When developing a dynamic programming algorithm, the sequence of steps…
2025
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:
- A.
B, C, A, D
- B.
B, A, C, D
- C.
C, B, A, D
- D.
C, B, D, A
Attempted by 313 students.
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Correct answer: D
Correct sequence: Characterize the structure of an optimal solution → Recursively define the value of an optimal solution → Compute the value of an optimal solution (bottom-up) → Construct an optimal solution from computed information.
Characterize the structure of an optimal solution: Identify how an optimal solution can be formed from optimal solutions to smaller subproblems. This step reveals the problem decomposition and dependencies between subproblems.
Recursively define the value of an optimal solution: Write a recurrence (or memoized relation) that expresses the optimal value in terms of optimal values of the identified subproblems.
Compute the value of an optimal solution (typically bottom-up): Use dynamic programming to fill a table of subproblem values according to the recurrence so that each value needed is available when computed.
Construct an optimal solution from computed information: Reconstruct the actual solution using the computed table and any stored choices or parent pointers (commonly by backtracking).
Tip: While computing values, record the decisions (such as which choice yielded the optimum) so that reconstruction is straightforward and efficient.
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