Arrange the following steps in the correct order to solve the Knapsack problem…
2024
Arrange the following steps in the correct order to solve the Knapsack problem using Dynamic Programming.
(A) Define the base case when the capacity is zero (0) or no items are left to consider
(B) Compute the maximum value that can be obtained using items up to the i-th item and a knapsack capacity of 0
(C) Identify subproblems and their dependencies based on items weights and values
(D) Initialize a table to store results of subproblems
(E) Iterate through each item and each possible Capacity to fill the table
Choose the correct answer from the options given below:
- A.
(C), (D), (A), (E), (B)
- B.
(D), (C), (A), (E), (B)
- C.
(A), (C), (D), (E), (B)
- D.
(D), (A), (C), (E), (B)
Attempted by 67 students.
Show answer & explanation
Correct answer: C
Correct order and brief rationale:
Define the base case when the capacity is zero or no items are left to consider.
Identify subproblems and their dependencies based on item weights and values.
Initialize a table to store results of subproblems.
Iterate through each item and each possible capacity to fill the table using the recurrence relation.
Retrieve the final maximum value from the table (the maximum value achievable with all considered items for the target knapsack capacity).
Why this order?
Defining base cases first ensures boundary values are known for initializing the table.
Identifying subproblems dictates the table dimensions and the recurrence to use.
Initialising the table and then iterating populates all required subproblem results so the final answer can be read directly.
Note: The step that mentions computing the maximum value for capacity zero appears to be misstated; the intended final step is to read the computed maximum value for the target knapsack capacity (the answer stored in the table after filling).
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