![]() So let us define a function B(i, w) that returns the maximum value given a scope of items ( i) and the capacity of the knapsack ( w). What are we trying to optimize here? We are trying to maximize the value the combination of items that yields the highest value. So for example, v and creturns the value and size of the 2nd item. We define 2 containers: v and c, that contains the all the values of each item and the capacity they consume respectively, starting from index 1. The General SolutionĪ dp solution is usually derived from a recursive solution. I assume you have known a bit of dp as a prerequisite, though if you haven’t you can check out my beginner friendly hands-on intro: 445A – Boredom – CodeForces Tutorial. I will then explain how the general solution is derived and how dp is applied. Study the problem closely as I will referring to it throughout this guide. To get started, try and attempt The Knapsack Problem (KNAPSACK) from SPOJ. This post is merely my take on the problem, which I hope to provide a more hands-on approach. The 1-0 knapsack problem an optimization puzzle famously solved with dynamic programming (dp).
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