In hash table design, which option correctly lists two main types of collision resolution techniques and example methods used in each type?

Introduction / Context:
Hash tables are widely used for fast insertion and lookup of key value pairs. However, collisions occur when different keys hash to the same table index. Collision resolution techniques are strategies used to handle these collisions while preserving good average performance. Interview and exam questions often ask you to name the main categories of collision resolution and to give typical methods in each category. This question focuses on that conceptual understanding in the context of data structures and algorithms.

Given Data / Assumptions:

• We are discussing hash tables used in memory based data structures, not cryptographic hash functions.
• Two widely taught categories are open addressing and separate chaining.
• Typical methods in open addressing include linear probing, quadratic probing and double hashing.

Concept / Approach:
In open addressing, all elements are stored directly in the hash table array. When a collision occurs, the algorithm probes other slots according to a fixed rule until it finds an empty position. Linear probing checks the next slot, quadratic probing uses a quadratic step, and double hashing uses a second hash function to determine the probe sequence. In separate chaining, each cell of the hash table points to a linked list or another secondary structure where colliding elements are stored. The correct option must mention both categories and give appropriate examples of methods.

Step-by-Step Solution:
Step 1: Recall from theory that the two main types of collision resolution are open addressing and chaining.Step 2: List typical open addressing methods such as linear, quadratic and double hashing.Step 3: Recognise that chaining involves attaching a list of keys to each bucket to hold colliding entries.Step 4: Option A describes open addressing with its probing methods and separate chaining using linked lists.Step 5: Options B, C and D mention algorithms or techniques that do not represent standard hash collision resolution methods, so option A is correct.

Verification / Alternative check:
Data structures textbooks classify collision resolution schemes exactly in this way. They show diagrams of hash tables using linear probing and of hash tables where each slot refers to a chain of nodes. Sorting algorithms and tree structures can be used for other purposes, but they are not the primary names used for hash collision resolution categories. This confirms that option A reflects the standard classification.

Why Other Options Are Wrong:
Option B lists sorting algorithms, which are not designed to resolve hash collisions. Option C lists tree based methods without mentioning that trees are usually separate structures rather than primary hash collision resolution categories. Option D refers to random numbers and encryption, which may be used in hash function design but are not collision resolution techniques in the usual sense.

Common Pitfalls:
Students sometimes remember the names of individual methods like linear probing but forget the categories they belong to. Others confuse the hash function design with collision handling. To avoid mistakes, keep clear that collision resolution in hash tables is mainly about open addressing versus chaining, with probing rules as subtypes of open addressing.

Final Answer:
Open addressing techniques such as linear probing, quadratic probing and double hashing, and separate chaining techniques where each table slot points to a linked list of entries.