A game based on the Havel-Hakimi algorithm

I have not looked over the Havel-Hakimi algorithm yet, but here&#x27;s the best way I&#x27;ve found to solve these (with 100% success rate so far)<p>1. Pick the node with the highest degree 2. Make all the connections for that node until it has a value of zero by connecting it with the highest-value node that it isn&#x27;t already connected to<p>For example, in this scenario: <a href="http://i.imgur.com/O8MlWzz.png" rel="nofollow">http:&#x2F;&#x2F;i.imgur.com&#x2F;O8MlWzz.png</a><p>The way that I see it is that since the highest-degree node needs to make X number of connections, ensure it can make all of those connections before worrying about anything else. In this case, that means start by connecting the 4 to the next highest value node - the 3, then the 2, then the other 2, then the 1.<p>This leaves the following situation: <a href="http://i.imgur.com/9vZjafr.png" rel="nofollow">http:&#x2F;&#x2F;i.imgur.com&#x2F;9vZjafr.png</a><p>It&#x27;s kind of easy to see where it goes from there. Sure this is a simple example, but as I said it&#x27;s worked 100% of the time I&#x27;ve tried it.

This is nice! I got stuck and gave up when there got to be nodes with 6s on them, but that&#x27;s just because I&#x27;m in class.<p>Given that the only reason to select an edge right now is to delete it, perhaps the delete action could be mapped to a click, rather than a click plus a backspace. Also, a reset level button would be nice.

A greedy algorithm seems to be successful with the graphs in this game. Pick the node with the highest degree, connect it to the other nodes with the highest degrees, repeat.

It reminds me of the &#x27;bridges&#x27; game from Simon Tatham&#x27;s Portable Puzzle Collection. It has the additional restriction that edges cannot cross each other.<p><a href="http://www.chiark.greenend.org.uk/~sgtatham/puzzles/" rel="nofollow">http:&#x2F;&#x2F;www.chiark.greenend.org.uk&#x2F;~sgtatham&#x2F;puzzles&#x2F;</a><p>(Say goodbye to your productivity if you like puzzles).

If you want to reach people in the wide wide world, explain what a degree sequence is in the first paragraph! This is your chance for a bit of mathevangelism!

Crazy I just came across a game with the same exact mechanic in the last week. Can&#x27;t find it again though.

This should keep a completed level on the screen until you click to advance.<p>Also, deleting links needs some work: I think the hit detection is too small. Also, a mouse-only way to delete would be nice -- how about right clicking? Double clicking would be another possibility (and I assume more touch friendly).

Fun. I gave up when the number got to 9, because the cluster got messy. :(

Pretty fun game. I thought that greedy algorithm would not work with this problem, so I wrote a basic genetic algorithm to find a solution, refining it as I went.<p>Bit of overkill, but fun game overall !

Within 3 minutes of playing this game I was able to see what Havel-Hakimi algorithm is.

Congrats. You just showed maths far better than any of my high school classes.

Pretty fun game. Clever way to scout internships as well. Hah!

needs an animation for when you complete a graph.<p>reward my success!