You are about to set off on a challenging expedition, and you need to pack your knapsack (or backpack) full of supplies. You have a list full of supplies (each of which has a survival value and a weight …

The Knapsack problem can be reduced to the single-source shortest paths problem on a DAG (di-rected acyclic graph). This formulation can help build the intuition for the dynamic programming solution.

Optimal Substructure in the 0 1 Knapsack Problem Let O be an optimal subset of all n items with weight limit K. We want to show that O contains a solution to all sub instances (by induction). CASE 1: If O …

At subproblem C[j], what were our choices? Then, how do we backtrack from the very end, i.e. C[W], to the beginning? The knapsack algorithm runs in what's called pseudopolynomial time: polynomial in …

Knapsack is a core problem to Dynamic Programming, and it’s pretty easy to under-stand. Knapsack is a hard problem though; we don’t have or believe there is a polynomial time solution. It’s also a good …

Knapsack Problem • Given a knapsack with weight capacity , and given items of positive integer weights and positive integer values . (So, item has value and weight .)

Since the knapsack has a limited weight (or volume) capacity, the problem of interest is to figure out how to load the knapsack with a combination of units of the specified types of items that yields the …