Understanding-Collisions-in-Data-Structures.pptx

🚀 Understanding Collisions in Data Structures*🔍

In data structures, especially hash tables, collisions occur when two different keys produce the same hash value, leading to data conflicts. How do we handle this efficiently?

🔹 Collision Handling Techniques:
✅ Chaining: Storing multiple values at the same index using linked lists.
✅ Open Addressing: Finding another available slot using techniques like linear probing or quadratic probing.
✅ Double Hashing: Using a second hash function to resolve conflicts.

💡 Why is this important?
Collisions affect the efficiency of searching, inserting, and deletingoperations. Proper handling ensures faster data retrieval and optimal performance in applications like databases, caching, and cryptography.

📂 Want to learn more? Check out our presentation "Understanding Collisions in Data Structures" for a deep dive into real-world examples and best practices.

#DataStructures #Hashing #Collisions #ComputerScience #Programming #Algorithms

1. Understanding Collisions in Data Structures This presentation explores collisions in data structures. Collisions occur when distinct keys map to the same location. Understanding collisions is key for efficient data storage. Like two people assigned the same seat. by Mosiuoa Wesi

2. The Pigeonhole Principle Pigeonhole Principle The Pigeonhole Principle states that if you have more items than containers, at least one container must have 2 items. This principle is crucial for understanding collisions. Hashing and Collisions In hashing, having more keys than available slots guarantees collisions. For example, storing 11 elements in a hash table of size 10 will always result in at least one collision.

3. Separate Chaining 1 Definition Separate Chaining (open hashing) resolves collisions. Each hash table slot points to a linked list of key-value pairs. This method allows multiple elements to be stored at the same index. 2 Operations Insertion, search, and deletion operations occur within the chain. The average case performance is O(1+n/k). Here, k represents the number of slots in the table. 3 Python Example Lists can implement chaining in Python, to handle collisions. It involves appending colliding elements to the same list.

4. Open Addressing Techniques Linear Probing Check the next available slot. It wraps around, but is prone to clustering. Example: insert keys 18, 89, 26, 19 into a table of size 10, using hash function k mod 10 Quadratic Probing Check slots i + k^2. This approach reduces primary clustering. For example, insert keys 50, 70, 76, 85, 93 into a table of size 11, using hash function k mod 11. Double Hashing Use a second hash function to determine the step size. This avoids clustering. Example: hash1(key) = key % tableSize, hash2(key) = prime - (key % prime), where prime < tableSize

5. Impact on Performance 1 Time Complexity Collisions impact search and insertion time complexity. In the worst-case, all keys collide. This results in O(n) search time. 2 Load Factor A good hash function yields O(1) search and insertion time on average. The load factor affects performance. The load factor is the number of elements divided by the table size. 3 Rehashing Rehashing is dynamic resizing to maintain performance. By growing the size of the hashtable you reduce the load factor.

6. Choosing a Good Hash Function Minimize Collisions Selecting a suitable hash function minimizes collisions. A good hash function is crucial for performance. Desirable Properties Uniformity and efficiency are desirable properties of good hash functions. A hash function should distribute keys evenly. Common Pitfalls Avoid common pitfalls when designing hash functions. For instance, do not use only part of the key.

7. Real-World Applications Databases Hash tables are used in databases. They are useful for indexing and searching data records. Examples include MySQL and MongoDB. Caching Caching systems use hash tables to store frequently accessed data. This allows for quick retrieval. Examples are Redis and Memcached. Compilers In compilers, hash tables are used as symbol tables. Symbol tables provides efficient variable lookup. Cryptography Cryptography uses hash functions for data integrity and security. SHA-256 is an example of a hash function in cryptography.

8. Summary and Conclusion 1 Summary Recap of key concepts: collisions, resolution, and performance. 2 Importance Understanding collisions is key for design. 3 Future New research and strategies are underway. Collisions impact data structure performance. Addressing audience questions can clarify doubts. Future research will improve hashing.