Solve and extend the Knapsack problem

Q: Solve and extend the Knapsack problem

This question evaluates a candidate's understanding of dynamic programming for optimization problems, specifically the 0/1 knapsack formulation, space-optimized DP and the ability to reconstruct a chosen item set from compressed state.

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Question

You are given n items, each with an integer weight and value, and a knapsack capacity W. Implement 0/1 Knapsack to return the maximum total value and also reconstruct one optimal set of item indices. Provide an O(nW) time, O(W) space dynamic programming solution and explain how to reconstruct choices from the compressed state. Then outline how to adapt the solution to unbounded and bounded knapsack variants and analyze time and space complexity.

Solve and extend the Knapsack problem

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