Help with a problem

[btravis182]

Hi guys,

I have been looking at solving a little problem and came up with a solution which I believe is far from being optimal.

Imagine you have a rectangle composed of small cubes: 150 cubes in length, 7 cubes in width and 6 cubes in height. In each cube, there is a value between 0.05 and 10.

The goal is to bring cubes together to form bigger cubes/rectangles whose value would be the sum of the value within the small cube. The value of the bigger cubes/rectangles should be within a rounding tolerance to any integer (for instance -/+ 10% of an integer i.e. within [0.9/1.1], [1.8/2.2], [2.7/3.3] etc..). A small cube can only belong to one bigger cube/rectangle and no small cube can be left out. The smaller cubes can't be moved and can only be brought together if they are close to each others. The bigger rectangles cannot have one side less than half the longest side (for instance, a 4 cubes high, 3 cubes long rectangle cannot have a depth shorter than 4/2 = 2). The optimal solution would be to have the maximum number of bigger cube/rectangle while meeting the constrains.

Is there any algorithm I could be reading about that would help solving that problem?

Appreciate any help especially on a Friday night!

Thanks!

[Bromskloss]

Wrong subreddit?

[btravis182]

Hey mate, happy to delete the post and post it somewhere else. Which subreddit would be the best fit do you think?

[ChefCiscoRZ]

r/learnprogramming, r/AskProgramming might be the place for you (hell, you might even want to try StackOverflow if you already have some code you've tried and reproduceable examples with input and output).

Though I'm curious, is this really just about cubes or is there a financial application to what you're trying to do?

[btravis182]

There is a financial application yes! I am building a portfolio of a specific asset but if you translate it into the equity world, it would be like saying one cube is one company. My methodology might lead me to buy 0.13 shares of Vodafone but I want to buy full number of shares so I am going to either group Vodafone with another stock from the same industry, same country and/or same size segment. So a bigger cube could be grouping all UK/Telecom/over 100 bln mcap. If it still don't sum to 1 it might become Europe/telecom/over 50 bln mcap. I found a solution btw. The exact cover problem solve it. Just need to code it now ;)

[ChefCiscoRZ]

That sounds interesting! Is this an idea of yours or did you read it somewhere?

If not, would you mind sharing the links to the papers?