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1

I thought I would offer the brute force solution. The idea is to try every single track layout in turn. When constructing a layout, there are only three pieces that need to be taken into consideration: a left handed curve, a right handed curve and a straight. You can encode the track layout as a base 3 number with a width corresponding to the number of ...


-2

Assume that you start at the point (0, 0) going straight to the right. You need to add tracks until you reach the point (0, 0) again, this time straight from the left. There are two problems here: One is to reach the point (0, 0) coming from the left exactly. The other is to have no overlaps. To form a counter-clockwise circle you will need 12 curved ...


2

Since you already implemented IDA$^*$ you certainly understand why it expands more nodes than A$^*$, i.e., it starts from the start state with a new depth-first traversal in each iteration. Note first that, the overall number of nodes visited by IDA$^*$, while necessarily larger than A$^*$ is not that much larger. The reason is that the number of nodes at ...


4

Firstly, a frame challenge: A computer can create a valid layout using all of the tracks and if the algorithm is good, perhaps in a few seconds You don't need the algorithm to run in a few seconds. You need output in a few seconds. I don't see that there's anything stopping you from setting a brute force layout cruncher running on a computer in the ...


4

One possible solution to make this as simple as possible to quickly get a working algorithm would be as follows. The simplest layout is of course 12C (12 curved tracks all with the same orientation (relative to each other), and forming a simple circle. This will be the basis upon which we can build on. So the basic algorithm will be to maintain the 360 ...


2

We know that there are problems (like the halting problem) that absolutely cannot be solved by a computer because there is no algorithmic solution. But a human cannot solve those problems either. We also know that there are problems that humans can solve, but which we do not know how to solve with a computer with our current state of knowledge and ...


1

The answer is simple. Assume you are making a robot for interacting with other people. The first thing that it needs is to recognize people who it sees. Another application is in self-driving cars. If the car is not able to see the road and read the signs or break when it sees a dangerous obstacle ahead, how could it drive in a safe way? There are a lot ...


2

As you correctly point out, the original formula is valid (in every model either there is some element for which p or q doesn't hold, or p and q hold for all elements). To prove that your formula is valid, you cannot use resolution directly. Recall that with resolution, you can derive the empty clause from a clause set iff the clause set is unsatisfiable. ...


0

Someone who owns (an abstract of) the book might be able to give you a better contextualized answer, but in general models and simulations are subject to certain 'laws' that the systems they represent usually are not. In the case of multi-agent systems, one of these is the fact that some agent gets to act first on a given time step, even though the designer ...


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