Question $1$:

a$.$ Define advanced algorithms and explain why they are necessary in computer science and

problem$-$solving.

b$.$ Provide an example of a real$-$world problem that can be effectively solved using advanced

algorithms. Explain why this problem is suitable for such algorithms.

Divide and Conquer Algorithms

Question $2$:

a$.$ Describe the divide and conquer algorithmic paradigm. Provide an intuitive explanation of

how it works and its key characteristics.

b$.$ Choose a well$-$known problem $($e$.$g$.,$ merge sort, quicksort$)$ and explain how it can be solved

using a divide and conquer approach. Provide a high$-$level algorithmic description.

Dynamic Programming

Question $3$:

a$.$ Define dynamic programming and explain its significance in solving optimization problems.

b$.$ Select a classic dynamic programming problem $($e$.$g$.,$ the Fibonacci sequence, the knapsack

problem$)$ and describe the recursive and iterative approaches to solving it$.$ Discuss the time and

space complexity of each approach.

Algorithm Complexity Analysis

Question $4$:

a$.$ Discuss the importance of analyzing algorithm complexity. Explain how algorithmic efficiency

impacts real$-$world applications.

b$.$ For each of the following algorithms: divide and conquer, dynamic programming, and a

simple linear search, provide their time complexity in Big$-$O notation. Compare and contrast

their efficiency.