This is more of a general computer science/graph traversal
question than a perl question; but I'm coding in perl
and I know that this is a very smart crowd so I thought I'd see what
help you could offer.
I've recently started playing the online game CashWars (note:
this post is not a troll to get people to play CashWars, but if you
do want to try it out, use the following link CashWars
and I will get some nominal credit for refering you).
The game is played on a 721x721 grid. Every day you get
so many moves (I'm currently at 350 per day, but you can have
as many as 600). Moving 1 square horizontally or vertically
costs 1 movement point. Certain squares contain resources (Oil)
that you can gather. You can only gather resources from
a particular square once per day. I have a large list of the squares that
contain oil. What I am trying to do is compute an "optimal or near optimal path"
to visit as many oil squares as possible in a given number of
moves from a particular starting location.
I've already tried out a few algorithms:
weighting - I weigh each of the 4 squares adjacent to the current
square based on some function of the distance from that square to
nearby untapped squares with oil in them. I've tried a few diffrent weighting algorithms and this hueristic
has worked ok.
spanning tree - I read that a spanning-tree algorithm can be
used to produce a close-to-optimal solution to the Travelling Salesman Problem so I decided
to give it a try. It did slightly better than the weighting algorithm, but I feel I could
do better (since my problem isn't the classic TSP "visit every node in the minimum # of moves" problem, it is "visit
as many nodes as possible in N moves" which is slightly diffrent and would lead to diffrent optimizations).
limited game tree - I store the 200 current best paths, then I add all possible moves to each one, and then rate the paths again;
keeping only the 200 best out of that lot (best is determined by total path length to # of oil suqares ratio). This
is the best algorithm so far, but I still feel that I can do better.
I'd like the other monk's thoughts about any other
hueristics or algorithms that I could try that
might give a good solution to this "visit as many X as possible
in Y moves" problem.
I can post my code for any of those algorithms I've
tried already if anyone is interested.