Solution

The correct answer is Option 4

Key Points

• Dynamic programming is a technique used to solve optimization problems by breaking them into smaller sub-problems and solving each sub-problem only once.
• The steps to follow when developing a dynamic programming algorithm involve understanding the structure of the problem, defining the solution recursively, computing the solution, and then constructing the result.

Detailed Explanation

• Step 1 - Characterize the structure of an optimal solution: This involves understanding how the solution to the problem can be broken into smaller sub-problems. For example, in the case of the Fibonacci sequence, the nth Fibonacci number depends on the (n-1)th and (n-2)th Fibonacci numbers.
• Step 2 - Recursively define the value of an optimal solution: Write a recurrence relation or formula that represents the solution to the problem in terms of its sub-problems.
• Step 3 - Compute the value of an optimal solution, typically in a bottom-up fashion: Solve the problem iteratively using a table (array) to store intermediate results. This avoids recalculating the same sub-problem multiple times, which is what makes dynamic programming efficient.
• Step 4 - Construct an optimal solution from computed information: Once the value of the optimal solution is computed, use the stored information in the table to reconstruct the actual solution to the problem.

Order of Steps:

1. Characterize the structure of an optimal solution (Step C).
2. Recursively define the value of an optimal solution (Step B).
3. Compute the value of an optimal solution, typically in a bottom-up fashion (Step D).
4. Construct an optimal solution from computed information (Step A).

Hence, the correct sequence is: C, B, D, A, which corresponds to Option 4.