What are some characteristics of Dynamic Programming?

Dynamic Programming (DP) is a powerful algorithmic technique used to solve complex problems by breaking them down into simpler subproblems. Here are some key characteristics of Dynamic Programming:

Characteristics of Dynamic Programming

1. Optimal Substructure:

   • A problem exhibits optimal substructure if an optimal solution to the problem contains optimal solutions to its subproblems. This means that the problem can be broken down into smaller, simpler subproblems which can be solved independently and combined to form the solution to the original problem[3][6].

2. Overlapping Subproblems:

   • Dynamic Programming is particularly useful for problems where the same subproblems are solved multiple times. Instead of solving these subproblems repeatedly, DP solves each subproblem once and stores the result for future use. This avoids redundant computations and improves efficiency[3][6].

3. Memoization (Top-Down Approach):

   • This technique involves solving the problem recursively and storing the results of subproblems in a table (usually an array or a hash map) to avoid redundant calculations. This approach is also known as the top-down approach[6].

4. Tabulation (Bottom-Up Approach):

   • In contrast to memoization, tabulation involves solving the problem iteratively and filling up a table based on the results of smaller subproblems. This approach is also known as the bottom-up approach and avoids the overhead of recursive function calls[6].

5. State Representation:

   • In DP, the problem is represented in terms of states. Each state represents a subproblem, and the solution to the problem is built by combining the solutions of these states. The state representation helps in defining the recurrence relation and the base cases[1][3].

6. Recurrence Relation:

   • A recurrence relation is a mathematical expression that relates the solution of a problem to the solutions of its subproblems. It is used to define how the solution to the problem can be constructed from the solutions of its subproblems[1][3].

7. Base Cases:

   • Base cases are the simplest subproblems that can be solved directly without further breaking them down. They serve as the stopping condition for the recursion in...