Explain different types of algorithmic approaches and What are the steps you will follow to design analgorithm

There are several types of algorithmic approaches, including:

1. Brute Force Algorithms: These are straightforward methods of solving a problem, usually directly based on the problem's statement and definitions of the concepts involved.

2. Divide and Conquer Algorithms: These algorithms work by breaking down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly.

3. Greedy Algorithms: These algorithms make the locally optimal choice at each stage with the hope of finding a global optimum.

4. Dynamic Programming Algorithms: These algorithms solve complex problems by breaking them down into simpler subproblems, solving each of those just once, and storing their solutions - ideally using a memory-based data structure.

5. Backtracking Algorithms: These algorithms test for solution(s) towards the goal as soon as it is found, the solution is written and the algorithm terminates.

To design an algorithm, you can follow these steps:

1. Problem Definition: Clearly define the problem. What are the inputs? What are the desired outputs?

2. Analysis: Understand the problem thoroughly and determine the appropriate data structures that should be used, identify the algorithmic paradigm, and estimate the resources needed.

3. Algorithm Design: Design the algorithm step by step. Make sure each step is clear and unambiguous.

4. Testing and Debugging: Test the algorithm with different data sets. If any errors are found, debug to correct the errors.

5. Implementation: Implement the algorithm using a suitable programming language.

6. Review: Review the algorithm to ensure it is implemented correctly and is efficient in solving the problem.