0/1 Knapsack

Explore how to solve the 0 1 Knapsack problem by applying dynamic programming techniques. Understand how to maximize the total value of items within a weight capacity, ensuring each item is either fully included or excluded. Gain practical skills for efficiently optimizing solutions in coding interviews.

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Statement

You are given $n$ items whose weights and values are known, as well as a knapsack to carry these items. The knapsack cannot carry more than a certain maximum weight, known as its capacity.

You need to maximize the total value of the items in your knapsack, while ensuring that the sum of the weights of the selected items does not exceed the capacity of the knapsack.

If there is no combination of weights whose sum is within the capacity constraint, return $0$ .

Notes:

An item may not be broken up to fit

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