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.

The knapsack problem is based on the subset sum problem. Given a sequence of n positive numbers x1, x2, . . . xn, and a number K, does there exist a subsequence whose terms total K? This problem …

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 …

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 …

Here we give a pseudo-polynomial time algorithm that solves Knapsack optimally by using dynamic programming. The term pseudo-polynomial means polynomial if the input is given in unary encoding …

The first approach is suitable when knapsack capacity is small. With large knapsack, the first approach is not advisable from computation as well as memory requirement point of view.