Constraint satisfaction to optimize item selection for bundles in Minecraft

Summary

I read a blog post on how Many Hard Leetcode Problems are Easy Constraint Problems and was pleasantly surprised at how approachable MiniZinc was compared to other solver software I have been exposed to, and the examples given helped me to understand how to apply it to a domain I was already familiar with. I have always wanted to be able to get more familiar with using constraint satisfaction as a way to solve problems, so I decided to create a solver to help optimize storage space for Minecraft using constraint satisfaction to help learn how to use this tool. I will outline my thought process and how I reached the solution I came up with. Game Mechanics In Minecraft, your player inventory is limited. You have 27 inventory slots, 9 hotbar slots, 4 armor slots, 4 temporary crafting slots, 1 offhand slot, and 1 temporary slot for the result of crafting. Each slot can either contain a single item, a small stack of 16, or a full stack of 64 items, depending on the item. Often when adventuring, you will come across many rare and powerful items and accumulate many items in your inventory slots, but they may be stacks of items that are not at maximum capacity for that inventory slot. Once your inventory is full, you cannot pick up new items. Using bundles, you can consolidate your inventory and pick up more items. A bundle is an item that can store up to a stack’s worth of mixed item types within itself in a single inventory slot. Items can be individually selected and taken out of the bundle via the inventory menu. Item stack sizes (top row) and the number of bundle slots they take up (middle row). Sticks stack to 64, so they take up one bundle slot; ender pearls stack to 16, so they take up four; and swords do not stack, so they take up the whole bundle. So, for instance, a bundle may have 32 sticks and 8 ender pearls inside, which take up a total of (32×1)+(8×4)=64 bundle slots. Creating an Optimizer Using the MiniZinc Playground, we can model our player’s inventory and ...