Brainstorming with factoring #

In the last post I described how I sometimes describe a problem with a matrix, and then look at the matrix transpose to see if it gives me new ideas. Another technique I use is to look for a factoring.

In algebra, factoring transforms a polynomial like 5x² + 8x - 21 into (x + 3)·(5x - 7). To solve 5x² + 8x - 21 = 0, we can first factor into (x + 3)·(5x - 7) = 0. Then we say that x + 3 = 0 or 5x - 7 = 0. Factoring turns a problem into several easier problems.

x 3
5x 5x² 15x
-7 -7x -21

Let's look at an example: I have six classes, File, EncryptedFile, GzipFile, EncryptedGzipFile, BzipFile, EncryptedBzipFile. I can factor these into a matrix:

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Brainstorming with transpose #

Sometimes I get stuck and look for a way to think about a problem a different way. There are some problems that you can view in the form of a matrix/table. The structure looks like this:

1 A1 B1 C1 D1 E1
2 A2 B2 C2 D2 E2
3 A3 B3 C3 D3 E3
4 A4 B4 C4 D4 E4
5 A5 B5 C5 D5 E5

There are rows and columns, and I'm trying to work on the cells. Let's try an example from a simple game:

Attack Defend Special
Fighter sword armor slam
Mage fireball reflect freeze
Thief dagger dodge disarm

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Improving hexagon map storage diagram #

Last week, I decided to improve the map storage section of the hexagon guide. This section had a diagram that suggested the use of a 2D array, but then it presented formulas that didn't look like what was shown. Reader feedback made me realize this section was confusing. I was mixing two separate steps here.

  1. Store the map in a 2D array.
  2. Slide the rows to the left to save space.
Hexagon map storage: grid, and also slide left


Improving island shaping for map generation #

One of my goals for 2019 is to improve my existing pages. This week I improved the island map section of my noise-based map generation page.

Island map generation: you figure it out