The Knapsack Problem

The Knapsack Problem is a classic problem in computer science - You have a knapsack and several items to pack into it. Each item has a weight and a value, and you can only carry up to a maximum weight. Find a combination of items to pack, such that you remain under the weight limit, but you maximize the value of the items selected.


ERRATA NOTICE: Please check the pinned comment for errors and corrections in this video.



While seemingly straightforward, this problem requires a surprising amount of thought to solve! In this video, we look at the naive recursive solution first, before moving on to a far more efficient dynamic programming solution!

= Timestamps =
00:00 Introduction
00:47 Contents Page
01:33 Definition of the Knapsack Problem
02:16 Why a greedy solution wouldn't work
03:34 Introduction to recursive solution
04:17 Visual explanation of recursive solution
10:47 Final recursive trace (if you want to skip the explanation and want to just see it happen)
12:33 Python code for recursive solution
20:22 Complete Code
21:27 Discussing other variants (eg. Multiple selection variant)
22:45 Discussion of Time Complexity / Efficiency
23:56 Dynamic Programming Solution - Description of Memo Table
26:00 Dynamic Programming Solution - Decision making process
28:52 Dynamic Programming Solution - Full Trace
34:32 Dynamic Programming Solution - Conclusion & Time Complexity
35:38 Conclusion

= CODE DOWNLOAD =
To view and download the code written in this video, check out the following Bitbucket repository: https://bitbucket.org/nerdfirst/knapsack-problem

To download, first click on "Downloads" in the left sidebar. Then, in the subsequent page, click "Download Repository".

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