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Dynamic programming (DP) It is defined as a programming method that transforms a decision-making problem is divided into multiple sub-problems (Abubakar et al., 2023). Then, the sub-problems are solved to find the overall solution for the initial decision-making problem.
Top-Down approach Top-Down uses memoization to avoid recomputing the same subproblem again. Lets solve the same Fibonacci problem using the top-down approach. Top-Down starts breaking the problem unlike bottom-up. Fibonacci(4) - Go and compute Fibonacci(3) and Fibonacci(2) and return the results.
A top-down approach starts with the big picture, then breaks down into smaller segments. A bottom-up approach is the piecing together of systems to give rise to more complex systems, thus making the original systems subsystems of the emergent system.
Dynamic programming is a computer programming technique where an algorithmic problem is first broken down into sub-problems, the results are saved, and then the sub-problems are optimized to find the overall solution which usually has to do with finding the maximum and minimum range of the algorithmic query.
Top-Down DFS is suitable for problems where you need to track cumulative information (e.g., paths or distances from the root). Bottom-Up DFS is useful when you need to gather results from subtrees and combine them at each level.
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The seven steps in the development of a dynamic programming algorithm are as follows: 1- Establish a recursive property that gives the solution to an instance of the problem.
A bottom-up process is characterized by an absence of higher-level direction in sensory processing, whereas a top-down process is characterized by a high level of direction of sensory processing by more cognition, such as goals or targets (Biederman, 19).

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