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0-1 Knapsack

version (2.92 KB) by Petter
Solves the 0-1 knapsack problem with positive integer weights.


Updated 12 Feb 2009

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Uses dynamic programming to solve the problem, see for example .

Cite As

Petter (2021). 0-1 Knapsack (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (7)

Karsten Labusch

It works perfectly, but is it possible to change the code, for the case that the values of my items are all the same and i get every combination of items who fit in the constraint?

Ansuman Mahapatra

Works perfectly.

Nithin S

I am trying to use this inside a matlab function block where weights, value and capacity of knapsack are inputs to the block. I am facing an error "Computed maximum size is not bounded.
Static memory allocation requires all sizes to be bounded."
this is happening at line A = zeros(length(weights)+1,W+1);

how do I overcome this error ?

Chetan Viraktamath

John D'Errico

Fast, it seems to work. Help is good. Problems are repaired. I can't ask for more.


Thanks for the suggestions. A new version has been uploaded.

I am sometimes annoyed by the fact that I have to download and unpacka .zip file before looking at code for an algorithm. Publishing knapsack.m itself provided a way for the user to view the code without downloading anything. But the error looke unprofessional and it has been removed.

John D'Errico

Please let others rate your work. Rating your own stuff highly says nothing about the code, but perhaps drops you closer to the level of a spammer on the FEX like Marco. So let the rating system do its job. I know that you think your stuff is good. So does every eager high school student who posts their last homework assignment.

In the particular case of this utility. I'll first suggest that there is no reason to publish the code for knapsack itself. See there was an error generated when you tried it.

How about the help? It too is lacking. It is not terrible, but still lacking. Here is the relevant part of the help block.

% WEIGHTS : The weight of every item
% VALUES : The value of every item
% CONSTRAINT : The weight constraint of the knapsack
% BEST : Value of best possible knapsack
% AMOUNT : The amount to use of each item (0 or 1)

See that there appear to be two return arguments, but your help does not tell us what order they are in. In fact, when only one output argument is returned, it looks to be the second of the two outputs. I won't suggest what your code actually does. That is your job.

There was a nicely written H1 line in the help. Well done in that respect. I also found error checks in the code.

Finally, the best code would include a simple example in the help itself. I know, you will claim there is one in the demo file. But when people actually download this, they will often look to the help rather than search for some other file.

MATLAB Release Compatibility
Created with R2008b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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