4 ms·

I think it would be quite interesting to know more about how you approached this problem for solution, than the solutions presented by the program itself .. I d

by torpor 17y ago

I think it would be quite interesting to know more about how you approached this problem for solution, than the solutions presented by the program itself .. I didn't really get much of the details about how you'd sorted through this from your post .. perhaps a followup topic? Its really great, btw .. I play with this toy with my son on a regular basis, and found myself just a few days ago wondering what is the maximum number of shapes we can build with the set .. okay, this got a bit screwed up by the addition of another mini-set gifted to my son by a friend, so there is room for improvement in my thinking now that I've learned what you have discovered. Nice job!

jgrahamc 17y ago
I tried to explain how it works in the comments in the code. Probably worth reading them in detail as they do explain the algorithm used. My thought process was something like this (over a number of days grabbing time when I could): Emulate a human selecting pieces and clicking them together. Model pieces as straight lines of the right length. There are two important things: how long the line is and how much it modifies the angle at which the next piece will join. Thus all I need is to keep track of the position of the end of the last piece added and the angle. Spend a while figuring out the trigonometry and getting that code working correctly. To generate the permutations I realized that the process could be split into three parts: 1. Always place the bridge. Since there's one just add it at the end. 2. Separate the straights and curves. Generate all the permutations of clockwise and anticlockwise curved pieces. To do that I used the trick of all 12-bit binary numbers between 0 and 2^12-1. 3. Then insert the straight pieces between the curved pieces in all places possible. Feed each possible track layout into code that builds the track and check that the end pieces match up. Add code to eliminate end pieces that join impossibly (come from the wrong angle), add code to remove duplicates caused by rotation and reflection. Once I got that working I then wrote code in Processing to draw a pretty picture.
- fhars 17y ago
  You might be able to speed it up considerably by adding 2a. Continue with next iteration unless the turning number of the sequence of curves is a whole number. You add 1/8 to the turning number for each clockwise curve and subtract 1/8 for each CCW (for numerical stability you would rather add of subtract 1 and check for multiples of 8).

by torpor 17y ago

jgrahamc 17y ago

I tried to explain how it works in the comments in the code. Probably worth reading them in detail as they do explain the algorithm used. My thought process was something like this (over a number of days grabbing time when I could): Emulate a human selecting pieces and clicking them together. Model pieces as straight lines of the right length. There are two important things: how long the line is and how much it modifies the angle at which the next piece will join. Thus all I need is to keep track of the position of the end of the last piece added and the angle. Spend a while figuring out the trigonometry and getting that code working correctly. To generate the permutations I realized that the process could be split into three parts: 1. Always place the bridge. Since there's one just add it at the end. 2. Separate the straights and curves. Generate all the permutations of clockwise and anticlockwise curved pieces. To do that I used the trick of all 12-bit binary numbers between 0 and 2^12-1. 3. Then insert the straight pieces between the curved pieces in all places possible. Feed each possible track layout into code that builds the track and check that the end pieces match up. Add code to eliminate end pieces that join impossibly (come from the wrong angle), add code to remove duplicates caused by rotation and reflection. Once I got that working I then wrote code in Processing to draw a pretty picture.

fhars 17y ago
You might be able to speed it up considerably by adding 2a. Continue with next iteration unless the turning number of the sequence of curves is a whole number. You add 1/8 to the turning number for each clockwise curve and subtract 1/8 for each CCW (for numerical stability you would rather add of subtract 1 and check for multiples of 8).