What's the fastest way to find deepest path in a 3D array?

Question

I\'ve been trying to find solution to my problem for more than a week and I couldn\'t find out anything better than a milion iterations prog, so I think it\'s time to ask someon

Answer 1

I think you should be able to do it in O(N). When you parse your input, assign each node a 'caveNumber' initialized to 0. Set it to a valid number whenever you visit a cave:

CaveCount = 0, IsolatedCaveCount=0
AllSizes = new Vector.
For each node, 
   ProcessNode(size:0,depth:0);

ProcessNode(size,depth):
   If node.isCave and !node.caveNumber 
       if (size==0) ++CaveCount
       if (size==0 and depth!=0) IsolatedCaveCount++
       node.caveNumber = CaveCount
       AllSizes[CaveCount]++
       For each neighbor of node, 
            if (goingDeeper) depth++
            ProcessNode(size+1, depth).

You will visit each node 7 times at worst case: once from the outer loop, and possibly once from each of its six neighbors. But you'll only work on each one once, since after that the caveNumber is set, and you ignore it.

You can do the depth tracking by adding a depth parameter to the recursive ProcessNode call, and only incrementing it when visiting a lower neighbor.