Dynamic Programming (DP) is a programming paradigm and algorithmic technique used to solve complex optimization problems by breaking them down into overlapping subproblems. It is based on the idea of storing the results of subproblems in a table (or memoization) to avoid redundant computations and to efficiently solve the larger problem.

Dynamic Programming typically follows these steps:

1. Characterize the structure of an optimal solution:

- Understand the problem and determine the components of an optimal solution.
- Identify the subproblems involved and how they relate to the larger problem.

2. Define the value of an optimal solution recursively:

- Formulate a recursive relationship that relates the value of the larger problem to the values of its subproblems.
- Express the optimal solution as a function of the optimal solutions of its subproblems.

3. Determine the order of solving subproblems:

- Identify the dependencies between subproblems.
- Choose an order that ensures the subproblems needed to solve a given subproblem have already been solved.

4. Build a table or memoization data structure:

- Create a table or memoization data structure to store the results of the subproblems.
- Initialize the table with base cases or initial values.

5. Fill in the table or memoization data structure:

- Use the recursive relationship to fill in the table or memoization data structure, solving the subproblems bottom-up.
- Ensure that each entry of the table is computed only once by utilizing the stored results of previously solved subproblems.

6. Derive the solution to the original problem:

- Extract the solution to the larger problem from the filled table or memoization data structure.
- Combine the solutions of subproblems to obtain the optimal solution.

Dynamic Programming is often used to solve optimization problems such as the Knapsack problem, the Traveling Salesman Problem, shortest path problems (like Dijkstra's algorithm), sequence alignment, and many others. It can be applied to problems that exhibit the overlapping subproblems and optimal substructure properties.

By using dynamic programming, we can avoid the exponential time complexity that may arise from redundant calculations and achieve more efficient solutions with polynomial time complexity.

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