When developing a dynamic programming algorithm, the sequence of steps followed is:
A. Construct an optimal solution from computed information.
B. Recursively define the value of an optimal solution.
C. Characterize the structure of an optimal solution.
D. Compute the value of an optimal solution, typically in a bottom-up fashion.
Choose the correct answer from the options given below:

Correct option is D

Dynamic Programming (DP) is a technique used to solve optimization problems by breaking them into simpler sub-problems and solving each only once. The standard methodology for developing a DP algorithm follows a well-defined sequence of steps. First, we characterize the structure of the optimal solution. Next, we define the value of the optimal solution recursively. Then, we compute this value, typically in a bottom-up manner using tabulation. Finally, if needed, we construct the optimal solution using the stored computed values. Thus, the correct step-by-step order is: C → B → D → A.
Information Booster:
1. C. Characterize the structure of an optimal solution:
· Identify the components and relationships within the problem that make it suitable for DP.
· Helps in understanding how the solution to a problem depends on its sub-problems.
2. B. Recursively define the value of an optimal solution:
· Express the solution in terms of smaller instances using recurrence relations.
· Forms the basis of the DP transition.
3. D. Compute the value of an optimal solution, typically in a bottom-up fashion:
· Implement the recurrence using tabulation or memoization.
· Reduces time complexity by storing solutions of sub-problems.
4. A. Construct an optimal solution from computed information: Retrieve or reconstruct the final answer from the computed values (often using backtracking or pointers).
Additional Knowledge:
· Dynamic programming is applied when the problem has overlapping sub-problems and optimal substructure.
· Common examples include Longest Common Subsequence, Knapsack, Matrix Chain Multiplication, etc.