A clock puzzle is game in which a clock has random numbers as the face value. The goal is to find a path across every face value only once. From any position, the only valid movements are n positions clockwise, or n positions counter clockwise where n is the face value of the current position.
The clock puzzle is essentially a Hamiltonian path problem where every node has at most 2 links away from it. This feature reduces the complexity of the problem significantly.
The proposed solution consists in modeling the problem with binary search tree and searching with a depth first algorithm. This approach is complete, it will find every solution to any given puzzle, but it will be slow, because it is a blind search without heuristics. this algorithm is estimated to be O(2^n).
On a UNIX-like system you need to have installed:
- gcc (GNU Collection Compiler)
- glib 2.0 (Utility library from GNOME)
- json-c (JSON Library written in C)
Clone this repo and then use make to build. The executable file is main.
make
./main
You can build a program that tests our functions using assert.h like this:
make test
./test
After building, you can use main as a command line tool.
If you have clock that looks like this: [3, 1, 3, 1 ,2, 3]
pass it using the -i flag like this:
./main -i 3 1 3 1 2 3
The output in STDOUT will be a JSON formatted list of states. This particular clock yields this result:
[ [ 1, 0 ], [ 1, 0, 3 ], [ 1, 0, 3, 2 ], [ 1, 0, 3, 2, 5 ], [ 1, 0, 3, 2 ], [ 1, 0, 3 ], [ 1, 0, 3, 4 ], [ 1, 0, 3, 4, 2 ], [ 1, 0, 3, 4, 2, 5 ] ]
Each number is a position in the clock array. The last item is a valid solution