs generate the same hash code, are reduced by this characteristic.
  • Avalanche Effect: A small change in the input should lead to a significant change in the resulting hash code. This property ensures that similar inputs generate distinct hash codes, reducing the likelihood of collisions.
  • Non-reversibility: It should be computationally infeasible to reverse-engineer the original input from its hash code. Hash functions are designed to be one-way functions, protecting the integrity and security of the data.

Common Hash Functions: Each hash function has its advantages and disadvantages and is frequently utilized in practice. Here are a few noteworthy instances:

  • The input key is divided by the size of the hash table in this straightforward hash function, and the result is used as the hash code. Although simple to create, if the size of the hash table is not carefully chosen, it may result in poor distribution.
  • The key is multiplied by a fixed fraction in this method, and the resultant fraction is then used as the hash code. It performs well with prime table sizes and has a better distribution than the division approach.
  • The Polynomial Rolling Hash method interprets the characters in the input as the coefficients of a polynomial and evaluates it at a selected base. It is frequently used in string hashing. For related strings, it reduces collisions and offers a good distribution.
  • Hash functions that are developed with strong cryptographic features include MD5, SHA-1, and SHA-256. They are frequently employed for data security and integrity because of their extreme homogeneity and non-reversibility.


Collisions in hash tables happen when several keys produce the same hash code. Effective collision handling is essential for sustaining the functionality and effectiveness of hash tables. In this post, we will examine popular methods for resolving collisions and examine how they affect performance.

  • One of the easiest methods for resolving collisions is separated chaining. Colliding elements are kept in separate linked lists connected to each hash table record. The new element is added to the linked list at the appropriate index whenever there is a collision.

By using this method, all elements with the same hash code can be correctly stored and retrieved.

Performance Analysis: The average number of collisions and the size of the linked lists are two variables that affect separate chaining’s performance. The average length of the linked lists will ideally be minimal, resulting in quick retrieval times, with a well-distributed hash function. In the worst situation, though, multiple keys could provide the same hash code, causing the linked lists to grow large and slow down performance. When the load factor—the proportion of elements to table size—exceeds a predetermined level, the hash table must be resized to reduce this risk.

  • Open addressing is an alternate collision resolution method that involves moving clashing components to different places inside the hash table. By searching the table until an open spot is located, the objective is to find an empty slot.
    • If a collision occurs, the method checks the following slot (linearly, one after the other) until an empty position is discovered. The benefit of this strategy is the cache-friendly memory access, but it can also cause clustering, where elements tend to group and produce lengthy sequences of occupied slots.
    • Quadratic Probing: By utilizing a quadratic function to increase the probe sequence, quadratic probing tries to reduce clumping. The technique employs a quadratic increment rather than looking for the following empty slot in a linear fashion. As an illustration, if the first collision happens at index i, the subsequent probe is at index I + 12, then i + 22, I + 32, and so on.
    • Double Hashing: When using double hashing, the distance between probe places is determined using a second hash algorithm. The approach employs the secondary hash function to calculate the subsequent probe index when a collision occurs. This approach offers a more even distribution and helps lessen clumping.


Analysis: Since all elements are kept in the hash table itself, open addressing techniques perform better in the cache than in separate chaining. The time needed to find an open spot likewise grows as the table fills up and collisions rise. Longer retrieval times may result from this, particularly if the load factor is significant. Achieving high speed with open addressing also depends on selecting the right step sizes and secondary hash functions.

  • Load Factor: The load factor is the proportion of the size of the table to the number of elements stored in the table. A high load factor makes collisions more likely and can reduce the hash table’s effectiveness. Performance can be maintained by resizing the hash table when the load factor rises above a specific level.
  • Distribution of Hash Codes: The distribution of hash codes is directly influenced by the strength of the hash function. A hash function that is evenly distributed reduces collisions and improves performance in general. A hash function that offers a consistent distribution of hash codes should be chosen or created.
  • Collision Resolution Method: The hash table’s performance is affected by the collision resolution method you choose. When collisions are few, separate chaining works well and enables constant-time operations. Even though open addressing strategies improve cache efficiency, when the table fills up, clustering and longer retrieval times can occur.
  • Resizing and rehashing: As the hash table’s element count increases, these operations are required to maintain performance. Rehashing redistributes the current elements using the new table size, whereas resizing entails expanding the table’s size to accommodate more elements. Although these actions have significant overhead, they are necessary to guard against excessive collisions and performance deterioration.

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