Principle of Dynamic programming:-

 

-The principle of dynamic programming is based on a systematic approach to solving complex problems by breaking them down into simpler, overlapping subproblems and solving each subproblem only once, storing the results to avoid redundant computations.

 

Control Abstraction of Dynamic Programming:-

 -Control abstraction in programming is like a roadmap for a program.

-It defines how the program should flow without diving into the details of how each part works.

-This helps make programs easier to understand, design, and maintain. In the context of the dynamic programming, it follows a set of steps:

 

1. Modular Functions/Methods: Breaking down dynamic programming into smaller, specialized functions or methods     simplifies problem-solving.

2. Encapsulated Subproblem Logic: Each function or method focuses on solving one specific part of the problem, making the     code more organized.

3. Reusability: By encapsulating control flow, you can use the same dynamic programming logic for different problems with     minimal adjustments.

4. Testing and Debugging: Independent subproblems are easier to test and debug, simplifying issue identification and resolution.

 

The time analysis of control abstraction:-

 

-The time analysis of control abstraction in the context of dynamic programming involves examining the computational complexity and performance of breaking down complex problems into smaller, modular subproblems.

 

1. Modular Functions/Methods: Breaking a problem into smaller functions or methods generally adds a small overhead in terms of function calls. The time complexity of calling these functions is usually O(1).

2. Encapsulated Subproblem Logic: The encapsulation of subproblem logic doesn't significantly affect the time complexity because the same computations are performed

3. Reusability: Reusing the same dynamic programming algorithm for different problems without modifying the core logic can lead to time savings.

4. Testing and Debugging: Control abstraction makes testing and debugging more efficient, but the time spent on these activities is not part of the algorithm's time complexity. It's a development and maintenance consideration.