Hash Function Design:

For the hashing function Division Method, Multiplication Method,

and Jenkins Hashing.

Explain its mathematical formulation and properties, including

uniformity, efficiency, and collision resistance.

Discuss the advantages and disadvantages of each hash function

in terms of performance and security.

Collision Resolution Methods:

Describe three collision resolution methods used to handle

collisions in hashing: Chaining, Open Addressing $($Linear

Probing$),$ and Double Hashing.

For each collision resolution method, explain its operation,

advantages, and limitations$.$

Compare and contrast the performance of these collision

resolution methods in terms of memory overhead, average case,

and worst$-$case time complexity.

Hash Table Implementation:

Implement a hash table data structure in a programming

language of your choice $($Python$,C++).$

Choose one of the hash functions and collision resolution

methods studied in Tasks $1$ and $2,$ respectively, and integrate

them into your hash table implementation.

Test your hash table implementation with a set of sample data to

ensure correct functionality and evaluate its performance.

Practical Applications of Hashing:

Research and identify three practical applications of hashing in

computer science and software engineering.

For each application, describe how hashing is used to solve a

specific problem or optimize a particular operation.

Provide real$-$world examples or case studies illustrating the

effectiveness of hashing in these applications.