Step-by-Step 0/1 Knapsack Problem in JavaScript (Dynamic Programming)

Introduction Finding the best items to put in a bag is a common problem in computer science. This problem is called the “0/1 Knapsack Problem.” In simple words, you have a bag with a weight limit. You have many items, each with its own weight and value. You want to fill the bag so that the total value is as high as possible, but the total weight does not exceed the limit.

In this article, you will see:

1. A clear definition of the problem.

2. A step-by-step explanation of the code in JavaScript.

3. A link to the full code in my GitHub repository.

This tutorial uses simple English so that readers at an intermediate level (B1) can follow. At the end, you will also find detailed steps on how to share it on LinkedIn and how to make code snippets look nice using external tools.

1. Problem Definition

Imagine you have a bag that can hold up to 50 units of weight. You also have seven items:

• Item 1: weight = 31, value = 70

• Item 2: weight = 10, value = 20

• Item 3: weight = 20, value = 39

• Item 4: weight = 19, value = 37

• Item 5: weight = 4, value = 7

• Item 6: weight = 3, value = 5

• Item 7: weight = 6, value = 10

Your goal is to choose some of these items so that:

• The total weight ≤ 50

• The total value is as high as possible

You cannot cut an item in half. Either you take the whole item (1) or you do not take it (0). This is why it is called 0/1 Knapsack.

2. Code Explanation

Below is the full function in JavaScript. We use a table (matrix) to build the solution by dynamic programming.

3. Link to the GitHub Repository

You can find the full code with README and more examples here:

https://github.com/marcosSanchez-

dev/LeetCode/blob/main/The%20Knapsack%20Problem/index.js

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