Data structure for Rush Hour solver taboo list

Question

I'm using Breadth First Search to solve a rush hour game. It works fine, but it takes really long on difficult boards. I am using a taboo list to avoid states I already discovered, to avoid insane memory usage and improve the run time.

I think this taboo list is the main cause of the long run time. It does drastically improve the time compared to normal BFS, but it's still too slow. Currently I'm using a normal list (C#'s List and the List.Contains method). I'm sure there are better options.

I'm storing my boards as a list of Cars + a width, height and target point (where your car should end up). a Car is stored as 2 points (top-left and bottom-right) that completely describe the car (since they can only be placed horizontally or vertically).

Some things I can think of:

A trie
Something with hash codes
Huge Dictionaries (?)

What is a good/the best data structure for my problem? Thanks for the help.

Edit 1: Pseudocode (X is the taboo list type):

void Solve(Board b)
    Queue q = {b};
    X taboo = {b};
    while (q not empty)
        Board next = q.Dequeue();
        foreach (Board succ in next.Successors)
            if (succ.IsSolved)
                PrintSolution();
                return;
            if (!taboo.Contains(succ))
                q.Enqueue(succ);
                taboo.Add(succ);
    WriteLine("No solution found");

Edit 2: The solution was using a HashSet. (see below)

I'm on the verge of suggesting that you use a HashSet without actually knowing if I am answering the right question. Could you please clarify the way in which the taboo list is used by posting some example code? — gooid, Nov 01 '13 at 16:43
I've added the pseudocode of my BFS algorithm. I think a HashSet is indeed the best solution, but the problem is I don't know a good hash function. Can you suggest one? — Wouter Florijn, Nov 01 '13 at 17:52
Stupid answer, but are you absolutely sure the taboo list really improves the performance? Have you tried without it? — Per Lundberg, Nov 01 '13 at 17:57
Update: Finding a working hash function was really easy, since the cars are always stored in the same order. For those interested, I'll add the function to my question. @PerLundberg: Yes I've tried it without a taboo list and it exploded my laptop (memory errors and very long run time). — Wouter Florijn, Nov 01 '13 at 18:01
@WouterFlorijn - You are allowed to post your solution in an answer. — chappjc, Nov 01 '13 at 18:52
@chappjc: good point (in the other comment). I deleted the answer so that the one who deserves the credit (= Wouter) will get it. — Per Lundberg, Nov 01 '13 at 18:53

score 1 · Accepted Answer · answered Nov 02 '13 at 16:40

Found the answer (or at least AN answer) thanks to other people's comments. I used C#'s HashSet datastructure with the following hash function for boards:

public override int GetHashCode()
{
    int hash = 0;
    int mul = 1;
    foreach (Car c in Cars.Values)
    {
        hash += (c.P1.X + c.P1.Y * W) * mul;
        mul += W * H;
    }
    return hash;
}

This seems to work fine and give unique hash codes for every board (correct me if I'm wrong), assuming cars are always stored in the same order and P1 represents the car's top-left point.

With this solution, I can now solve Rush Hour boards that require 50 moves in less than 0.5s, with reasonable amounts of memory usage.

score 0 · Answer 2 · answered Nov 07 '14 at 20:25

This one is inefficient but it works for me, since my RushHour overall is pretty fast.

public string HashCode()
{
    StringBuilder str = new StringBuilder();
    foreach (Car car in this.Positions)
    {
        //#yolo
        str.Append(string.Format("#{0}({1},{2})#", car.Original, car.Vector.X, car.Vector.Y));
    }
    return str.ToString();
}

Data structure for Rush Hour solver taboo list

2 Answers2