Collision Resolution By Separate Chaining

Click Here to view videos related to this article.
- X
Collision resolution by Chaining
🔗
Click here to suggest a better video or view suggestions..

Hash tables are fantastic tools for storing and retrieving data quickly. They work by using a special function, called a hash function, to convert a key (like a name or ID) into an index (a slot number) in an array. Ideally, each key gets its own unique slot. However, sometimes the hash function generates the same index for two or more different keys. This is called a collision. Imagine trying to assign two different students the same locker number – things get messy!

Since collisions can happen, we need strategies to handle them gracefully. Separate Chaining is one of the most common and intuitive methods used to resolve these collisions. This article will explain how it works in a simple way.

What is Separate Chaining?

Separate Chaining is a technique used in hash tables to handle collisions. The main idea is simple: instead of trying to find an alternative empty slot when a collision occurs, we allow multiple key-value pairs to occupy the same slot.

How? We make each slot in the hash table array point to a linked list (or sometimes another type of collection like a dynamic array or a balanced tree). When a collision happens (meaning a new key hashes to an index that already has data), we simply add the new key-value pair to the linked list associated with that index.

Tip

Think of the hash table array like a row of mailboxes in an apartment building. Each mailbox has a number (the index). Usually, each mailbox holds letters for one apartment. But with Separate Chaining, if multiple people share an apartment (a collision), all their letters go into the same mailbox, perhaps stored neatly inside one large envelope or folder (the linked list).

How Separate Chaining Works

Let’s break down the process for the main hash table operations when using Separate Chaining.

Insertion

  1. Hash the Key: Take the key of the data you want to insert and apply the hash function to get an index (a slot number) in the array.
  2. Go to the Index: Navigate to the array slot corresponding to this index.
  3. Check the List: Look at the linked list starting at this slot.
  4. Add the Element:
    • If the list is empty (no previous element hashed to this index), create a new list with the key-value pair as the first element.
    • If the list is not empty (a collision!), simply add the new key-value pair as a new node to the existing linked list (often at the beginning or end, depending on the implementation).

Tip

Adding the new element at the beginning of the linked list is usually faster (O(1)) than adding it at the end, as you don’t need to traverse the entire list first.

  1. Hash the Key: Apply the hash function to the key you are searching for to get its index.
  2. Go to the Index: Go to the calculated slot in the array.
  3. Traverse the List: Sequentially search through the linked list associated with that index. Compare the key you are looking for with the key of each element in the list.
  4. Find or Not Find:
    • If you find an element with a matching key, you’ve found your data! Return the corresponding value.
    • If you reach the end of the list without finding the key, it means the key is not present in the hash table.

Deletion

  1. Hash the Key: Calculate the index for the key you want to delete using the hash function.
  2. Go to the Index: Navigate to the corresponding slot in the array.
  3. Traverse and Find: Search through the linked list at that index to find the element with the matching key.
  4. Remove the Element: Once found, remove the element (node) from the linked list according to standard linked list deletion procedures. If the key is not found in the list, do nothing.

Advantages and Disadvantages

Separate Chaining is popular for several reasons, but it also has drawbacks.

  • Advantages:

    • Simple Implementation: The concept is relatively straightforward to understand and implement.
    • Handles High Load Factors: The hash table can function reasonably well even when it’s quite full (high load factor), as performance degradation is gradual. Performance depends more on the length of the chains than the overall fullness of the array itself.
    • Easy Deletion: Deleting elements is simple – just remove the node from the linked list.

  • Disadvantages:

    • Memory Overhead: Linked lists require extra memory to store pointers (the links between nodes).
    • Potential for Long Chains: In the worst-case scenario (e.g., a poor hash function or unlucky data), many keys could hash to the same index, creating a very long linked list. Searching this list would become slow, similar to searching a regular linked list (O(n)).
    • Cache Performance: Traversing linked lists can sometimes be slower than accessing contiguous array elements (used in Open Addressing) because list nodes might be scattered in memory, leading to poorer cache performance.

Time Complexity

The efficiency of Separate Chaining depends heavily on the load factor (α), which is the ratio of the number of elements (n) to the number of slots (m) in the hash table (α = n / m). A good hash function distributes keys evenly, keeping the linked lists (chains) short on average.

  • Average Case: Assuming a good hash function and a reasonable load factor, the average length of a chain is α. (Remember that the load factor (α = n / m) tells us roughly how many items (n) are stored per slot (m), on average.) Therefore, the average time complexity for search, insertion, and deletion is O(1 + α). If the load factor α is kept constant (e.g., by resizing the table when it gets too full), these operations can be considered O(1) on average.
  • Worst Case: If all n keys hash to the same index, they all end up in a single linked list. In this scenario, search, insertion (if checking for duplicates), and deletion take O(n) time, as we might need to traverse the entire list.

Separate Chaining provides a robust way to handle hash collisions, balancing simplicity with generally good performance, especially when using a good hash function and managing the load factor.

What’s Next?

Understanding Separate Chaining gives you a solid foundation in handling hash table collisions. While it’s a widely used and effective technique, it’s not the only one! Exploring other methods can help you appreciate the different trade-offs involved and choose the best approach for specific scenarios. Consider diving into these related topics:

  • Open Addressing: Discover a different family of collision resolution techniques where all elements are stored directly within the hash table array itself, using various probing methods like Linear Probing, Quadratic Probing, and Double Hashing to find empty slots.
  • Comparing Collision Resolution Techniques: See a direct comparison between Separate Chaining and various Open Addressing methods, highlighting their respective strengths and weaknesses.
  • Load Factor and Rehashing: Learn how the fullness of a hash table affects performance and how resizing (rehashing) helps maintain efficiency, which is crucial for both Separate Chaining and Open Addressing.